HFE 742 HFE 742: Understanding and Aiding Human Decision Making Fall 2004 Ray Hill Department of...

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HFE 742: Understanding and Aiding HFE 742: Understanding and Aiding Human Decision MakingHuman Decision Making

Fall 2004Fall 2004

Ray HillRay Hill

Department of Biomedical, Industrial & Department of Biomedical, Industrial & Human Factors EngineeringHuman Factors Engineering

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DECISION ANALYSISDECISION ANALYSIS

•What is the hardest decision you have ever had to What is the hardest decision you have ever had to make?make?

•Have you ever had to make a decision and they Have you ever had to make a decision and they later have to explain or defend that decision?later have to explain or defend that decision?

•Since we all have to make decisions, we are all Since we all have to make decisions, we are all Decision MakersDecision Makers of a sort and can benefit from of a sort and can benefit from the study of decision making.the study of decision making.

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DECISION DOMAINSDECISION DOMAINS

•Personal domainPersonal domain

Where to live; college to attend; car to buy; etcWhere to live; college to attend; car to buy; etc

•Business domainBusiness domain

Introduce the new product; bid on a contract; hireIntroduce the new product; bid on a contract; hire

•Government domainGovernment domain

How to allocate money; where to get involvedHow to allocate money; where to get involved

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DECISION ROLESDECISION ROLES

•Those who study decisions will be referred to as Those who study decisions will be referred to as decision analysts while those that make the decision analysts while those that make the decisions will be referred to as the decision makers.decisions will be referred to as the decision makers.

•Why do you think we would want to separate the Why do you think we would want to separate the roles of the decision analyst and the decision roles of the decision analyst and the decision maker?maker?

•Proper decision making requires collaboration Proper decision making requires collaboration among the decision makers and the decision among the decision makers and the decision analysts in order to find the best solution based on analysts in order to find the best solution based on insights versus positioninsights versus position

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WHY DECISIONS ARE HARDWHY DECISIONS ARE HARD

•Decisions are hard for a number of structural, Decisions are hard for a number of structural, emotional, and organizational reasonsemotional, and organizational reasons

Structural – uncertainty, trade-offs, complexityStructural – uncertainty, trade-offs, complexity

Emotional – anxiety, multiple objectives, Emotional – anxiety, multiple objectives, competitioncompetition

Organizational – lack of consensus, differing Organizational – lack of consensus, differing perspectivesperspectives

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•Do you think your personal decisions are going to Do you think your personal decisions are going to be be easiereasier or or harderharder than the decisions one might than the decisions one might be faced with in business or in government?be faced with in business or in government?

•What might be some of the reasons, both obvious What might be some of the reasons, both obvious and less obvious, for this difference in level of and less obvious, for this difference in level of complexity between decisions from the personal complexity between decisions from the personal domain and decisions from the business or domain and decisions from the business or government domain?government domain?

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•Hebert Simon distinguished between programmed Hebert Simon distinguished between programmed and non-programmed decisions.and non-programmed decisions.

Programmed decisions are more routineProgrammed decisions are more routine

Non-programmed are non-routineNon-programmed are non-routine

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•There are other reasons decisions are hardThere are other reasons decisions are hard

ConsequencesConsequences

UncertaintyUncertainty

AmbiguityAmbiguity

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AmbiguityAmbiguity



CAU Model, SkinnerCAU Model, Skinner

HIGHHIGHMEDIUMMEDIUM

LOWLOW

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AmbiguityAmbiguity



CAU Model, SkinnerCAU Model, Skinner

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WHAT MAKES A GOOD DECISIONWHAT MAKES A GOOD DECISION

•What is a good decision?What is a good decision?

•What is a good outcome?What is a good outcome?

•Does a good decision always lead to a good outcome?Does a good decision always lead to a good outcome?

Name some examples. . .Name some examples. . .

•A good decision emerges as the result of valid decision making process (of which there are a few as we will see)A good decision emerges as the result of valid decision making process (of which there are a few as we will see)

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““When you come to a fork in the road, take it”When you come to a fork in the road, take it”

Yogi BerraYogi Berra

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HISTORYHISTORY

•Operational research, quantitative management, based on repetitive actionsOperational research, quantitative management, based on repetitive actions

Got its start during World War IIGot its start during World War II

•Failed to focus on needs of executive decision makingFailed to focus on needs of executive decision making

In particular their more complex, strategic problemsIn particular their more complex, strategic problems

•Technique needed for logical guidance on complex, uncertain situationsTechnique needed for logical guidance on complex, uncertain situations

•DA combines DA combines systems analysissystems analysis and and statistical decision theorystatistical decision theory

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HISTORYHISTORY•Problems typical of DA application are:Problems typical of DA application are:

UniqueUnique ImportantImportant Contain uncertaintyContain uncertainty Have long-run implicationsHave long-run implications Contain complex preferencesContain complex preferences

•DA arose in the late 60s, early 70s and balances DA arose in the late 60s, early 70s and balances the following OR considerations:the following OR considerations: Mathematical modelingMathematical modeling Computer implementationComputer implementation Quantitative analysis and decision makingQuantitative analysis and decision making

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HISTORYHISTORY

•DA also incorporated the following aspects of DA also incorporated the following aspects of human decision makinghuman decision making

Management experienceManagement experience

Management judgmentManagement judgment

Management preferencesManagement preferences

•The art of DA involves “capturing” the above from The art of DA involves “capturing” the above from the managers and decision makersthe managers and decision makers

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TERMINOLOGYTERMINOLOGY

•DecisionDecision

A conscious irrevocable allocation of resources with A conscious irrevocable allocation of resources with the purpose of achieving a desired objectivethe purpose of achieving a desired objective

•UncertaintyUncertainty

Something that is unknown or not perfectly knownSomething that is unknown or not perfectly known

•OutcomesOutcomes

Depend on alternative chosen and the uncertainties Depend on alternative chosen and the uncertainties impacting itimpacting it

•ValueValue

Something the decision maker wants and can Something the decision maker wants and can tradeofftradeoff

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•ObjectiveObjective

Something specific the decision maker wants to Something specific the decision maker wants to achieveachieve

•Decision MakerDecision Maker

Anyone with the authority to allocate the necessary Anyone with the authority to allocate the necessary resources for the decision being maderesources for the decision being made

•Subjective ProbabilitySubjective Probability

Classical approach to probability called the Classical approach to probability called the “frequentist” approach“frequentist” approach

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•Decision ContextDecision Context

This is the particular decision situation and this This is the particular decision situation and this context determines which objectives must be context determines which objectives must be consideredconsidered

•A Good DecisionA Good Decision

Logically consistent with our state of information Logically consistent with our state of information and incorporates possible alternatives with their and incorporates possible alternatives with their associated probabilities and potential outcomesassociated probabilities and potential outcomes

•Requisite Decision ModelRequisite Decision Model

Includes all objectives that matter and only those Includes all objectives that matter and only those that matter; no new intuitions arrive on modelthat matter; no new intuitions arrive on model

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Some Case Some Case StudiesStudies

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DA PROCESSDA PROCESS

Problem Structure

Deterministic Analysis

Probabilistic Analysis Evaluation

Initial Solution

Ref: Ragsdale, Spreadsheet Modeling andRef: Ragsdale, Spreadsheet Modeling andDecision AnalysisDecision Analysis

Decision

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RATIONAL MODEL PROCESSRATIONAL MODEL PROCESS

9.Evaluate9.Evaluate

0.Agenda0.Agenda 1.Problem1.Problem

8.Monitor8.Monitor

6.Select6.Select 5.Compare5.Compare

4.Forecast4.Forecast

2.Objectives2.Objectives

3.Alternatives3.Alternatives

7.Implement7.Implement

Decision AnalysisDecision Analysis

Ref: Golub, Decision Analysis: Ref: Golub, Decision Analysis: An Integrated ApproachAn Integrated Approach

EvaluationEvaluation

AdministrationAdministration

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HOWARD PROCESSHOWARD PROCESS

Deterministic Phase

Probabilistic Phase

Informational Phase Decision

Prior

Information

Information Gathering

Act

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SMART ModelSMART Model

•Simple Multi-Attribute Rating TechniqueSimple Multi-Attribute Rating Technique

Identify the decision makerIdentify the decision maker

Identify the alternative courses of actionIdentify the alternative courses of action

Identify relevant attributes of the decision problemIdentify relevant attributes of the decision problem

Measure each alternative along each attributeMeasure each alternative along each attribute

Determine a weight for each attributeDetermine a weight for each attribute

Evaluate the weighted score for each alternativeEvaluate the weighted score for each alternative

Make a provisional decisionMake a provisional decision

Perform sensitivity analysisPerform sensitivity analysis

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CLEMEN PROCESSCLEMEN PROCESS

See page 6, Figure 1.1See page 6, Figure 1.1

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Deterministic MethodsDeterministic Methods

•These assume we can neither predict accurately nor These assume we can neither predict accurately nor describe probabilistically the outcome to be encountereddescribe probabilistically the outcome to be encountered

Also referred to as methods for decision making under Also referred to as methods for decision making under “uncertainty”“uncertainty”

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Deterministic ExampleDeterministic Example

•Hartsfield International Airport in Atlanta, Georgia, is one of Hartsfield International Airport in Atlanta, Georgia, is one of the busiest airports in the world.the busiest airports in the world.

Commercial development around the airport prevents it from Commercial development around the airport prevents it from building additional runways to handle the future air traffic building additional runways to handle the future air traffic demands. demands.

Plans are being developed to build another airport outside Plans are being developed to build another airport outside the city limits -- two possible locations for the new airport the city limits -- two possible locations for the new airport have been identified, but a final decision is not expected for have been identified, but a final decision is not expected for another year.another year.

•The Magnolia Inns hotel chain intends to build a new facility The Magnolia Inns hotel chain intends to build a new facility near the new airport once its site is determined.near the new airport once its site is determined.

Land values around the two possible sites for the new airport Land values around the two possible sites for the new airport are increasing as investors speculate that property values are increasing as investors speculate that property values will increase greatly in the vicinity of the new airport.will increase greatly in the vicinity of the new airport.

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1) Buy the parcel of land at location A.1) Buy the parcel of land at location A.

2) Buy the parcel of land at location B.2) Buy the parcel of land at location B.

3) Buy both parcels.3) Buy both parcels.

4) Buy nothing.4) Buy nothing.

The AlternativesThe Alternatives

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1) The new airport is built at location A.1) The new airport is built at location A.

2) The new airport is built at location B.2) The new airport is built at location B.

The OutcomesThe Outcomes

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1

234

5678

9

A B C

Land Purchased Airport is Built at Locationat Location(s) A B

A $13 ($12)B ($8) $11

A&B $5 ($1)None $0 $0

Payoff Matrix

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•If the future state of nature (airport location) were If the future state of nature (airport location) were known, it would be easy to make a decision.known, it would be easy to make a decision.

•Failing this, a variety of non-probabilistic decision Failing this, a variety of non-probabilistic decision rules can be applied to this problem:rules can be applied to this problem: MaximaxMaximax MaximinMaximin Minimax regretMinimax regret LaplaceLaplace HurwiczHurwicz

•No decision rule is always best and each has its No decision rule is always best and each has its own weaknesses.own weaknesses.

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The Maximax Decision RuleThe Maximax Decision Rule

•Identify the maximum payoff for each alternative.Identify the maximum payoff for each alternative.

•Choose the alternative with the largest maximum Choose the alternative with the largest maximum payoff.payoff.

Weakness – Consider the following payoff matrix

State of NatureDecision 1 2 MAX

A 30 -10000 30 <--maximumB 29 29 29

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The Maximax Decision RuleThe Maximax Decision Rule

Land Purchased Airport is Built at Locationat Location(s) A B MAX

A $13 ($12) $13 <--maximumB ($8) $11 $11

A&B $5 ($1) $5None $0 $0 $0

Payoff Matrix &Maximax Decision Rule

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The Maximin Decision RuleThe Maximin Decision Rule

•Identify the minimum payoff for each alternative.Identify the minimum payoff for each alternative.

•Choose the alternative with the largest minimum Choose the alternative with the largest minimum payoffpayoff


State of NatureDecision 1 2 MIN

A 1000 28 28B 29 29 29 <--maximum

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The Maximin Decision RuleThe Maximin Decision Rule

Land Purchased Airport is Built at Locationat Location(s) A B MIN

A $13 ($12) ($12)B ($8) $11 ($8)

A&B $5 ($1) ($1)None $0 $0 $0 <--maximum

Maximin Decision RulePayoff Matrix &Maximin Decision Rule

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Minimax Regret Decision RuleMinimax Regret Decision Rule

•Compute the possible regret for each alternative Compute the possible regret for each alternative under each state of nature.under each state of nature.

RegretRegret: the difference between the maximum : the difference between the maximum payoff possible for a specific outcome and the payoff possible for a specific outcome and the payoff actually obtained when a specific alternative payoff actually obtained when a specific alternative is chosen and that outcome is encounteredis chosen and that outcome is encountered

•Identify the maximum possible regret for each Identify the maximum possible regret for each alternative.alternative.

•Choose the alternative with the smallest Choose the alternative with the smallest maximum regret.maximum regret.

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Minimax Regret Decision RuleMinimax Regret Decision Rule

Land Purchased Airport is Built at Locationat Location(s) A B Max

A $0 $23 $23B $21 $0 $21

A&B $8 $12 $12 <--minimumNone $13 $11 $13

Regret Matrix &Minimax Regret Decision Rule

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Anomalies with Minimax Regret RuleAnomalies with Minimax Regret Rule Consider the following payoff matrix State of Nature

Decision 1 2 A 9 2 B 4 6


A 0 4 4 <--minimumB 5 0 5

The regret matrix is:

Note that we prefer A to B. Now let’s add an alternative...

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Adding an AlternativeAdding an Alternative Consider the following payoff matrix State of Nature

Decision 1 2 A 9 2 B 4 6C 3 9


A 0 7 7B 5 3 5 <--minimumC 6 0 6

The regret matrix is:

Now we prefer B to A?

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Laplace CriterionLaplace Criterion

•Identify the average payoff for each alternative.Identify the average payoff for each alternative.

•Choose the alternative with the largest average Choose the alternative with the largest average payoffpayoff

Implicitly assumes that each outcome is equally Implicitly assumes that each outcome is equally likely.likely.

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LAPLACE CRITERIONLAPLACE CRITERION

Land Purchased Airport is Built at Locationat Location(s) A B EMV

A $13 ($12) $0.5B ($8) $11 $1.5

A&B $5 ($1) $2.0 <--maximumNone $0 $0 $0.0

Probability 0.5 0.5

Payoff Matrix &Laplace Criterion

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Decision Making Under Uncertainty Decision Making Under Uncertainty (cont.)(cont.)

HURWICZ CRITERIONHURWICZ CRITERION

•Best action is the one with the largest weighted Best action is the one with the largest weighted average of its maximum and minimum payoffsaverage of its maximum and minimum payoffs

Requires one to specify an “optimism index” Requires one to specify an “optimism index” as as the weight given to the maximum payoff, where 0 the weight given to the maximum payoff, where 0 1 1

•Often, rather than selecting a value of Often, rather than selecting a value of a priori, a priori, one makes an evaluation by plotting the Hurwicz one makes an evaluation by plotting the Hurwicz scores for each alternative as a function of the scores for each alternative as a function of the optimism index optimism index , and examines regions where a , and examines regions where a given alternative “dominates”given alternative “dominates”

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HURWICZ CRITERION PLOT

($25.0)($20.0)($15.0)($10.0)

($5.0)$0.0$5.0

$10.0$15.0$20.0$25.0$30.0

Optimism Index

Payo

ff

A B

Max $13 $11Min ($8) ($12)Opt Index

0.00 ($8.0) ($12.0)0.05 ($7.0) ($10.9)0.10 ($5.9) ($9.7)0.15 ($4.9) ($8.6)0.20 ($3.8) ($7.4)0.25 ($2.8) ($6.3)0.30 ($1.7) ($5.1)0.35 ($0.7) ($4.0)0.40 $0.4 ($2.8)0.45 $1.5 ($1.7)0.50 $2.5 ($0.5)0.55 $3.6 $0.70.60 $4.6 $1.80.65 $5.7 $3.00.70 $6.7 $4.10.75 $7.8 $5.30.80 $8.8 $6.40.85 $9.9 $7.60.90 $10.9 $8.70.95 $12.0 $9.91.00 $13.0 $11.0

ACTIONS

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Probabilistic MethodsProbabilistic Methods

•These assume the possible outcomes (states These assume the possible outcomes (states of nature) can be assigned probabilities that of nature) can be assigned probabilities that represent their likelihood of occurrence. represent their likelihood of occurrence.

Also referred to as methods for decision Also referred to as methods for decision making under “risk”making under “risk”

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Determining ProbabilitiesDetermining Probabilities•For decision problems that occur more than once, we can For decision problems that occur more than once, we can often estimate these probabilities from historical data. often estimate these probabilities from historical data.

•Other decision problems (such as the Magnolia Inns Other decision problems (such as the Magnolia Inns problem) represent one-time decisions where historical problem) represent one-time decisions where historical data for estimating probabilities don’t exist. data for estimating probabilities don’t exist. In these cases, probabilities are often assigned subjectively In these cases, probabilities are often assigned subjectively based on interviews with one or more domain experts. based on interviews with one or more domain experts.

•Highly structured interviewing techniques exist for Highly structured interviewing techniques exist for soliciting probability estimates that are reasonably soliciting probability estimates that are reasonably accurate and free of the unconscious biases that may accurate and free of the unconscious biases that may impact an expert’s opinions. impact an expert’s opinions.

We will focus on techniques that can be used once We will focus on techniques that can be used once appropriate probability estimates have been obtained.appropriate probability estimates have been obtained.

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Expected Monetary ValueExpected Monetary Value

Selects alternative with the largest expected monetary value (EMV)

EMVi is the average payoff we’d receive if we faced the same decision problem numerous times and always selected alternative i.

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Expected Monetary ValueExpected Monetary Value

Land Purchased Airport is Built at Locationat Location(s) A B EMV

A $13 ($12) ($2.0)B ($8) $11 $3.4 <--maximum

A&B $5 ($1) $1.4None $0 $0 $0.0

Probability 0.4 0.6

Payoff Matrix &EMV Decision Rule

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EMV CautionEMV Caution

•The EMV rule should be used with caution in one-The EMV rule should be used with caution in one-time decision problems. time decision problems.


State of NatureDecision 1 2 EMV

A 15,000 -5,000 5,000 <--maximumB 5,000 4,000 4,500

Probability 0.5 0.5

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Expected Regret or Opportunity LossExpected Regret or Opportunity Loss Selects alternative with the smallest expected regret or

opportunity loss (EOL)

The decision with the largest EMV will also have the smallest EOL.

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Expected Regret or Opportunity LossExpected Regret or Opportunity Loss

Land Purchased Airport is Built at Locationat Location(s) A B EOL

A $0 $23 $13.8B $21 $0 $8.4 <--minimum

A&B $8 $12 $10.4None $13 $11 $11.8

Probability 0.4 0.6

Regret Matrix &EOL Decision Rule

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A Baseball Card ExampleA Baseball Card Example

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DECISION ANALYSISDECISION ANALYSIS

•Baseball Card Game:Baseball Card Game:

At a baseball card show, an exhibitor offers At a baseball card show, an exhibitor offers customers a chance to play a game in which 16 customers a chance to play a game in which 16 baseball cards are laid out on a table in specific baseball cards are laid out on a table in specific positions numbered 3 through 18. The dollar value positions numbered 3 through 18. The dollar value of each card is also displayed, depicted as followsof each card is also displayed, depicted as follows

#3#3

$10$10

#4#4

$5$5

#9#9

25¢25¢

#8#8

50¢50¢

#7#7

50¢50¢

#6#6

$1$1

#5#5

$1$1

#11#11

25¢25¢

#12#12

50¢50¢

#17#17

$10$10

#16#16

$5$5

#15#15

$1$1

#14#14

50¢50¢

#13#13

50¢50¢

#10#10

25¢25¢

#18#18

$100$100

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Baseball Card GameBaseball Card Game

For $1.00, a player can roll 3 dice one time and is For $1.00, a player can roll 3 dice one time and is awarded the card at the position given by the sum awarded the card at the position given by the sum of the 3 dice.of the 3 dice.

•Would you be willing to play this game?Would you be willing to play this game?

•Would you be willing to offer this game if you were Would you be willing to offer this game if you were the exhibitor?the exhibitor?

–What do you need to know or assume to answer What do you need to know or assume to answer these questions?these questions?

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Decision AnalysisDecision Analysis

•A rational method for making decisions which A rational method for making decisions which assumes that the decision-maker can specify:assumes that the decision-maker can specify:

1. A set of m possible 1. A set of m possible actionsactions or or alternativesalternatives that that are available to the decision makerare available to the decision maker

•Denoted ADenoted A11, A, A22, . . ., A, . . ., Amm

2. A set of n possible “states of nature,” 2. A set of n possible “states of nature,” “outcomes,” or possible ““outcomes,” or possible “futuresfutures” that could be ” that could be encounteredencountered

•Denoted FDenoted F11, F, F22, . . ., F, . . ., Fnn

–These constitute the set of possible conditions that These constitute the set of possible conditions that could be encountered and which, generally, are could be encountered and which, generally, are notnot under the decision-maker’s influence or controlunder the decision-maker’s influence or control

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Decision Analysis (continued)Decision Analysis (continued)3. An 3. An evaluation measureevaluation measure that describes the payoff, that describes the payoff, profit or consequences of taking a specific action and profit or consequences of taking a specific action and encountering a specific outcomeencountering a specific outcome

•These are defined for all combinations of actions and These are defined for all combinations of actions and outcomes and are denotedoutcomes and are denoted

EEijij = = value associated with taking action i and value associated with taking action i and experiencing future jexperiencing future j

GOALGOAL: Select the best alternative taking all of the : Select the best alternative taking all of the possible futures into accountpossible futures into account

This depends on:This depends on:

•what the decision-maker defines as “best”what the decision-maker defines as “best”

•what is known about the possible outcomeswhat is known about the possible outcomes

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AssumptionsAssumptions

•The set of futures is The set of futures is mutually exclusivemutually exclusive and and exhaustiveexhaustive

•One of the possible future must occurOne of the possible future must occur

•The occurrence of one future precludes the The occurrence of one future precludes the occurrence of any other future.occurrence of any other future.

•The occurrence of any specific future is not The occurrence of any specific future is not influenced by the alternative selected.influenced by the alternative selected.

•The occurrence of a specific future can not usually The occurrence of a specific future can not usually be predicted with certainty.be predicted with certainty.

How we select a best action, then, usually depends How we select a best action, then, usually depends on what we are willing to assume about the on what we are willing to assume about the occurrence of the possible futures.occurrence of the possible futures.

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Decision Making Under CertaintyDecision Making Under Certainty

•Assumes we Assumes we knowknow, for sure, which outcome will , for sure, which outcome will be encounteredbe encountered

““Best action” is thus the one that optimizes the Best action” is thus the one that optimizes the evaluation measure or payoff for that outcomeevaluation measure or payoff for that outcome

•If larger values of the evaluation measure are If larger values of the evaluation measure are preferred, then the best action is that action i* for preferred, then the best action is that action i* for whichwhich

EEi*i* = max{E = max{E11, E, E22, . . ., E, . . ., Emm}.}.

– If the evaluation measures are not quantifiable If the evaluation measures are not quantifiable (owing to intangible or subjective comparisons), (owing to intangible or subjective comparisons), then one can often find the best alternative by then one can often find the best alternative by systematically comparing alternatives pair-wise systematically comparing alternatives pair-wise using a prioritization matrix approachusing a prioritization matrix approach

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Decision Making Under RiskDecision Making Under Risk

•Assumes we can’t predict precisely which of the Assumes we can’t predict precisely which of the possible outcomes will be encountered but that we possible outcomes will be encountered but that we can specify their probabilities of occurrence. can specify their probabilities of occurrence.

•e.g., if the exhibitor is using “fair” dice in the e.g., if the exhibitor is using “fair” dice in the baseball card game, these should be straightforward baseball card game, these should be straightforward to determineto determine

•We assume we can quantify the relative likelihood We assume we can quantify the relative likelihood that each of the possible futures will occur by that each of the possible futures will occur by specifyingspecifying

PPjj = Probability that future j will occur = Probability that future j will occur

PPjj is often called the “prior probability” of is often called the “prior probability” of experiencing the jexperiencing the jthth outcome or state of nature outcome or state of nature

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Selecting Among Alternatives Under RiskSelecting Among Alternatives Under Risk

•Expected Value CriterionExpected Value Criterion

Best action is the one that optimizes the expected Best action is the one that optimizes the expected value of the evaluation measure given the prior value of the evaluation measure given the prior probabilitiesprobabilities

We compute this expected value for each alternative We compute this expected value for each alternative i = 1, 2, . . ., m viai = 1, 2, . . ., m via

E(V)E(V)ii = E = Ei1i1PP11 + E + Ei2i2PP22 + + + E + EininPPnn

•This is simply the weighted average of the evaluation This is simply the weighted average of the evaluation measures for alternative i and each future j = 1, 2, . . ., measures for alternative i and each future j = 1, 2, . . ., n, weighted by the probability that future j will occur.n, weighted by the probability that future j will occur.

–This is sometimes referred to as “Bayes’ Criterion” and This is sometimes referred to as “Bayes’ Criterion” and the action selected is called the “Bayes’ Action.”the action selected is called the “Bayes’ Action.”

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Example – Baseball Card GameExample – Baseball Card Game

Q: How are “payoffs” Q: How are “payoffs” computed here?computed here?

Q: How are probabilities Q: How are probabilities computed here?computed here?

Q: Would Q: Would youyou be willing to be willing to playplay this game? this game?

Q: Would you be willing to Q: Would you be willing to offer this game (if you were offer this game (if you were the exhibitor)?the exhibitor)?

PAYOFFSActions

Play Game

Do NotPlay

3 0.0046 9.00 0.004 0.0139 4.00 0.005 0.0278 0.00 0.006 0.0463 0.00 0.007 0.0694 -0.50 0.008 0.0972 -0.50 0.009 0.1157 -0.50 0.0010 0.1250 -0.75 0.0011 0.1250 -0.75 0.0012 0.1157 -0.50 0.0013 0.0972 -0.50 0.0014 0.0694 -0.50 0.0015 0.0463 0.00 0.0016 0.0278 4.00 0.0017 0.0139 9.00 0.0018 0.0046 99.00 0.00

ExpectedPayoff: 0.32 0.00

"Future"(Sum of 3

Dice) Pj

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Decision Making Under UncertaintyDecision Making Under Uncertainty•Assumes we can neither predict accurately nor Assumes we can neither predict accurately nor describe probabilistically the future to be describe probabilistically the future to be encounteredencountered

Various criteria can be used to select the best Various criteria can be used to select the best actionaction

MAXIMIN CRITERION: “Criterion of Pessimism”MAXIMIN CRITERION: “Criterion of Pessimism”

Best action is the one that has the largest Best action is the one that has the largest (maximum) minimum payoff.(maximum) minimum payoff.

•Protects against the worst that can happenProtects against the worst that can happen

•Best action provides the best of all the “worst case” Best action provides the best of all the “worst case” scenariosscenarios

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MAXIMAX CRITERION: “Criterion of Optimism”MAXIMAX CRITERION: “Criterion of Optimism”

Best action is the one that has the largest Best action is the one that has the largest (maximum) maximum payoff.(maximum) maximum payoff.

Hopes that the best will happenHopes that the best will happen

LAPLACE CRITERION: “Criterion of ‘Rationality’ ”LAPLACE CRITERION: “Criterion of ‘Rationality’ ”

Best action is the one that has the largest average Best action is the one that has the largest average value or payoff,value or payoff,

•Assumes that each outcome is equally likely.Assumes that each outcome is equally likely.

For a given action I = 1, 2, . . ., m:For a given action I = 1, 2, . . ., m:

Average payoff (value) = [EAverage payoff (value) = [Ei1i1 + E + Ei2i2 + … + E + … + Einin]/n]/n

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Q: Which action should be selected Q: Which action should be selected using the Maximin Criterion?using the Maximin Criterion?

Q: Which action should be selected Q: Which action should be selected using the Maximax Criterion?using the Maximax Criterion?

Q: Which action should be selected Q: Which action should be selected using the Laplace Criterion?using the Laplace Criterion?

PAYOFFSActions

Play Game

Do NotPlay

3 9.00 0.004 4.00 0.005 0.00 0.006 0.00 0.007 -0.50 0.008 -0.50 0.009 -0.50 0.00

10 -0.75 0.0011 -0.75 0.0012 -0.50 0.0013 -0.50 0.0014 -0.50 0.0015 0.00 0.0016 4.00 0.0017 9.00 0.0018 99.00 0.00

Maximum: 99.00 0.00

Minimium: -0.75 0.00

Average: 7.53 0.00

"Future"(Sum of 3

Dice)

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•Best action is the one with the largest weighted Best action is the one with the largest weighted average of its maximum and minimum payoffsaverage of its maximum and minimum payoffs

Requires one to specify an “optimism index” Requires one to specify an “optimism index” as the as the weight, where 0 weight, where 0 1 1

•For a given action i, the “Hurwicz score” isFor a given action i, the “Hurwicz score” is

HHii = = ·Max{E·Max{Ei1i1,E,Ei2i2,. . .,E,. . .,Einin} + (1-} + (1-)·Min {E)·Min {Ei1i1,E,Ei2i2,. . .,E,. . .,Einin} }

Often, rather than selecting a value of Often, rather than selecting a value of a priori, one a priori, one makes an evaluation by plotting each Hmakes an evaluation by plotting each Hii as a function as a function of the optimism index of the optimism index , and examines regions where , and examines regions where a given alternative “dominates”a given alternative “dominates”

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Example – Baseball Card GameExample – Baseball Card GameQ: Which action should be Q: Which action should be selected using the Hurwicz selected using the Hurwicz Criterion?Criterion?

•Obviously depends on our Obviously depends on our choice for an optimism index, choice for an optimism index, as computed & shown at leftas computed & shown at left

•See also chart on next pageSee also chart on next page

Q: What is the “breakeven Q: What is the “breakeven optimism index” for this optimism index” for this situation?situation?

i.e., for what value of i.e., for what value of would would we be indifferent between we be indifferent between playing the game or not?playing the game or not?

ActionsPlay

GameDo Not

PlayMax. Payoff: 99.00 0.00Min. Payoff: -0.75 0.00

Optimism Index0.00 -0.75 0.000.05 4.24 0.000.10 9.23 0.000.15 14.21 0.000.20 19.20 0.000.25 24.19 0.000.30 29.18 0.000.35 34.16 0.000.40 39.15 0.000.45 44.14 0.000.50 49.13 0.000.55 54.11 0.000.60 59.10 0.000.65 64.09 0.000.70 69.08 0.000.75 74.06 0.000.80 79.05 0.000.85 84.04 0.000.90 89.03 0.000.95 94.01 0.001.00 99.00 0.00

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Hurwicz Scores

-10

0

10

20

30

40

50

60

70

80

90

100

0.0 0.2 0.4 0.6 0.8 1.0Optimism Index

Sco

re

Play Game

Do NotPlay

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MINIMAX REGRET CRITERIONMINIMAX REGRET CRITERION

RegretRegret: the difference between the maximum : the difference between the maximum payoff possible for a specific outcome and the payoff possible for a specific outcome and the payoff actually obtained when a specific action is payoff actually obtained when a specific action is taken and that outcome is encountered, i.e.,taken and that outcome is encountered, i.e.,

Regret = RRegret = Rijij = Max{E = Max{E1j1j,E,E2j2j,…,E,…,Emjmj} - E} - Eijij

•Best action is the one with the smallest Best action is the one with the smallest (minimum) maximum regret(minimum) maximum regret

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PAYOFFS REGRETSActions Actions

Play Game

Do NotPlay

Maximum Payoff

Play Game

Do NotPlay

3 9.00 0.00 9.00 0.00 9.004 4.00 0.00 4.00 0.00 4.005 0.00 0.00 0.00 0.00 0.006 0.00 0.00 0.00 0.00 0.007 -0.50 0.00 0.00 0.50 0.008 -0.50 0.00 0.00 0.50 0.009 -0.50 0.00 0.00 0.50 0.00

10 -0.75 0.00 0.00 0.75 0.0011 -0.75 0.00 0.00 0.75 0.0012 -0.50 0.00 0.00 0.50 0.0013 -0.50 0.00 0.00 0.50 0.0014 -0.50 0.00 0.00 0.50 0.0015 0.00 0.00 0.00 0.00 0.0016 4.00 0.00 4.00 0.00 4.0017 9.00 0.00 9.00 0.00 9.0018 99.00 0.00 99.00 0.00 99.00

Maximum: 0.75 99.00

"Future"(Sum of 3

Dice)

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Questions?Questions?

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Other Selection Rules Under RiskOther Selection Rules Under Risk•Most-Probable Future CriterionMost-Probable Future Criterion

Best action is the one that corresponds to the future Best action is the one that corresponds to the future with the largest probability of occurrencewith the largest probability of occurrence

•Disregards all but the most probable futureDisregards all but the most probable future

– Q: What does this suggest for the baseball card game?Q: What does this suggest for the baseball card game?

•Aspiration Level CriterionAspiration Level Criterion

Best action is the one that optimizes the expected Best action is the one that optimizes the expected value of the evaluation measure given the prior value of the evaluation measure given the prior probabilities among those alternatives that guarantee probabilities among those alternatives that guarantee a desired level of “achievement” will be meta desired level of “achievement” will be met

– Q: Which action would be selected if one wanted to be Q: Which action would be selected if one wanted to be sure that no more than 50¢ lost per play of the game?sure that no more than 50¢ lost per play of the game?

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HFE 742 HFE 742: Understanding and Aiding Human Decision Making Fall 2004 Ray Hill Department of...

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Transcript of HFE 742 HFE 742: Understanding and Aiding Human Decision Making Fall 2004 Ray Hill Department of...