Claiming a Large Slice of a Small Pie: Asymmetric …€¦ · Claiming a Large Slice of a Small...

Claiming a Large Slice of a Small Pie: Asymmetric Disconfirmation inNegotiation

Richard P. LarrickDuke University

George WuUniversity of Chicago

Three studies show that negotiators consistently underestimate the size of the bargaining zone indistributive negotiations (the small-pie bias) and, by implication, overestimate the share of the surplusthey claim (the large-slice bias). The authors explain the results by asymmetric disconfirmation:Negotiators with initial estimates of their counterpart’s reservation price that are “inside” the bargainingzone tend to behave consistently with these estimates, which become self-fulfilling, whereas negotiatorswith initial “outside” estimates revise their perceptions in the face of strong disconfirming evidence.Asymmetric disconfirmation can produce a population-level bias, even when initial perceptions areaccurate on average. The authors suggest that asymmetric disconfirmation has implications for confir-mation bias and self-fulfilling-prophecy research in social perception.

Keywords: confirmation bias, learning from feedback, negotiation, self-fulfilling prophecy, trianglehypothesis

Consider a common negotiation scenario. Jill posts an ad for aused car. It is listed for $2,800, but she is willing to accept $2,300.After several rounds of posturing, arguing, and conceding, she andthe buyer arrive at a price of $2,450. Jill is quite satisfied that shehas cleared her $2,300 limit by $150. When a friend asks howmuch higher she could have pushed the buyer, Jill states confi-dently, “Given the fuss he was making, I don’t think he wouldhave gone above $2,500.” In Jill’s mind, she has done very well forherself. According to her estimate, there was only a $200 range inwhich she and her counterpart could have reached agreement, andthat she claimed 75% of this pie. But consider the followingquestion: What is the buyer’s estimate of Jill’s limit? How much ofthe “pie” does he think he obtained?

In this article, we argue that most negotiators leave a distributivenegotiation believing that they have pushed their opponents closeto their limits. Such a belief has two consequences: Negotiatorstend to underestimate the size of the pie or bargaining zone (thesmall-pie bias) and, by implication, believe that they have receiveda larger share of the surplus than they actually have (the large-slicebias). We consider two principal causes of the small-pie andlarge-slice biases: Flawed hypothesis testing and motivated rea-soning. First, we suggest that there is an asymmetry in the discon-firmation of incorrect beliefs. Some classes of erroneous judg-ments are disconfirmed reliably, whereas others are self-fulfilling.

Specifically, negotiators with initial beliefs of their opponent’s truelimit that are “inside” the bargaining zone are unlikely to havethese incorrect beliefs disconfirmed, whereas those with initial“outside” estimates learn that their estimates are too extreme.Second, negotiators may be motivated to believe that they areeffective negotiators and that they performed well in a givennegotiation. Although the motivation to self-enhance almost cer-tainly contributes to the small-pie bias in real-world negotiation,we argue that flawed hypothesis testing is a sufficient cause of thebias, and we therefore make it the focus of this article.

These results have implications for both the negotiation andsocial-perception literatures. For negotiation researchers, we sug-gest that these biases are systematic and robust and therefore haveimportant practical consequences for everyday negotiations. Thesebiases extend a large body of work on cognitive biases in negoti-ation, pioneered by Neale and Bazerman (1991), that has includeddemonstrations of anchoring (Galinsky & Mussweiler, 2001;Whyte & Sebenius, 1997), correspondence bias (Morris, Larrick,& Su, 1999), fixed-pie bias (Thompson & DeHarpport, 1994;Thompson & Hastie, 1990), and stereotyping (Kray, Thompson, &Galinsky, 2001) in negotiation. For social-perception researchers,we propose that asymmetric disconfirmation is a general phenom-enon that occurs in social interactions other than negotiation.These results highlight the role the feedback environment plays inproducing accurate—and inaccurate—social inferences.

The degree to which social perceptions are inaccurate has beendebated in the social-psychology literature. A major theme hasbeen that erroneous social perceptions tend to be self-fulfilling(Jones, 1986; Merton, 1948; Miller & Turnbull, 1986; Rosenthal &Jacobson, 1968; Snyder & Swann, 1978). Decades of researchhave demonstrated that initially inaccurate expectations can bemaintained through a variety of processes, including perceptualand behavioral confirmation (Jones, 1986), positive test strategies(Klayman & Ha, 1987), and biased samples of evidence (Zucker-man, Knee, Hodgins, & Miyake, 1995). However, the ubiquity of

Richard P. Larrick, Fuqua School of Business, Duke University; GeorgeWu, Graduate School of Business, University of Chicago.

We thank Craig Fox and David Schkade for their useful comments onthis work. Preliminary research was presented in 2000 at the BehavioralDecision Research in Management conference, Tucson, Arizona.

Correspondence concerning this article should be addressed to RichardP. Larrick, Fuqua School of Business, Duke University, PO Box 90120,Durham, NC 27708; or to George Wu, Graduate School of Business,University of Chicago, 5807 South Woodlawn, Chicago, IL 60637. E-mail:[email protected] or [email protected]

Journal of Personality and Social Psychology Copyright 2007 by the American Psychological Association2007, Vol. 93, No. 2, 212–233 0022-3514/07/$12.00 DOI: 10.1037/0022-3514.93.2.212

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this pattern of error in perception has been questioned (Jussim,1991; Miller & Turnbull, 1986). In a provocative challenge to thistradition, Jussim (1991) argued that the “strong constructivistperspective” in social psychology has neglected accuracy in socialperception and emphasized error and bias. He analyzed the con-ditions under which confirmation of initial beliefs should be re-garded as accurate or erroneous and concluded that the evidencefor self-fulfilling prophecies in naturalistic settings is thin.Jussim’s critique suggests that there may not be a general tendencytoward error, and thus, it is important to understand the conditionsthat foster or impede accuracy. We propose that the concept ofasymmetric disconfirmation contributes to this debate by identify-ing an important moderator of accuracy (Jussim, 1991; Miller &Turnbull, 1986).

In the next section, we describe how asymmetric disconfirma-tion in negotiation produces the small-pie and large-slice biases. Inthe following section, we describe how our research contributes tothe larger debate about accuracy in social perception and theconstructive role that moderators play in this debate. Following thepresentation of three studies demonstrating the small-pie andlarge-slice biases, we present a formal model of asymmetric dis-confirmation in the General Discussion. In the remainder of theGeneral Discussion, we suggest other social phenomena that ex-hibit asymmetric disconfirmation and consider other implicationsof the small-pie and large-slice biases.

The Small-Pie Bias as Asymmetric Disconfirmation

In a distributive negotiation, the bargaining zone is defined bythe highest price the buyer will pay and the lowest price the sellerwill accept (Fouraker & Siegel, 1963). These amounts are fre-quently termed reservation prices, bottom lines, or limits. Anysettlement within the bargaining zone leaves both parties better offthan walking away without a deal. The surplus is the differencebetween the buyer’s reservation price and the seller’s reservationprice and is often colloquially called the pie. At the individual

level, there is a small-pie bias if the seller underestimates thebuyer’s true reservation price or the buyer overestimates the sell-er’s true reservation price. We refer to such estimates as beinginside the bargaining zone. In contrast, we refer to estimates asoutside the bargaining zone when sellers overestimate the buyer’sreservation price or buyers underestimate the seller’s reservationprice. An inside estimate and an outside estimate are illustrated inthe two panels of Figure 1.

Why might people leave a negotiation with the perception of asmall pie? The quality of a postnegotiation estimate of an oppo-nent’s reservation price depends on (a) the accuracy of a negoti-ator’s prenegotiation estimate, (b) the diagnosticity of informationreceived during the negotiation, and (c) the process that a negoti-ator uses to revise the initial estimate on the basis of new infor-mation. Although we discuss the first step for completeness, ourstudies focus on the role of the remaining two steps in producingthe small-pie bias. In particular, our studies suggest that biasedinitial beliefs are sufficient but not necessary for generating asmall-pie bias.

Initial Beliefs

Savvy negotiators walk into a negotiation with some sense oftheir counterpart’s reservation price (Raiffa, 1982). What deter-mines whether these initial estimates are inside or outside the truereservation price? Estimates may be based on sound research butmay also be influenced by less relevant information (Neale &Bazerman, 1991; Whyte & Sebenius, 1997). For example, nego-tiators often use their own reservation price to estimate theiropponent’s limit (Bottom & Paese, 1999; Diekmann, Tenbrunsel,& Galinsky, 2003). Thus, one’s own reservation price may serve asan anchor (Tversky & Kahneman, 1974), in which case estimatesare more likely to be inside the zone in large bargaining zones(where adjustments from the anchor are likely to be insufficient)than in small bargaining zones.

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Figure 1. A hypothetical bargaining zone. Two different sellers make prenegotiation estimates of the buyer’sreservation price (RP), one outside the bargaining zone (left panel), and one inside the bargaining zone (rightpanel). The “outside” estimate is disconfirmed, whereas the “inside” estimate is maintained.

213SMALL-PIE BIAS IN BARGAINING

Although anchoring may produce initial inside estimates insome situations, we are agnostic about whether negotiators tend toenter negotiations with inside or outside estimates of their oppo-nents’ bottom lines. In fact, our studies manipulate the accuracy ofinitial judgments and the degree to which these judgments areinside or outside the bargaining zone. We do propose, however,that there is an asymmetry in how inside and outside estimates arerevised during a negotiation: Inside estimates will tend to persist,whereas outside estimates will tend to be driven toward andperhaps inside the truth (see Figure 1). We illustrate this asymme-try in the next two sections.

Revising Initial Estimates That Are Outside the Zone

We hypothesize that inaccurate estimates outside the bargainingzone will tend to be disconfirmed, such that they end up close toor perhaps even inside the bargaining zone (Bottom & Paese,1999). Ambitious estimates are likely to lead to ambitious openingoffers (Galinsky & Mussweiler, 2001; Galinsky, Mussweiler, &Medvec, 2002) that are outside the opponent’s reservation price.These offers will be rejected, as they must be. This will tend toproduce a more protracted negotiation process (Bottom & Paese,1999), require more concession making, and create the impressionthat agreement was difficult to reach (Morris et al., 1999). Thus,the number of rejected offers and the process of haggling will tendto disconfirm the ambitious misestimate.

Consider the left panel of Figure 1. The buyer is willing to payas much as $2,700, whereas the seller requires a minimum of$2,300. A seller who overestimates the buyer’s reservation price at$2,900 might start ambitiously, demanding $3,100. This ambitiousoffer is firmly rejected.1 The buyer responds with a counter-offerof $2,200 to give himself some room to concede. He digs in as hisconcessions start to approach his reservation price. After severalrounds of concessions from both sides, the sale concludes at$2,600. In this case, the seller has several of her offers rejected andobserves several counter-offers well below $2,900. On the basis ofthis evidence, her initial outside estimate at $2,900 is revisedtoward the true reservation price, and she walks out of the nego-tiation believing that the buyer’s reservation price is $2,750.

This process of disconfirmation is reinforced by the skewednature of the evidence acquired during a negotiation. In a distrib-utive negotiation, skilled negotiators tend to follow a culturallyshared script that will, in general, enhance their performance(Cohen, 1989). They know that they should not reveal their bottomline to their counterpart and that ambitious offers and small con-cessions can enhance their final share of the surplus (Thompson,2001). Finally, skilled bargainers know that they need to give theimpression of a limit that is more favorable than their true limit.Thus, in a negotiation with a skilled bargainer, the perceiverobserves a series of cues all systematically biased to suggest thatthe opponent has a reservation price that is more favorable than itactually is. This biased sample serves to disconfirm ambitiousestimates. Indeed, to the extent that bargainers trust such biasedinformation, initial estimates that are outside the zone might beoverly disconfirmed, such that estimates end up being inside thezone.

It is important to note that it is relatively costless for negotiatorsto give the impression of a reservation price more favorable thanit actually is. Economists have described this kind of behavior as

“cheap talk” and have argued that information of this sort has littleor no diagnostic value (Farrell & Rabin, 1996). Thus, why woulda negotiator not maintain his or her initial estimate in the face ofsuch cheap talk? We suggest that negotiators fail to discountsufficiently for the strategic actions of the other party because of aprimacy or anchoring process. Even though negotiators mightunderstand that bluffing is “part of the game,” this misleadinginformation can still influence their perceptions (Cain, Loewen-stein, & Moore, 2005). Gilbert, Krull, and Malone (1990) haveshown that it is difficult to discount false information, even whenone is forewarned. The mind seems to start with the assumptionthat evidence is true before adjusting insufficiently for its unreli-ability. This tendency to be influenced by posturing in negotiationcould be considered the competitive equivalent to the reactionsthat people have to acquiescence in cooperative interaction (seeZuckerman et al., 1995). In both cases, the samples of responsesare biased but are not appropriately recognized as so by perceivers.Below, we discuss how motivated reasoning may also contribute tothe acceptance of cheap talk.

Revising Initial Estimates That Are Inside the Zone

In the previous section, we outlined the process by which initialestimates outside the zone are likely to be revised. Now considera seller who begins a negotiation believing that the buyer’s reser-vation price is lower than it actually is, at $2,500, in the right panelof Figure 1. An inside estimate such as this is maintained in partthrough behavioral-confirmation processes (Jones, 1986). Mostskilled negotiators open with offers better than what they thinkthey can actually obtain to give themselves room to bargain.However, an offer that is more extreme than an initial insideestimate (perhaps $2,700 in this case) might still be near or insidethe opponent’s reservation price, thus providing little opportunityfor disconfirmation. As negotiators make concessions from theiroffer, they are likely to find that reaching agreement is easy(Bottom & Paese, 1999) and that they end up at a final price neartheir initial inside estimate. Inside estimates, therefore, can set offa cycle of behavior that maintains the erroneous estimate. Anexception to this self-fulfilling cycle occurs when the opponentalso has an inside estimate and also makes an unambitious firstoffer. This can disconfirm the negotiator’s inside estimate. How-ever, even in the rare instances when negotiators learn that theirinside estimate is wrong, they will virtually never receive infor-mation that would lead them to infer the true reservation price.

In sum, we hypothesize that two different fates await initialbeliefs that are inside or outside the zone (see Figure 2). Outsidebeliefs tend to be disconfirmed, as bargainers encounter rejectionsof their offers. Initial estimates that are outside the bargaining zonemay even be driven inside the bargaining zone if cheap talk istaken as diagnostic. In contrast, inside estimates encounter a “sup-portive” environment. They tend to be self-fulfilling, maintained inpart through behavioral confirmation. Inside estimates lead tounambitious offers that thus provide little opportunity for discon-

1 For simplicity, we refer to first offers by both buyers and sellers asoffers, even though first offers made by sellers are often referred to asdemands (because the seller is demanding that the buyer pay that amount),whereas first offers made by buyers are just referred to as offers (becausethe buyer is offering the seller that amount).

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firmation. Inside estimates will also be “confirmed” by the biasedsample of evidence they encounter in the form of the opponent’scheap talk.

Motivated Reasoning

Why might negotiators take bluffs about limits, extreme offers,and other cheap talk to be diagnostic of a small bargaining zonewhen an alternative attribution is that they are bargaining in a largezone with a cagey bargainer? We suggest that there may bemotivational reasons in addition to the cognitive reasons describedabove. First, bargainers are motivated to see themselves as clevererthan their opponent (Galinsky & Mussweiler, 2001; Kramer, New-ton, & Pommerenke, 1993). Second, it is simply more pleasant tobelieve that one has conceded little value, rather than much value,to the opponent. A large literature exists showing that people tendto hold favorable views of themselves, their abilities, and theiroutcomes in life (Taylor & Brown, 1988). In part, these favorableimpressions are driven by motivated reasoning, or the tendency torecruit information consistent with desired outcomes (Kunda,1990).

We believe that motivated reasoning certainly contributes to thesmall-pie and large-slice biases in many everyday settings. In thatsense, the small-pie and large-slice biases are overdetermined.However, we believe that asymmetric disconfirmation is sufficient

for producing these patterns. To address this concern, we designedour studies to minimize self-enhancement by giving participantsimmediate feedback (Studies 1–3) and incentives for accuracy(Study 3). In each of these ways, we tried to reduce the role ofmotivated reasoning in the small-pie and large-slice biases andemphasize the role of asymmetric disconfirmation.

Asymmetric Disconfirmation as a General Moderator ofAccuracy

We have proposed a pattern of systematic biases that arise innegotiation because erroneous beliefs are asymmetrically discon-firmed—some errors are corrected by feedback, but others areself-fulfilling. We believe that this pattern of asymmetric discon-firmation in negotiation has two important implications for thedebate about accuracy in social perception. First, negotiation is anideal setting for studying issues of accuracy. Negotiation providesstrong incentives to form accurate impressions about a counter-part’s bargaining situation (De Dreu, Koole, & Steinel, 2000;Thompson, 2001). Negotiation’s mixed-motive nature promptsnegotiators to be suspicious of their counterparts’ ulterior motivesand therefore to process situational information more carefully(Fein, 1996; Schul, Mayo, & Burnstein, 2004). Unlike many socialperceivers, negotiators are motivated to look beyond behavior—in

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Figure 2. A hypothetical bargaining zone. The left panel shows a hypothesized distribution of prenegotiationestimates and postnegotiation estimates made by buyers (triangles) and by sellers (circles). Even thoughprenegotiation estimates are accurate on average, the postnegotiation estimates are inaccurate and “inside” onaverage. The right panel shows the sellers’ postnegotiation estimates plotted as a function of the sellers’prenegotiation estimates. RP � reservation price.


this case, cheap talk—to understand their counterparts’ true situ-ations.

Second, asymmetric disconfirmation speaks to the accuracydebate by emphasizing feedback as a moderator of accuracy.Social-perception researchers have shown that the goals of per-ceivers (E. R. Smith, 1998) and targets (Hilton & Darley, 1985;D. M. Smith, Neuberg, Judice, & Biesanz, 1997) in social inter-action moderate the accuracy of perceptions. However, a class ofmoderators that has received less attention is the feedback envi-ronment in which hypotheses are tested (Einhorn & Hogarth, 1978;Klayman & Ha, 1987). Hogarth (2001) proposed that there are“kind” and “wicked” environments in which to learn. Kind envi-ronments provide immediate, concrete, and unbiased evidenceabout one’s initial beliefs, whereas wicked environments providedelayed, ambiguous, or biased evidence (Hogarth, McKenzie,Gibbs, & Marquis, 1991). The feedback environment we havedescribed in distributive negotiation is what might be termedselectively wicked: Outside estimates encounter clear disconfirm-ing evidence, often yielding more accurate perceptions, whereasinside estimates encounter supportive evidence, preserving initialinaccuracy.

An interesting implication of asymmetric disconfirmation is thatit can yield final perceptions that are systematically biased at thepopulation level, even when the distribution of initial individualbeliefs is accurate on average. This can be seen in the right panelof Figure 2. In the figure, we have assumed that sellers’ prenego-tiation estimates of buyers’ limits are distributed around and cen-tered on the truth—that is, they are imperfect but accurate onaverage. However, the distribution of postnegotiation estimates isskewed and has an average value smaller than the true reservationprice. Thus, this feedback environment can take accurate but noisyjudgments (i.e., judgments with random error around the truereservation price) and convert them to biased judgments (i.e.,judgments that systematically underestimate the true reservationprice). In the model depicted in Figure 2, the magnitude of the finalpopulation-level bias increases with the proportion of initial indi-vidual estimates that are inside the zone.

We believe that this pattern has interesting consequences for thedebate on accuracy in social perception. First, not all erroneousbeliefs are self-fulfilling (Jussim, 1991): Outside estimates aredisconfirmed. Second, the direction of error determines the likeli-hood of disconfirmation in these environments: Inside estimatestend to be self-fulfilling. Thus, feedback environments with thisstructure do moderate when individual errors are corrected orself-fulfilling. However, these structures nonetheless can yieldpopulation-level biases from initial distributions of individual be-liefs that are accurate on average.

The notion of asymmetric disconfirmation is useful for thedebate about accuracy in social perception. It shifts the debatefrom general claims about accuracy or inaccuracy to an emphasison diagnosing feedback environments. By identifying asymmetricenvironments, researchers can predict circumstances in which bi-ased perceptions at the population level are systematic and robust.In the General Discussion, we offer a general model of asymmetricdisconfirmation that includes a population of targets that vary intheir reservation prices, rather than assuming a single value. Weshow that the general model produces a triangular pattern oflearning that is conceptually similar to Kelley and Stahelski’s(1970) triangle hypothesis.

Overview of Studies

We present three studies that demonstrate the small-pie andlarge-slice biases and highlight the role that asymmetric discon-firmation plays in producing the biases. In Study 1, we manipu-lated the size of the bargaining zone, and in Study 2, we manip-ulated expectations about the other party’s reservation price. Thus,in both studies, some negotiators started with expectations outsidethe bargaining zone and some negotiators started with expectationsinside the bargaining zone.

Both studies showed that errors are asymmetrically discon-firmed: Initial estimates inside the bargaining zone are maintained,whereas initial estimates outside the bargaining zone are corrected.Study 3 showed that the biases occur even when we minimize theself-enhancement motivation by heightening accuracy motivation.In the General Discussion, we present a formal analysis of asym-metric disconfirmation using data from the studies.

Study 1: Manipulation of Zone Size

To test the asymmetric-disconfirmation hypothesis, we manip-ulated whether participants tended to begin the negotiation withestimates inside or outside the bargaining zone by varying the sizeof the bargaining zone. Participants were assigned to either a smallor large bargaining-zone condition. In the large-zone condition, wehypothesized that prenegotiation estimates would tend to fall in-side the zone, and this would be sufficient to generate the small-piebias. In the small-zone condition, we hypothesized that prenego-tiation estimates would tend to fall outside the zone but that thesewould be disconfirmed in the negotiation process, leading to finalestimates that were near, or possibly inside, the true reservationprice. Finally, we expected a stronger small-pie bias in the large-zone condition than in the small-zone condition, because a greaterproportion of initial estimates would fall inside the bargainingzone in the large-zone condition than in the small-zone condition.2

To reduce the role of self-enhancement, we constrained thetendency to inflate performance by leading participants to expectfeedback on their estimates. Thus, unlike negotiators in real-worldinteractions, our participants expected and received immediate,accurate feedback on their counterparts’ reservation prices shortlyafter making their final reservation price estimates. In such a case,inflated estimates faced the possibility of swift and clear discon-firmation. A number of researchers have found that imminentfeedback significantly constrains motivated reasoning (Armor &Taylor, 2002; Gilovich, Kerr, & Medvec, 1993; Larrick & Boles,1995; Savitsky, Medvec, Charlton, & Gilovich, 1998; Shepperd,Ouellette, & Fernandez, 1996), because it is easier to hold inflatedviews of the self when there is no reality check than when realityis likely to disappoint.

Method

Participants. Participants were 264 masters of business ad-ministration (MBA) students at the University of Chicago’s Grad-

2 This design yielded dyads in which buyers and sellers tended to sharethe same type of erroneous expectations: In the small zone, both partiestypically had inside estimates, and in the large zone, both typically hadoutside estimates. Study 2 crossed expectations factorially.

216 LARRICK AND WU

uate School of Business who were enrolled in several MBA classesin negotiation.

Procedure. Negotiators were randomly assigned to one of twoconditions: A small-zone condition (n � 118) and a large-zonecondition (n � 154). Participants negotiated the sale of a batch ofheadlamps between a manufacturer (the “seller”) and an end user(the “buyer”). Participants were randomly assigned to the role ofeither the buyer or seller, and each individual was given a case thatprovided some background material for the negotiation. The caseprovided participants with their respective reservation prices, aswell as some information that helped them to estimate the otherparty’s reservation price (such as information on comparable costsand prices). In the large-zone condition, the seller’s reservationprice was $10 per headlamp, and the buyer’s reservation price was$35 per headlamp. Thus, the large bargaining zone was (10, 35). Inthe small-zone condition, the bargaining zone was (17, 23).

Participants prepared for the negotiation prior to class and wereasked to fill out a brief prenegotiation questionnaire. The ques-tionnaire asked them to provide an assessment of the other party’sreservation price. Specifically, the seller was asked “What is yourassessment of the buyer’s maximum willingness to pay (per unit)?In other words, what is your best guess as to the buyer’s reserva-tion price (your reservation price is $10 [17])?” The parentheticalremark about their own reservation price was intended to eliminateconfusion about the meaning of “maximum willingness to pay”and to ensure that the seller assessed the buyer’s reservation price(White & Neale, 1991). The wording for the buyer was similar,except that buyers were asked to estimate “the seller’s minimumwillingness to accept.” We also asked participants to indicate howconfident they were in their assessment of their opponent’s reser-vation price on a scale of 1 (extremely confident) to 7 (extremelyunsure). (In reporting this scale, we reverse it for ease of interpre-tation.)

Participants were then given 45 min to negotiate. Once thenegotiation was finished, buyers and sellers each completed apostnegotiation questionnaire, in which they indicated whetherthey reached an agreement and, if so, for what price. Participantswere asked to estimate their opponents’ reservation prices, usingthe same wording described above, and to indicate their confidencelevel in their estimates, using the scale from the prenegotiationquestionnaire. Participants also recorded the seller’s first offer andthe buyer’s first offer. For 90% of dyads in this study, there wasperfect agreement on each side’s first offer; when dyad membersdisagreed, we used the seller’s report, a practice followed inStudies 2 and 3. After completing the postnegotiation question-naire, participants were debriefed and informed about their oppo-nents’ reservation prices.

Results

Outcomes. All but 1 of the 77 dyads in the large-zone condi-tion reached agreement, with an average settlement of $21.12(SD � 5.63). The one impasse was omitted.3 In the small-zonecondition, 56 of the 59 dyads settled, with an average price of$20.02 (SD � 1.61). Four dyads in the small-zone condition settledoutside the bargaining zone and were omitted along with the threeimpasses.

Some negotiators gave reservation-price estimates for their part-ners that fell between their own reservation price and the final

negotiated price. (This occurred in the large-zone condition for 10of the 77 sellers and 8 of the 77 buyers and in the small-zonecondition for 3 of the 59 buyers and 4 of the 59 sellers.) Theseparticipants either did not understand the reservation-price ques-tion or believed that their opponents accepted a deal outside thezone. We chose to be conservative and omitted these dyads. (Ifincluded, these dyads would increase the size of the small-pie andlarge-slice biases.) We also omitted one dyad in the large-zonecondition, because the seller’s estimate of the buyer’s reservationprice was an extreme outlier (more than 10 standard deviationsfrom the overall mean). We were left with 60 dyads in thelarge-zone condition and 48 dyads in the small-zone condition.

Reservation-price estimates. The top panel of Figure 3 plotsthe pre- and postnegotiation reservation-price estimates for thelarge-zone condition. In the large-zone condition, the postesti-mates were almost identical to the preestimates. The preestimatesfor both roles were significantly inside the zone, as were thepostestimates (all comparisons by t tests, ts � 7, p � .0001). Incontrast, preestimates were outside the zone on average in thesmall-zone condition (see the bottom panel of Figure 3), whereaspostestimates were inside the zone. (Final estimates were signifi-cantly inside the zone for the sellers but not for the buyers.)Because these data are dyadic, and the postestimates may not beindependent, we present fuller statistical tests in the dyadic-analysis sections (a practice followed in Studies 2 and 3, as well).

Dyadic analysis of reservation prices. It is instructive to lookat how the estimates changed during the negotiation. To measurethe extent to which estimates were inside or outside the truereservation price, we calculated a difference between the true valueand the estimate. Seller’s estimates of the buyer’s reservationprices were calculated as estimated reservation price minus actualreservation price; buyer’s estimates of the seller’s reservationprices were calculated as actual reservation price minus estimatedreservation price. Thus, for both roles, a positive sign indicated anoutside estimate and a negative sign an inside estimate.

Figure 4 plots the shift in estimates for each dyad for both thelarge- and small-zone conditions. The left panel plots, for eachdyad, the buyer’s and seller’s perceptions of their opponents’reservation prices before the negotiation. The right panel plotsthese perceptions following the negotiation. (For this graph, wedivided the differences by the actual zone size to express themagnitude and direction of error as percentages. We performstatistical tests on the unscaled differences and report those meansin the text. However, graphing the measure as a percentage facil-itates comparisons between conditions and across studies.)

We analyzed this difference measure in a Zone Size (large vs.small) � Time (pre vs. post) � Role (buyer vs. seller) multivariateanalysis of variance (MANOVA), where the last two measureswere analyzed within-dyad. We used dyad as the level of analysis,because we did not have specific predictions about the effect ofrole and wanted to collapse across role. However, either pooling

3 It is possible to calculate an estimated-size-of-zone statistic for theimpasses. If included, impasses would increase the size of the small-piebias, because participants tended to perceive a negative zone in such cases.However, because there is no settlement price, we cannot calculate animputed-share statistic. To make the analysis comparable and conservative,we omitted these dyads.


the roles or analyzing the roles separately would risk overstatingdegrees of freedom if the judgments of the dyad members were notindependent. Using dyad as the level of analysis reduces the

degrees of freedom for the error term by half, creating a conser-vative test of our hypotheses. This analysis tests for what we willcall a weak small-pie bias, which occurs when the average estimate

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Figure 3. Average estimates by buyers and sellers of the other role’s reservation price in Study 1. The top panelis for the large-zone condition, for which the actual reservation prices were $10 and $35. The bottom panel isfor the small-zone condition, for which the actual reservation prices were $17 and $23. Asterisks indicatesignificant differences from the buyer’s correct reservation price and seller’s correct reservation price. *p � .05.***p � .001.

218 LARRICK AND WU

of the two parties is inside the bargaining zone. For example, if theseller’s estimate is inside the zone by 4 and the buyer’s estimate isoutside the zone by 2, the average estimate is inside the zone by(�4 � 2)/2 � �1. (All dyads that fall to the bottom left of thedashed lines in Figure 4 show a weak small-pie bias.)

There was an unexpected main effect of role, such that sellers(M � �5.01) gave estimates that were more inside than did buyers(M � �2.75), F(1, 111) � 8.64, p � .001, �2 � .07. There wasalso an anticipated main effect of zone size, such that bargainers’estimates were more inside in the large zone (M � �8.53) than inthe small zone (M � �0.76), F(1, 111) � 274.89, p � .001, �2 �.71. There was no main effect of time, F(1, 111) � 2.16, p � .14.The main effect of zone size was qualified by the expected inter-action with time, F(1, 111) � 14.65, p � .001, �2 � .12, whichillustrates the asymmetric disconfirmation process: In the largezone, initial estimates fell well inside the zone and changed verylittle during the negotiation, becoming slightly less “inside”(Mpre � �9.14 vs. Mpost � �7.92). Thus, there was a large andsustained small-pie bias in the large-zone condition. In the small-zone condition, initial estimates fell outside the zone and movedinside over time (Mpre � 2.14 vs. Mpost � �0.62), generating amodest small-pie bias. All means were significantly different from0 by a simple-effects test, p � .05.

We define a dyad as exhibiting a strong small-pie bias if boththe buyer and seller have inside (negative) estimates. (All dyadsthat fall in the bottom left quadrant in Figure 4 exhibit a strongsmall-pie bias.) In the large-zone condition, 92% of dyads (55 of60) exhibited a strong small-pie bias prior to negotiating, with thesame proportion showing a strong small-pie bias after the negoti-ation (Wilcoxon z � 0, p � 1.00). In the small-zone condition,only 10% of dyads (5 of 48) exhibited a strong small-pie biasentering the negotiation, but 50% (24 of 48) finished the negoti-ation with a strong small-pie bias, which is a significant change(Wilcoxon z � 3.80, p � .001).

Dyadic analysis of imputed share. We next test the large-slicebias by calculating a measure we call imputed share.4 Consider a

dyad in the large-zone condition that reached agreement at $20, inwhich the seller’s postestimate of the buyer’s reservation price is$25, and the buyer’s postestimate of the seller’s reservation priceis $15. These estimates imply that the seller believes that thebargaining zone is $15 (25 � 10), her surplus is $10 (20 � 10),and that her share of the pie is $10 of the $15 pie, or 67%.Similarly, the buyer’s imputed share is 75%: (35 � 20)/(35 � 15).

We calculated the imputed share for both the buyer and theseller and show them by dyad in the top panel of Figure 5. Weanalyzed the imputed share in a Zone Size (large vs. small) � Role(buyer vs. seller) MANOVA, where role was a within-dyad mea-sure. The overall average estimate of 65% was significantly greaterthan 50%, F(1, 106) � 179.44, p � .001, �2 � .63 (we subtracted50% from all imputed shares before performing the MANOVAand tested the constant term against 0). There was an unexpectedmain effect of role (Mbuyer � 62% vs. Mseller � 69%), F(1, 106) �5.71, p � .02, �2 � .05; an expected main effect of zone size(Mlarge � 73% vs. Msmall � 58%), F(1, 106) � 42.55, p � .001,�2 � .29; and no significant interaction. In the large-zone condi-tion, the imputed share for buyers (M � 71%) and sellers (M �74%) were both significantly larger than 50%, buyer t(59) � 9.99,p � .0001, seller t(59) � 11.21, p � .0001. In the small-zonecondition, the imputed share for sellers (M � 63%) was signifi-cantly higher than 50%, t(47) � 3.86, p � .001, but not for buyers(M � 53%), t(47) � 1.23, p � .22. The sum of these quantities

4 It is important to note that although the small-pie bias and the large-slice bias are closely related, one does not by necessity imply the other. Itis possible to have a large-slice bias without a small-pie bias or a small-piebias without a large-slice bias. Consider the following example of such adivergence: A bargaining zone ranges from 10 to 20, the buyer’s estimateof the seller’s reservation price is 15, the seller’s estimate of the buyer’sreservation price is 30, and the settlement price is 16. In this case, there willbe a large-slice bias (the sum of imputed shares is .83 � .3 � 1.13) but nosmall-pie bias. Thus, we analyze the measures separately in our studies,despite their close relationship.

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Figure 4. Change in pre- to postnegotiation estimates in Study 1, by dyad and zone size. The panels plot thedegree to which estimates for the seller and buyer are inside versus outside the actual reservation price (RP) inpercentage terms (amount inside or outside divided by size of the bargaining zone). The left panel depictsprenegotiation estimates, and the right panel depicts postnegotiation estimates. The dotted line indicates that thedyad has, on average, correctly estimated the zone size. Dyads to the southwest of the dotted line underestimatedthe zone size, whereas dyads to the northeast overestimated the zone size.


exceeded 100% for 59 of the 60 dyads in the large zone and for 32of 48 dyads in the small zone.

Dyadic analysis of confidence. Confidence was analyzed in aZone Size (large vs. small) � Role (buyer vs. seller) � Time (pre vs.post) MANOVA, with the last two measures tested within-dyad. The

only significant effect was a main effect for time, F(1, 102) � 137.81,p � .001, �2 � .57. Average confidence increased significantlyduring the negotiation from 3.25 to 4.42 (after reverse scoring so that7 corresponded to extremely confident). The effects were equallystrong for buyers and for sellers (both ts � 7, p � .0001).

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Figure 5. Imputed share of the bargaining zone for buyer and seller by dyad for Study 1 (top panel), Study 2(middle panel), and Study 3 (bottom panel). The diagonal line indicates deals in which the dyad’s imputed sharesums to 100%. Data points above the line indicate overestimation at the dyadic level; data points below the lineindicate underestimation.

220 LARRICK AND WU

First offers. First offers represent an important mechanism bywhich preestimates that are inside the zone become self-fulfilling.This mechanism is driven by the fact that initial estimates and firstoffers tend to be highly correlated (Galinsky & Mussweiler, 2001).In the large-zone condition, the correlation between the sellers’preestimate and their first offer was .42 ( p � .001), whereas thecorrelation between the buyers’ preestimate and their first offerwas .11 ( p � .19). (This difference in degree of correlation reflectsa classic asymmetry in distributive negotiation. When the seller’sreservation price is close to zero, buyers are constrained by a floorin both their estimates of the seller’s reservation price and theiropening offer, leading to a restricted range for both measures.Sellers never face this constraint. Study 2 avoided this floor.)

In the large-zone condition, only 16 of the 60 sellers and 2 of the60 buyers made first offers that were outside the bargaining zone.Thus, it is not surprising then that only 4 sellers and 1 buyer gaveoutside estimates following the negotiation. By contrast, in thesmall-zone condition, 45 of the 48 sellers and 41 of the 48 buyersmade first offers that were outside the bargaining zone. Thus,many more bargainers—17 sellers and 12 buyers—gave finalestimates that were outside the zone.

Discussion

Study 1 demonstrated both the small-pie and large-slice biases.We found a strong tendency in this negotiation to underestimatethe size of the bargaining zone (small-pie bias) and therefore tooverestimate the share of the bargaining zone claimed (the large-slice bias). In this study, we tested two extreme conditions: one inwhich the bargaining zone was much larger than negotiators ini-tially believed and one in which the zone was considerably smallerthan initially believed. In both cases, we found reliable small-pieand large-slice biases, although the biases were, in absolute terms,considerably smaller in the small zone than in the large zone.

These data support an asymmetric disconfirmation process. Thelarge-zone condition showed that initial beliefs inside the zone aresufficient to generate the effect, as initial beliefs inside the zonetended to lead to first offers inside the zone. Indeed, it was almostimpossible for negotiators who made a first offer inside the zone tohave their inaccurate estimate fully disconfirmed. By contrast, themajority of negotiators in the small-zone condition began withestimates and first offers outside the zone. Nevertheless, it appearsthat their counterparts’ behavior led them to revise their judgmentstoward and often inside the bargaining zone. Together, the twoconditions demonstrate that those who began with estimates out-side the zone tended to be driven inside the zone, whereas thosewith estimates inside the zone changed their estimates very little.

Study 1 also suggests two boundary conditions on ourasymmetric-disconfirmation proposal. First, in the large-zone con-dition, the preestimates that were furthest inside did move towardthe actual reservation price, though they remained very muchinside the zone. Thus, estimates that are sufficiently far inside thezone may be revised in the direction of the correct reservationprice (as discussed in the introduction) but, critically, not nearlyenough to undo the small-pie bias. Second, although we foundsmall-pie and large-slice biases in the small-zone condition, theywere relatively small in absolute terms.

We believe that self-enhancement played a relatively minor partin our findings. First, there was an accuracy motivation prior to

and during the negotiation to correctly estimate the other party’sreservation price. In other words, most negotiators knew that acritical part of being successful in distributive negotiation is hav-ing an accurate picture of their counterparts’ bottom lines (Raiffa,1982). Second, our negotiators were told that they would learntheir opponents’ actual reservation prices immediately after com-pleting the postnegotiation questionnaire, which should have in-creased accuracy motivation. Nevertheless, it is hard to determineexactly how much self-enhancement contributes to these biases. InStudy 2, we used additional measures to demonstrate that asym-metric disconfirmation, and not motivation, is the more parsimo-nious explanation for these results.

Study 2: Manipulation of Initial Expectations

In Study 1, we manipulated whether participants tended to beginthe negotiation with estimates inside or outside the bargainingzone by manipulating the zone size. In Study 2, we used analternative method of creating inside and outside estimates: ma-nipulating initial perceptions. We provided participants with esti-mates of their opponents’ reservation prices that were accurate,inside the zone, or outside the zone. Although conceptually simi-lar, this method has the advantage that the bargaining zone is heldconstant in size across all conditions. We also manipulated expec-tations for sellers and buyers factorially. In Study 1, members of adyad shared expectations—both tended to have inside estimates inthe small zone, and both tended to have outside estimates in thelarge zone. In Study 2, we created some dyads in which onepartner had inside estimates and the other had outside estimates.

We hypothesized a pattern of final reservation-price estimatessimilar to that found in Study 1. Initial estimates inside the zoneshould generate the small-pie bias, as these estimates will bemaintained through behavioral confirmation. In contrast, initialestimates outside the zone should be disconfirmed in the negoti-ation process, and these estimates will move toward the truereservation price and perhaps even inside the bargaining zone.

Finally, we asked sellers and buyers to estimate the settlementrate and average settlement price among all dyads. These addi-tional measures helped us to separate the role of biased informa-tion from motivated reasoning in producing the small-pie bias. Ifnegotiators are primarily self-enhancing, they should report thatother dyads frequently failed to settle and that other negotiators inthe same role as themselves settled for a less favorable price. Bothof these would be evidence for a better-than-average effect. Ifnegotiators are primarily updating their beliefs on the basis ofbiased information garnered during a negotiation, then only thesettlement rate should be biased downward, but price should not bedistorted. Thus, to the extent to which biased information leads toperceptions of a small zone, we expect participants to predict thatother dyads agreed to prices similar to their own—that is, there isa “sweet spot” to hit in a small zone, and any pair that reachesagreement will find it.

Method

Participants. Participants were 266 MBA students at the Uni-versity of Chicago’s Graduate School of Business who were en-rolled in several executive MBA sections of a managerial decision-making and negotiation course.


Procedure. Participants completed a negotiation with thesame cover story used in Study 1. The buyer’s reservation pricewas $46, and the seller’s reservation price was $34. Thus, thebargaining zone was (34, 46). The case provided participants withtheir respective reservation prices, as well as some information thathelped them to estimate the other party’s reservation price. Inaddition, both the seller and buyer were given explicit expectationsabout their opponent’s reservation price. These expectations weredescribed as being a “best guess” by an analyst within their firmwho did “not have much information to base a guess upon.”Guesses were therefore expressed as a range of values. Buyerswere supplied with a “best guess” of the minimum the seller wouldbe willing to accept (i.e., the seller’s reservation price). Sellerswere supplied with a “best guess” of the buyer’s maximum. Wemanipulated expectations of the bargaining zone size such thatbuyers and sellers were given correct expectations, expectationsthat were outside the zone, or expectations that were inside thezone. Participants were randomly assigned to one of nine (3 � 3)conditions in which we manipulated expectations about the seller’sreservation price and the buyer’s reservation price factorially.

In the correct-expectations condition, buyers (n � 43) were toldthat the analyst who provided the best guess estimated that theseller “would be willing to take as little as $34/unit, although theactual limit could be as low as $24/unit and as high as $44/unit.”The sellers (n � 47) were given similar instructions: The buyer“would be willing to pay as much as $46/unit, although the actuallimit could be as low as $36/unit and as high as $56/unit.” Thus,the guess given to buyers and sellers was their counterpart’s actualreservation price, although there was considerable uncertaintyaround that guess.

In the inside-expectations condition (n � 45 for sellers, n � 43for buyers), the buyer and seller were given best guesses thatunderestimated the size of the bargaining zone: $42 as a guess forthe seller’s reservation price (with a range of $32–$52) and $38 asa guess for the buyer’s reservation price (with a range of $28–$48). Finally, participants in the outside-expectations condition(n � 41 for sellers, n � 47 for buyers) were provided with guessesthat overestimated the size of the bargaining zone: $26 as a guessfor the seller’s reservation price (with a range of $16–$36) and $54as a guess for the buyer’s reservation price (with a range of$44–$64). It is important to note that in all cases, the correctreservation prices, $34 for the seller and $46 for the buyers, werecontained in the ranges provided.

Participants completed a prenegotiation questionnaire almostidentical to that used in Studies 1 and 3. They were asked toprovide an assessment of the other party’s reservation price and anassessment of their own confidence.

Participants negotiated for 45 min, after which they completeda postnegotiation questionnaire, in which both buyers and sellersindicated whether there was a settlement, the settlement price inthe case of settlement, the seller’s first offer, and the buyer’s firstoffer. Participants were asked to estimate their opponents’ reser-vation prices and indicate their confidence level in their estimates,using the same scale as in the prenegotiation questionnaire. Wealso asked participants to estimate what percentage of pairsreached agreement and the average settlement price for the pairsthat reached a deal.

Results

Outcomes. One hundred twenty-eight out of the 133 dyads(96%) reached agreement. The average settlement price across allconditions was $39.89 (SD � 4.00). Three of the settlements wereoutside of the bargaining zone. We omitted these three dyads andthe five impasses from the remaining analysis. Although settle-ment prices varied as a function of prenegotiation expectations inthe expected way (e.g., prices were higher when the buyer had aninside expectation and the seller had an outside expectation), theywere not significantly different across the conditions.

As in Study 1, some participants estimated a reservation pricefor their partner that fell between the participant’s own reservationprice and final negotiation price (25 of the 125 sellers who reachedagreement and 9 of the 125 buyers who reached agreement).Inclusion of these dyads exaggerates the small-pie and large-slicebiases. As in Study 1, we chose to be conservative and omitted the34 resulting dyads, leaving 91 dyads.

Reservation-price estimates: Seller. As predicted, the negoti-ation led parties to revise their estimates of the other party’sreservation price differentially by condition. We consider the shiftfrom prenegotiation to postnegotiation estimates of the opponent’sreservation price, beginning with the seller’s estimate of the buy-er’s reservation price (Figure 6). The anchoring manipulation wassuccessful in that the prenegotiation estimates were $40.31,$47.09, and $51.40, compared with the anchors of $38, $46, and$54, in the inside, correct, and outside conditions, respectively. Allestimates were significantly different from each other betweenconditions (ts � 2, p � .05). As may be seen in Figure 6, sellersin the correct and outside conditions were outside the correctreservation price of $46. These estimates shifted following thecompletion of the negotiation. The final estimates for the inside,correct, and outside conditions were $40.65, $43.36, and $44.67,respectively, all inside the zone.

Reservation-price estimates: Buyer. We next consider thebuyer’s estimate of the seller’s reservation price (Figure 6). Theprenegotiation estimates were $27.36, $32.49, and $35.60 in theoutside, correct, and inside conditions, respectively, comparedwith the correct reservation price of $34. As expected, theseestimates were close to the respective anchors: $26, $34, and $42.Means were significantly different between conditions (ts � 3, p �.01), except for the comparison between the correct and insideconditions (t � 1.74, p � .087). As with the sellers, the buyers’estimates shifted toward the inside of the bargaining zone follow-ing the completion of the negotiation. Estimates for all threeconditions were greater than $34 and hence inside the zone:$34.87, $34.87, and $37.18 for the outside, correct, and insideconditions, respectively.

Dyadic analysis of reservation prices. We tested the weaksmall-pie bias by analyzing the pre- and postnegotiationreservation-price estimates by dyad (Figure 7). As in Study 1, wecalculated the degree to which reservation-price estimates wereinside or outside the zone and analyzed the means in a SellerExpectation (inside vs. correct vs. outside) � Buyer Expectation(inside vs. correct vs. outside) � Role (buyer vs. seller) � Time(pre vs. post) MANOVA. The last two variables were within-dyadvariables.

There was the predicted main effect for time. Initial estimateswere outside the zone (M � 1.38), and final estimates were inside

222 LARRICK AND WU

the zone (M � �2.31), F(1, 78) � 51.35, p � .001, �2 � .40. Themain effect of time was qualified by significant interactions withthe expectation manipulations. There was a Time � Seller Expec-tation interaction, such that initial estimates were outside the zonein the outside (M � 3.06) and correct (M � 2.77) conditions andinside the zone in the inside (M � �1.71) condition, but finalestimates were inside the zone in all conditions (Ms � �1.93,�1.77, and �3.24, respectively), F(2, 78) � 9.80, p � .001, �2 �.30. There was a similar Time � Buyer Expectation interaction(prenegotiation, Moutside � 4.69, Mcorrect � �.09, and Minside ��.48; postnegotiation, Moutside � �2.02, Mcorrect � �2.44, and

Minside � �2.47), F(2, 78) � 4.58, p � .013, �2 � .11. All finalestimates in these analyses were significantly less than 0 by asimple-effects test, p � .05. Overall, the number of dyads exhib-iting a strong small-pie bias increased significantly, from 27% (25of 91) entering the negotiation to 64% (58 of 91) following thenegotiation (Wilcoxon z � 4.92, p � .0001).

Dyadic analysis of imputed share. The imputed share for boththe buyer and the seller were calculated as described in Study 1and are shown by dyad in the middle panel of Figure 5. Weanalyzed the imputed share in a Buyer Expectation (outside vs.correct vs. inside) � Seller Expectation (outside vs. correct vs.

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Figure 6. Average estimates by buyers and sellers of the opposing role’s reservation price in Study 2, bycondition. Outside, correct, and inside refer to the manipulation of initial expectations. Average prenegotiationand postnegotiation estimates are shown. Asterisks indicate significant differences from the buyer’s correctreservation price of $46 and from the seller’s correct reservation price of $34. *p � .05. ***p � .001.

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Figure 7. Change in pre- to postnegotiation estimates in Study 2, by dyad. The panels plot the degree to whichestimates for the seller and buyer are inside versus outside the actual reservation price (RP) in percentage terms(amount inside or outside divided by size of the bargaining zone). The left panel depicts prenegotiation estimates,and the right panel depicts postnegotiation estimates. The dotted line indicates that the dyad has, on average,correctly estimated the zone size. Dyads to the southwest of the dotted line underestimated the zone size, whereasdyads to the northeast overestimated the zone size.


inside) � Role (buyer vs. seller) MANOVA, where role was awithin-dyad measure. The overall average estimate of 65% wassignificantly greater than 50%, F(1, 78) � 91.07, p � .001, �2 �.54. There were no significant main effects or interactions (Fs �2.7). The effect was equally strong for buyers (M � 63%), t(90) �4.78, p � .0001, and for sellers (M � 68%), t(90) � 6.30, p �.0001.

Dyadic analysis of confidence. Confidence was analyzed in aBuyer Expectation (outside vs. correct vs. inside) � Seller Expec-tation (outside vs. correct vs. inside) � Role (buyer vs. seller) �Time (pre vs. post) MANOVA, with the last two measures testedwithin dyad. The only significant effect was a main effect for time,F(1, 77) � 60.63, p � .001, �2 � .44. Average confidenceincreased significantly during the negotiation from 3.32 to 4.26.The increase was equal in magnitude for buyers and sellers (ts �5, p � .001).

First offers. We also examined self-reported first offers. Therewas a strong correlation between prenegotiation estimates and firstoffers; buyers, r(90) � .56, p � .0001; sellers, r(90) � .54, p �.0001. An implication of this strong correspondence is that nego-tiators with preestimates inside the zone should be more likely tomake first offers inside the zone. Overall, 22 of the 91 buyers’ firstoffers and 26 of the 91 sellers’ first offers were inside the bar-gaining zone. As expected, inside first offers were concentratedamong the buyers and sellers with prenegotiation estimates insidethe zone. Of the 56 sellers and 38 buyers with prenegotiationestimates inside the zone, 25 (45%) sellers and 15 (37%) buyersmade first offers inside the zone. In contrast, only 1 (3%) of the 35sellers with prenegotiation estimates outside the zone made a firstoffer inside the zone, and only 7 (14%) of the 50 such buyers didlikewise. These rates are statistically significant within each role;sellers, �2(1) � 18.43, p � .001; buyers, �2(1) � 6.26, p � .01.

Settlement-rate and price estimates. Finally, we asked bothbuyers and sellers to estimate the settlement rate and averagesettlement price. The estimated settlement rate was 77% for bothsellers and buyers, and it did not vary significantly across condi-tions but was significantly less than the actual settlement rate of95.6% for both buyers and sellers (ts � 10, p � .001). In contrast,estimates of settlement price were not significantly different fromthe actual settlement price of $39.89; buyers, M � 39.72, t(89) �0.44, p � .66; sellers, M � 40.23, t(89) � 0.72, p � .47.

Discussion

Study 2 replicated the results of the previous studies. Eventhough dyads overestimated the size of the bargaining zone onaverage prior to the negotiation, they underestimated the zone sizeonce the negotiation was finished. The vast majority of dyads hadtotal imputed shares that summed to more than 100%.

We manipulated prenegotiation expectations so that some ne-gotiators were more likely to have initial estimates outside thebargaining zone, and some were more likely to have estimatesinside the zone. Consistent with asymmetric disconfirmation, ne-gotiators who began with estimates outside the zone tended to bedriven inside the zone, whereas those with estimates inside thezone changed their estimates very little. It is interesting thatparticipants in the correct expectations condition began the nego-tiation with accurate perceptions of the size of the bargaining zoneon average and, as predicted, became less accurate as a result of

the negotiation dynamic, yet they reported higher confidence intheir postnegotiation estimates.

Finally, we asked participants to estimate the settlement rate andaverage settlement price. Participants systematically overestimatedhow many dyads would reach an impasse. This could be inter-preted as evidence for either self-enhancement (bargainers inflatedtheir performance) or for an inference on the basis of a biasedsample of evidence (bargainers found it difficult to settle with theiropponents). Evidence to distinguish between these interpretationsis provided by estimated settlement price. Both buyers and sellerswere remarkably accurate in estimating the average settlementprice. We believe this combined pattern is more consistent with thehypothesis testing explanation for the small-pie bias than with themotivational view. The biased sample of information obtainedduring the negotiation—rejected offers, bluffs about reservationprices, and so on—suggests that opponents are nearly impossibleto please. This information fuels both the small-pie bias and thetendency to overestimate the impasse rate but does not distortestimates of average settlement price. Their reasoning, we wouldargue, is that “if other dyads reached agreement—which wouldhave been difficult—the terms must look similar to mine, becausethe zone is so small.”

Study 3: Manipulation of Incentives for Accuracy

In Study 3, we tested the effect of self-enhancement on thesmall-pie and large-slice biases by making it more costly. Al-though we increased accuracy motivation in Studies 1 and 2through the use of immediate and concrete feedback on the truth,we wanted to heighten the motivation by paying participants foraccurate estimates. We ran two conditions: a control condition(comparable to the instructions in Studies 1 and 2) and an incentivecondition (in which participants were paid according to the accu-racy of their pre- and postnegotiation estimates of their counter-parts’ reservation prices). Giving a self-enhancing estimate in theincentive condition would come at a financial cost. Previous re-search has shown that accuracy motivation improves informationprocessing in negotiation (De Dreu et al., 2000).

Method

Participants. Participants in Study 3 were 156 MBA studentsat the University of Chicago’s Graduate School of Business whowere enrolled in several sections of an elective negotiation course.

Procedure. The basic negotiation was the same as in Studies 1and 2 with two notable exceptions. We changed the size of thebargaining zone so that the seller’s reservation price was $16 andthe buyer’s reservation price was $28 (16, 28). In addition, we rantwo conditions: a control condition (n � 39) and an incentivecondition (n � 37), in which participants were paid according tothe accuracy of their pre- and postnegotiation estimates of theircounterparts’ reservation prices. Participants in the incentive con-dition were paid $5 if their prenegotiation estimate was among the20% closest to the actual reservation price (including ties), asmeasured by the absolute difference between their estimated res-ervation price and the actual reservation price. They were also paid$5 if their postnegotiation estimate was among the 20% closestestimates (including ties). Thus, participants could earn up to $10.

As in Study 2, participants were given information to help themestimate the other party’s reservation price. Sellers were supplied

224 LARRICK AND WU

with a “best guess” of the maximum the buyer would be willing topay (i.e., the buyer’s reservation price). Specifically, they weretold that the analyst who provided the estimate did “not have muchinformation to base a guess upon” but estimated that the buyer“would be willing to take as little as $13/unit, although the actuallimit could be as low as $8/unit and as high as $18/unit.” Similarly,buyers were told that the seller “would be willing to pay as muchas $31/unit, although the actual limit could be as low as $26/unitand as high as $36/unit.” Note that these best guesses are both $3outside the correct reservation price. Sellers and buyers completedpre- and postnegotiation questionnaires as in Studies 1 and 2.

Results

Outcomes. Seventy-five out of the 76 dyads (99%) reachedagreement. The one impasse occurred in the incentive condition.The average settlement price across the two conditions was $22.43(SD � 2.83).

Two dyads were excluded from the remaining analyses: theimpasse and one settlement that occurred outside the bargainingzone. As in Studies 1 and 2, some participants estimated reserva-tion prices for their partners that fell between their reservationprice and the final negotiated price (6 sellers and 3 buyers). Thesedyads were omitted, leaving 66 dyads: 33 in the incentive condi-tion and 33 in the control condition.

Reservation-price estimates. Figure 8 shows the pre- and post-negotiation estimates of reservation prices, as well as significancetests versus the actual reservation prices for each mean. Thereservation-price estimates for both roles and both conditionsshowed the predicted pattern: Preestimates were outside the zone,

and postestimates were inside the zone. All but one (sellers in theincentive condition) of the means for final estimates were signif-icantly inside the actual reservation price.

Dyadic analyses of reservation-price estimates. Figure 9shows how reservation prices shifted from pre- to postnegotiation.As in Studies 1 and 2, we calculated a measure of the degree towhich estimates were inside or outside the zone. The means wereanalyzed in an Incentive (incentive vs. control) � Role (buyer vs.seller) � Time (pre vs. post) MANOVA, with the last two vari-ables being within-dyad measures. All effects involving the incen-tive variable were nonsignificant (Fs � 1), except for an unex-pected Incentive � Role interaction, F(1, 63) � 4.12, p � .047,�2 � .06. On average, reservation-price estimates were moreoutside for sellers in the control condition (M � 1.33) than in theincentive condition (M � .21), whereas the estimates were moreoutside for buyers in the incentive condition (M � .89) than in thecontrol condition (M � �.44). This pattern is most easily inter-preted by observing that reservation-price estimates in Figure 8were higher for both roles in the control condition than in theincentive condition. We do not have an explanation for this pat-tern. We do note that the small-pie bias was more symmetric in theincentive condition—where final inside estimates were of equalmagnitude for buyers and sellers and statistically significant forboth—than in the control condition.

As predicted, there was a significant main effect for time, suchthat initial estimates were outside the zone (M � 2.76) and finalestimates were inside the zone (M � �1.76), F(1, 63) � 115.98,p � .001, �2 � .65. The time variable did not interact significantlywith any other variables, and the pattern of means was similar in

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Figure 8. Average estimates by buyers and sellers of the opposing role’s reservation price in Study 3, byincentive condition. Average prenegotiation and postnegotiation estimates are shown. Asterisks indicate meansthat are significantly different from the correct reservation price ($28 for buyer, $16 for seller). *p � .05. **p �.01. ***p � .001.


both the control (Mpre � 2.95 vs. Mpost � �1.86) and incentiveconditions (Mpre � 2.55 vs. Mpost � �1.66). All means weresignificantly different from 0 by a simple-effects test, p � .05.Only 11% of dyads (7 of 66) exhibited the strong small-pie biasprior to negotiation, whereas 48% (31 of 66) exhibited the biasfollowing the negotiation (Wilcoxon z � 4.54, p � .0001). Theserates did not differ by condition.

Dyadic analysis of imputed share. The bottom panel of Fig-ure 5 plots the imputed shares of buyers and sellers by dyad. ACondition (incentive vs. control) � Role (buyer vs. seller)MANOVA was conducted with role as a within-dyad variable. Theanalysis showed that the mean imputed share of 59% was signif-icantly different from 50%, F(1, 64) � 32.50, p � .001, �2 � .34.There were no significant main effects or interactions (Fs � 1.0).The mean imputed shares for the buyers and sellers were, respec-tively, 59% and 60% in the incentive condition and 55% and 62%in the control condition. All means were significantly differentfrom 50% (ts � 2.70, ps � .05) except for the buyer controlcondition (ns). Seventy-three percent of dyads had imputed sharesthat summed to greater than 100%.

Dyadic analysis of confidence. Change in confidence wasanalyzed with a Condition (incentive vs. control) � Role (buyervs. seller) � Time (pre vs. post) MANOVA, with role and time aswithin-dyad variables. The analysis showed a significant increasein confidence from before to after the negotiation (Mpre � 3.27 vs.Mpost � 4.24), F(1, 64) � 63.10, p � .001, �2 � .50. There wasalso an unexpected but interpretable Condition � Time interaction,F(1, 64) � 8.51, p � .01, �2 � .12. Negotiators in the controlcondition increased in confidence more (Mpre � 3.20 vs. Mpost �4.53) than did negotiators in the incentive condition (Mpre � 3.34vs. Mpost � 3.95). It is interesting that incentives led negotiators toexpress less certainty about their estimates but not to be moreaccurate.

Discussion

The control condition replicated the results of Studies 1 and 2.Even though mean initial estimates of their opponents’ bottomlines were outside the bargaining zone, control-condition partici-pants’ final estimates nevertheless showed a small-pie bias. An

incentive condition was added in which participants were paid forthe accuracy of their estimates. Accuracy incentives, however, didnot alter the magnitude of the small-pie or large-slice biases. Thisresult is particularly noteworthy for two reasons. Paying partici-pants for their reservation-price estimates brought attention to thisquantity and informed less-savvy negotiators about the importanceof accurately estimating their opponents’ bottom lines. Second, theincentive also gave negotiators reason to pursue deliberate learningstrategies that they may not have used otherwise. Neither of thesetwo factors altered the effect we demonstrated in Studies 1 and 2.

General Discussion

Three studies demonstrated the small-pie bias—negotiators typ-ically leave the negotiation table believing that the bargaining zoneis smaller than it actually is. Negotiators’ final estimates of theiropponents’ reservation prices were consistently “inside” the actualreservation price. A consequence of this pattern is the large-slicebias—negotiators typically believe they have captured a largerpercentage of the pie than they actually have. In our studies,negotiators left the negotiation table thinking they had captured56%–72% of the pie on average.

The studies presented here were designed to demonstrate asym-metric disconfirmation processes by systematically inducing initialexpectations that were either inside or outside the true zone. Theresults show that initial inside estimates tended to remain insideduring the course of negotiation. Initial outside estimates, how-ever, were disconfirmed during negotiation. It is noteworthy thatoutside estimates were often driven not just to the true reservationprice but inside it. We believe this pattern is due to the fact thatnegotiators do not adjust sufficiently for the skewed sample ofevidence they receive during the course of the negotiation—that is,they are influenced by their opponents’ extreme offers, modestconcessions, and bluffs about limits.

We have argued that two principal factors produce these biases:asymmetric disconfirmation and motivated reasoning. We de-signed our studies to minimize the role of motivated reasoning tohighlight the dynamics of asymmetric disconfirmation. Studies1–3 provided immediate, accurate feedback on final reservation-price estimates, which we believe sharply constrained self-

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Figure 9. Change in pre- to postnegotiation estimates in Study 3, by dyad and incentive condition. The panelsplot the degree to which estimates for the seller and buyer are inside versus outside the actual reservation price(RP) in percentage terms (amount inside or outside divided by size of the bargaining zone). The left panel depictsprenegotiation estimates, and the right panel depicts postnegotiation estimates. The dotted line indicates that thedyad has, on average, correctly estimated the zone size. Dyads to the southwest of the dotted line underestimatedthe zone size, whereas dyads to the northeast overestimated the zone size.

226 LARRICK AND WU

enhancing estimates. Moreover, Study 3 provided direct incentivesto be accurate, with no effect on the magnitude of the small-piebias.5

The remainder of the General Discussion addresses the impli-cations of these results for social perception and for negotiation.The first section tests a formal model of asymmetric disconfirma-tion. The second section proposes other social inferences thatmight exhibit asymmetric disconfirmation. The final section con-siders implications of the small-pie and large-slice biases fornegotiation, including how they affect relationships and confi-dence.

Tests of Asymmetric Disconfirmation

In this section, we examine our experimental results in terms ofa formal theoretical model of asymmetric disconfirmation. Fig-ure 2 shows the theoretical prediction implied by asymmetricdisconfirmation: Initial inside estimates persist intact, whereasinitial outside estimates are disconfirmed toward the truth. We testthis theoretical prediction formally in two ways. First, we test foran asymmetry in the strength of the relationship between the initialand final estimates conditional on whether initial estimates wereinside or outside the zone. Initial inside estimates are rarely chal-lenged by contradictory evidence and thus tend to stay in place,whereas outside estimates are challenged, effectively must move,and therefore are much more noisily related to initial estimates.Formally, this process implies that final estimates will be stronglycorrelated with initial estimates when initial estimates are insidethe zone but weakly correlated when initial estimates are outsidethe zone. This is represented in the right panel of Figure 2 as aregion in which pre- and postestimates are linearly related (forinside estimates) and a region in which they are unrelated (foroutside estimates).

To test this specific prediction, we ran spline regressions bysplitting the initial estimates into inside and outside estimates andfixing a “knot,” or kink, at the actual reservation price. (A splineregression fits a piecewise linear function to the dependent vari-able, where the function is linear within an interval and continuousat the “knot”; see Marsh & Cormier, 2001.) Separate regressionswere run for buyers and sellers. The initial and final estimates were

normalized by dividing the amount by which the estimate wasinside or outside the zone by the actual zone size. This ratioconverts the measures to a percentage of zone size, making themeasures comparable across studies. The measure was zero if theestimate matched the actual reservation price, negative for aninside estimate, and positive for an outside estimate. For example,in Study 1s large-zone condition, an outside estimate of 40 for thebuyer’s reservation price received a value of (40 � 35)/25 � .20,whereas the value for an inside estimate of 25 was (25 � 35)/25 ��.40. Finally, the regression was fixed so that final estimates wereequal to initial estimates when initial estimates were accurate (i.e.,the intercept was constrained to be zero).

Table 1 shows the results of the regressions for each study andpooled over all studies. The pooled regression provides strongsupport for the asymmetric-disconfirmation hypothesis. For bothbuyers and sellers, final estimates were strongly related to initialinside estimates—indicating that estimates did not move much—but were uncorrelated with initial outside estimates. The splineregressions for the individual studies show the same basic pattern.The pooled spline regressions have adjusted R2s of 52% and 34%,indicating that they fit the data well and considerably better thanregressions that fit a single line, which have adjusted R2s of 27%and 15%, respectively.

As a second formal test of asymmetric disconfirmation, weconsider a very simple model of asymmetric disconfirmation andapply this model to our studies. Let RPb and RPs denote the truereservation prices of the buyer and seller, respectively, and ei and

5 In future research, it would be desirable to reduce the role of self-enhancement in other ways. We have begun preliminary studies taking adifferent tack. Building on the logic of actor–observer research (Jones &Nisbett, 1972; Storms, 1973), we have presented neutral observers withvideotapes of negotiations between study participants and measured theirperceptions of reservation prices. Specifically, observers were yoked to arole and given the same reservation-price expectations as were the partic-ipants themselves. If the small-pie bias is driven by the skewed sample ofevidence that arises during a negotiation, then neutral observers shouldshow the same biases as participants themselves do. Our initial findingsconfirm that observers are as prone to the small-pie bias as are actors.

Table 1Unstandardized Regression Coefficients From Spline Regressions, Regressing Final Reservation-Price Estimate on InitialReservation-Price Estimate

Role makingestimate

Study 1

Study 2 Study 3 PooledLarge Small

Coefficient SE Coefficient SE Coefficient SE Coefficient SE Coefficient SE

BuyerInside .64*** .08 .14 .29 .60*** .12 .42 .42 .55*** .08Outside �.20 .90 �.04 .08 .03 .06 �.32* .13 �.04 .04

SellerInside .68*** .06 .28 .15 .81*** .12 .44* .21 .63*** .06Outside �.02 .12 �.16 .11 �.06 .09 �.14 .09 �.10 .05

Note. Initial reservation-price estimates were divided into inside and outside estimates. The dependent variable in all cases was the final reservation-priceestimate.*p � .05. ***p � .001.


ef denote the negotiator’s initial and final estimates about thereservation price. The following model of the learning processcaptures the asymmetric-disconfirmation process. The seller’s fi-nal estimate is assumed to be the smaller of the buyer’s truereservation price and the seller’s initial estimate, ef � min(RPb, ei),and the buyer’s final estimate is assumed to be the larger of theseller’s true reservation price and the buyer’s initial estimate, ef �max(RPs, ei). According to this model, final estimates are equal toinitial estimates when initial estimates are inside the zone and areequal to the opponent’s actual reservation price when initial esti-mates are outside the zone. For Study 2, for example, the simplemodel generates average final reservation-price estimates of$35.91 and $43.39, very close to the empirical means of $35.62and $42.95. Table 2 shows the close correspondence of the modelwith actual empirical means for each of our studies. Paired t testsshowed no significant difference between final reservation-priceestimates and model predictions for six of the eight tests. Incontrast, final reservation-price estimates were significantly dif-ferent from initial estimates for six of eight tests and from actualreservation prices for seven of eight tests.6

We close by outlining a more general version of the model wejust proposed. It is described formally in the Appendix. Thegeneral model differs from the previous analyses in that it lets thetrue reservation price vary in a population rather than forcing it tobe fixed at a single value. This better captures the cross-section ofexperiences a population of negotiators would have or, alterna-tively, the longitudinal experience an individual would have overmultiple negotiations. The top panel of Figure 10 provides ahypothetical example in which there are a large number of buyersand sellers; there is a uniform distribution of reservation pricesacross buyers (as shown in the top row); and individual sellers, onaverage, have expectations that match the true reservation prices.If buyers and sellers are randomly paired in a market, sellers willhave accurate prenegotiation expectations in some cases (the un-

shaded areas) and inaccurate expectations in other cases (theshaded areas, where estimates are either initially too high or toolow). The simple model of belief revision described above yieldsthe triangular distribution of final perceptions, shown as X’s in thediagram. The result in this case is a systematic underestimation ofreservation prices (see the Appendix for a numerical example).

The triangle pattern in the top panel was deliberately designed toresemble the pattern depicted in Kelley and Stahelski’s (1970)famous “triangle hypothesis,” which posited that people who havecompetitive goals in mixed-motive interactions come to see allopponents as having competitive goals, but people with coopera-tive goals learn the true distribution of opponents’ goals. The basicmechanism they proposed was a behavioral confirmation process:Competitors, by defecting early in an interaction, elicit competi-tion from others, whereas cooperators elicit the full range ofresponses from different opponents. In the bottom panel of Fig-ure 10, we offer an interpretation of Kelley and Stahelski’s (1970)triangle hypothesis as a model of learning in prisoner’s-dilemmagames (PDGs). That is, we interpret it as a model of how expec-tations are updated in the specific environment of a PDG (cf.Diekmann et al., 2003; Miller & Holmes, 1975). The top row is thetrue distribution of tendencies in a population. The left columnconsists of initial expectations, which are depicted as being accu-rate on average. And the triangular pattern of X’s reflects the finalset of beliefs held after interaction.

The triangular patterns in Figure 10 would be expected after oneround of interaction in a population (cross-sectionally), as studiedhere. We speculate, however, that the pattern might also be ob-served after many rounds of interaction for one individual (longi-tudinally). Consider an inexperienced negotiator who has accurateperceptions about the size of the bargaining zone, on average,across a number of negotiations but occasionally errs inside oroutside the true zone. The logic of asymmetric disconfirmationsuggests that inside estimates are likely to persist, whereas outsideestimates are likely to be disconfirmed. Because beliefs are muchmore likely to be revised inward than outward, our negotiator may“learn” from this experience and generate more conservative esti-mates in subsequent negotiations. Indeed, a negotiator with initialestimates that are usually inside the bargaining zone (and hencepersist through behavioral confirmation) will come to believe thathis or her initial estimates are usually accurate. The result is that,in time, negotiators may come to expect all negotiations to bebattles over small pies. (Similarly, participants in PDGs whooccasionally mispredict their opponents’ goals would “learn” overmany interactions with different opponents that they tend to becompetitive.) Belief in a small pie and belief in competitive op-ponents are both “absorbing states” (Feller, 1968). Although spec-ulative, we find this dynamic aspect of the triangle hypothesis for

6 The model fit can also be gauged by calculating the mean absolutedifference (MAD) between the mean final reservation-price estimate and(a) the model prediction (MAD � .90), (b) the mean initial reservation-price estimate (MAD � 3.04), and (c) the actual reservation price (MAD �3.15) for the eight sets of means in the table. The absolute differencebetween mean final-reservation-price estimate and the model prediction issignificantly smaller than the two other differences (MAD � .90 vs. 3.15),t(7) � 2.66, p � .03; (MAD � .90 vs. 3.04), t(7) � 3.07, p � .02, whichwere not significantly different from each other (MAD � 3.15 vs. 3.04),t(7) � .07, p � .94.

Table 2Final Reservation-Price Estimates Tested Against a Model ofAsymmetric Disconfirmation, Initial Reservation-PriceEstimates, and Actual Reservation Price

Reservation price

Study 1

Study 2(n � 91)

Study 3(n � 66)

Small(n � 48)

Large(n � 60)

Estimate of buyer’s RPFinal estimate 22.21a 25.70a 42.95a 26.63a

Model prediction 21.91a 22.77b 43.39a 26.94a

Initial estimate 24.02b 24.19a,b 46.41b 30.58b

Actual 23.00b 35.00c 46.00b 28.00c

Estimate of seller’s RPFinal estimate 17.38a,c 16.53a 35.62a 18.16a

Model prediction 17.53a 17.62a 35.91a 16.45b

Initial estimate 13.72b 17.47a 31.52b 13.26c

Actual 17.00c 10.00b 34.00c 16.00d

Note. The model of asymmetric disconfirmation assumes that finalreservation-price (RP) estimates are equal to initial RP estimates if initialestimates are inside the zone and are equal to the actual RP if initialestimates are outside the zone. Means with different subscripts are signif-icantly different by paired t test at p � .05 when tested within a role andstudy.

228 LARRICK AND WU

individual learning—which was overlooked in the original form—intriguing.

Asymmetric Disconfirmation in Other Social Perceptions

Asymmetric disconfirmation has two essential features. First,judgments that deviate from the truth in one direction encounterdisconfirming evidence and are revised toward the truth. Second,judgments that deviate from the truth in the opposite directionrarely encounter disconfirming evidence and therefore are main-tained. The absence of disconfirming evidence may be due to anumber of factors, including behavioral and perceptual confirma-tion (Jones, 1986), biased samples of evidence (Zuckerman et al.,1995), and the absence of feedback (Einhorn & Hogarth, 1978).We have proposed that the small-pie and large-slice biases indistributive negotiation are products of asymmetric disconfirma-tion. To what extent might other social inferences be subject to thissame pattern of forces? We offer two brief examples.

One example is suggested in Miller’s (1999) work on self-interest. Miller and his colleagues (Miller & Ratner, 1996) haveproposed that there is a strong assumption in American culture thatpeople are self-interested. They have proposed that the belief iswidely held because of cultural injunctions and pluralistic igno-rance. This assumption then tends to be self-fulfilling throughbehavioral confirmation, as perceivers act toward others as if theywere greedy and untrustworthy (analogous to the competitors inKelley & Stahelski, 1970). To these compelling arguments wewould add a mechanism that follows from our analysis. Even if apopulation started with initially accurate beliefs on average aboutthe distribution of self-interest, it could, over many interactions,collectively display a tendency to perceive others as more self-interested than they actually were. The asymmetry in this caseoccurs because overestimates of self-interest are confirmed butunderestimates are disconfirmed. (A similar process might under-

lie the general belief that others are extrinsically motivated; Heath,1999; Markle, 2007.)

A second example is suggested by Einhorn and Hogarth’s(1978) classic analysis of learning from experience. They observedthat for many interpersonal decisions, such as job hiring andstudent admissions, candidates who are predicted to fall belowsome threshold of aptitude will be rejected, and decision makerswill receive little feedback on their actual aptitude. As a result,decision makers will rarely encounter false negatives (i.e., rejectedcandidates who were actually better than the threshold) and willremain confident in their ability to discern aptitude. (Denrell, 2005,recently made similar theoretical arguments to explain ingroupbias.) An overlooked implication of this feedback environment isthat general expectations of talent will become biased downwardwith experience. The bias occurs because some false positives willbe encountered among the accepted candidates, and this feedbackwill disconfirm overly positive predictions of talent; however,overly negative predictions of talent will not encounter discon-firming feedback and will be maintained. The net result is thatpeople will come to perceive others as less talented than they reallyare (once again, even if expectations were initially accurate onaverage).

Implications for Negotiation

The costs of the small-pie/large-slice biases. One implicationof these biases is that negotiators over time may become overcon-fident about their negotiating abilities. If negotiators always thinkthey are claiming 70% of the surplus, they will rarely stop toscrutinize their skills. A second implication is that negotiatorsconcede more of the surplus than they need to. Should they choose,they could press longer in a negotiation to try to claim more value.

A possible recommendation that follows from this research isthat negotiators should strive to err in the direction of outside, not

Buyer’s Actual RPSeller’sExpectation

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Figure 10. A generalized model of asymmetric disconfirmation yields a triangular pattern of learning.Inferences about reservation prices (RP; top panel) and a reinterpretation of Kelley and Stahelski (1970) as amodel of learning in prisoner’s-dilemma games (bottom panel).


inside, reservation-price estimates and make correspondingly am-bitious first offers. The drawbacks of this recommendation are thatextremely ambitious offers will lead to more negotiation impassesand may harm the relationship between the negotiators. However,we believe that this cost is more than outweighed by a number ofbenefits. First, Bottom and Paese (1999) have demonstrated em-pirically that the costs of inside and outside errors are not sym-metric. For a given zone size, negotiators are better off making themistake of an outside error than an inside error, because there is arange of outside errors that increases the amount of surplusclaimed in a fairly linear fashion without increasing the probabilityof impasse by much. Second, the large-slice bias may be robust toextreme offers. That is, the person on the receiving end of aggres-sive negotiation tactics may still walk away from the negotiationthinking he or she claimed 60% of the surplus! This was thepattern that held in the small-zone condition of Study 1. Theimplication is that the small-pie bias may spontaneously salve therelationship wounds caused by aggressive bargaining. An interest-ing future research question is whether knowledge of the small-piebias could help negotiators claim more value in distributive nego-tiations against negotiators who are unaware of the phenomenonand whether this benefit can come with little resulting harm to therelationship.

The benefits of the large-slice bias. Although this article hasemphasized inaccuracy in social perceptions, it should be notedthat inaccuracy is not always costly. For example, it is oftenbeneficial to relationships if partners have optimistic views of eachother (Murray, Holmes, & Griffin, 1996). Similarly, the large-slicebias is likely to be beneficial at a social level. Because the bias willtend to leave both negotiators satisfied with the terms of the deal,it will bode well for upholding the agreement and for the long-termrelationship between the parties (Tenbrunsel, Wade-Benzoni,Moag, & Bazerman, 1998; Valley, Neale, & Mannix, 1995). Thebias may also be functional at an individual level. A large numberof Americans feel apprehensive about negotiating (Small, Gelfand,Babcock, & Gettman, in press), which in part explains the attrac-tiveness of “no-haggle” automobile dealerships like Saturn andCarMax (Firm-price dealers, 1992). One beneficial byproduct ofthe large-slice bias may be an increase in confidence for otherwiseanxious negotiators. Ignorance can be bliss for those less sure oftheir ability (Larrick, 1993). For novice negotiators, the increasedwillingness to negotiate and take risks may lead to better personaloutcomes.

The large-slice bias in the field. One limitation of the currentstudies is that they were conducted only in an experimental setting.To address this, we offer preliminary evidence for the large-slicebias from an everyday negotiation. We asked participants in anexecutive MBA class on negotiation to consider their last carpurchase and their last housing purchase. For each purchase,participants reported the sales price, an estimate of the lowest pricethe seller would have accepted, and the highest price they wouldhave paid. The average imputed share was 63% for cars and 70%for houses, which were both significantly greater than 50%; cars,t(92) � 3.97, p � .0001; houses, t(93) � 6.01, p � .0001. Indeed,80% of the car buyers and 80% of the house buyers gave imputedshares of 50% or more. The large-slice bias appears to be alive andwell in everyday negotiation.

The small-pie bias in multiple-issue negotiation. These studieshave focused on inferences in a distributive price negotiation, but

not all negotiations involve just a single issue. How does thesmall-pie bias generalize to negotiations with multiple issues thatare valued differently by each side? First, we propose a straight-forward extension of the small-pie and large-slice biases tomultiple-issue negotiations: Negotiators may believe that theyhave pushed their counterparts to the limit on each of severalindividual issues. Second, there may be an additional and relatedbias among negotiators who understand the logic of finding mu-tually beneficial (integrative) trades (Raiffa, 1982; Thompson,2001). We have observed in our classes that students who reachagreement in a multiple-issue negotiation often believe that thereare no profitable trades left to be made, even though their agree-ments often leave value on the table. In some respects, this faultyconclusion may arise from the fixed-pie bias, or the failure torecognize differences in priorities (Thompson & Hastie, 1990).However, we think the bias occurs even for well-trained integra-tive bargainers because of processes akin to those underlying thesmall-pie bias. After a great deal of posturing, arguments aboutlimited concessions, and bluffs about priorities, both parties reachthe conclusion that the current deal is the best they can do. In fact,it often feels like it is the only possible deal (especially in multiple-party negotiations). In this case, the expanded pie is perceived tobe both small—because it was hard to find agreement—and fixedat its current size—there are no beneficial trades left to be made.Thus, each negotiator is likely to believe he or she has claimed notjust a large slice of the pie but a large slice of the largest possiblepie. We offer this as speculation and believe it would be aninteresting research direction to pursue.

Conclusion

Negotiators systematically leave the table believing that theyhave pushed the settlement price close to their opponent’s limit,thereby claiming a large slice of a small pie. Although small-pieperceptions in everyday negotiations are undoubtedly fueled byself-enhancement needs, we argued that the feedback environmentwas sufficient for the effect in our studies: Erroneous estimatesoutside the zone were disconfirmed, whereas erroneous estimatesinside the zone were self-fulfilling.

An important implication of asymmetric disconfirmation is thatit can lead to population-level biases, even when initial expecta-tions are accurate on average. We have speculated that other socialinferences might also be asymmetrically disconfirmed. We hopethat the construct of asymmetric disconfirmation contributes to theliterature on self-fulfilling prophecies by showing when socialbeliefs can be subject to systematic bias.

Finally, the issue of learning from feedback has long been animportant topic in psychology (Brehmer, 1980; Bush & Mosteller,1955; Einhorn & Hogarth, 1978; Estes, 1950) but has become ofincreasing importance to research in other fields (Camerer & Ho,1999; Denrell & March, 2001; Hoch & Deighton, 1989; Kagel,1995; March, 1991; Roth & Erev, 1995; Sunder, 1995). We hopethat the concept of asymmetric disconfirmation will be of value infuture research on learning from imperfect feedback.

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Appendix

A Model of Asymmetric Disconfirmation With Examples

We formalize asymmetric disconfirmation in the followingsimple model. Let denote the true state of the world, and ei

and ef denote the initial and final estimates about , respec-tively. In distributive negotiation, is the reservation price ofthe counterpart, ei is the initial estimate about the counterpart’sreservation price, and ef is the estimate about the counterpart’sreservation price at the end of the negotiation. In Kelley andStahelski’s (1970) studies, represents the prisoners’-dilemma-game counterpart’s goals, ei is the initial estimate about thecounterpart’s goals, and ef is the final estimate about the coun-terpart’s goals.

The following model of the learning process captures the es-sential ideas discussed in this article:

ef � min�, ei�

for the seller

and

ef � max�, ei� for the buyer. (A1)

In this model, negotiators learn the actual reservation price,unless their initial estimate is “inside” . To show that this modelimplies the triangle hypothesis, we consider sellers, but the sameanalysis applies to buyers. Suppose that there are n equally likelystates of the world, 1, . . . , n, where i � i � 1. The equal-probability assumption is not essential but is useful for generatingquantitative benchmarks. Equation 1 yields the following proba-bility distribution of final estimates:

Pr�ef�ei� � �0, ef � ei

n � 1 � i

n, ef � ei

1

n, ef � ei

(A2)

If we apply Equation 2 to the entire range of initial estimates,ei � 1, . . . , n, we get the triangle hypothesis, where elements ofthe matrix are:

Pr�ef�ei�

ei

ef

n. . . i

. . . 1

n 1

n

. . . 1

n

. . . 1

n. . . . . . . . . . . . . . . . . .i 0 . . . n � 1 � i

n

. . . 1

n. . . . . . . . . . . . . . . . . .1 0 . . . 0 . . . 1

It is easy to see that the triangle hypothesis results in a small-piebias. Let E( ) denote expected value. Then, if initial estimates areon average accurate, E�ei� � �i i/n, final estimates will bebiased, E�ef� � �i i/n, because E�ef� � �i E�ef� � i�/n,E�ef� � i� � i, for all i � n, and E�ef� � n� � n.

We illustrate the model with a numerical example based onFigure 10. Imagine that a market exists in which there are 25buyers and 25 sellers. The 25 buyers have reservation pricesthat range between $2,500 and $2,900, and there are an equalnumber (5) of buyers at each $100 increment. The averagereservation price for buyers is $2,700. Sellers have a similaruniform distribution of expectations, and thus sellers’ estimatesare imperfect but accurate on average. When buyers and sellersare randomly paired, they create the following joint distributionof dyads, under the simplifying assumption of a uniform jointdistribution:

Sellers’ initialRP estimate

($)

Buyers’ actual RP ($)

Total2,900 2,800 2,700 2,600 2,500

2,900 1 1 1 1 1 52,800 1 1 1 1 1 52,700 1 1 1 1 1 52,600 1 1 1 1 1 52,500 1 1 1 1 1 5

Total 5 5 5 5 5 25.

The matrix below applies the model and shows the count ofsellers with each final reservation-price estimate. Although sellersstarted with an accurate estimate of $2,700 on average, their finalestimate is $2,580, which is the weighted average of 1/25(2,900) � 3/25 (2,800) � 5/25 (2,700) � 7/25 (2,600) � 9/25(2,500), thus exhibiting a small-pie bias.

Sellers’ initialRP estimate

($)

Sellers’ final RP estimate ($)

Total2,900 2,800 2,700 2,600 2,500

2,900 1 1 1 1 1 52,800 0 2 1 1 1 52,700 0 0 3 1 1 52,600 0 0 0 4 1 52,500 0 0 0 0 5 5

Total 1 3 5 7 9 25.

Received June 7, 2004Revision received June 9, 2005

Accepted January 24, 2006 �


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