Rational foresight

Rational foresight• Three people legislature (i, j, k). Each member would like a pay rise

but realizes that constituents will not pleased with a representative voting to increase his or her own salary.

• The best of all possible worlds for legislator i (a or b or c) is for the other two legislators to vote yes, making the pay rise to pass, and voting nay to keep his/her good reputation in front of the costituents.

• The preference ordering on the outcomes are the same for all legislators:

1. Pn=Pass and vote nay2. Py=Pass and vote yes3. Fn=Fail and vote nay4. Fy=Fail and vote yes

Each legislator must make a public declaration on the motion to raise pay. They are called following alphabetical order:

1°: i2°: j 3°: k

yes no

yes

yes

no

no yes

yes

no no

no

yesyesno

i

j j

k k k k

PyPyPy

PyPyPn

PyPnPy

FyFnFn

PnPyPy

FnFyFn

FnFnFy

FnFnFn

i:j:k:

yes no

yes

yes

no

no yes

yes

no no

no

yesyesno

i

j j

k k k k

PyPyPy

PyPyPn

PyPnPy

FyFnFn

PnPyPy

FnFyFn

FnFnFy

FnFnFn

i:j:k:

i:j:

PyPy

PyPn

PnPy

FnFy

yes no

yes

yes

no

no yes

yes

no no

no

yesyesno

i

j j

k k k k

PyPyPy

PyPyPn

PyPnPy

FyFnFn

PnPyPy

FnFyFn

FnFnFy

FnFnFn

i:j:k:

i:j:

PyPy

PyPn

PnPy

FnFy

i: Py Pn

Strategic or sophisticated behaviour

• An individual does not merely asses options in front of her nose , choosing the one that seems best in terms of her (his) preferences

• He (She) knows that the choice before him (her) is one of a sequence of choices in an on going process

• Strategic behaviour may require individuals to make seemingly less-than-ideal choices at some points in order to secure superior outcomes at the end of the trail.

Gibbard-Satterthwaite Theorem• Def. Sophisticated individual: someone who may

misrepresent her true preferences, namely manipulate F, the social choice procedure.

• Theorem: assume a group G of at least 3 individuals and a set A of at least 3 alternatives. Also assume that any member of G may have, as his or her true preferences, any preference ordering over A (universal domain). Then every non dictatorial social choice procedure, F, is manipulable for some distribution of preferences.

Chauncey Depew and the seventeenth amendment

•C.D. simply by offering a cleverly formed amendment delayed for 10 years the adoption of the 17° Amendment of U.S. Constitution about the direct election of senators•Proposed Constitutional Amendment from the House:” The Senate of the United States shall be composed of two Senators from each state, elected by the people thereof, for six years; each Senator shall have one vote. The electors in each state shall have the qualifications requisite for electors of the most numerous branch of the state legislature”. 2/3 of Senators are required to emend the U.S. constitution•Almost all Democrats were in favour of the Const.Amend. ; Northeastern senators (mostly Repubblican) were against.

Preference ordering before the Depew killer amendment

Preference ordering

Northern Dem.(25)

Southern Dem.(35)

Northeastern Rep.(20)

Midwestern and Western Rep.(20)

1° Constitutional Amendment (C.A.)

C.A. Status quo C.A.

2° Status Quo

Status Quo

C.A. Status Quo

C.A Vs SQ = 80:20

Chauncey Depew’s killer amendment

•Proposed amendment to the Constitutional Amendment from the House:” The Senate of the United States shall be composed of two Senators from each state, elected by the people thereof, for six years; each Senator shall have one vote. The electors in each state shall have the qualifications requisite for electors of the most numerous branch of the state legislature. (and) the qualifications of citizens entitled to vote for U.S. Senators and Representatives in Congress shall be uniform in all states, and Congress shall have the power to enforce this article by appropriate legislation and to provide for the registration of citizens entitled to vote, the conduct of such elections, and the certification of the result. ”.•In effect Depew proposed to come back to the strict federal control of elections in southern states (even by the Army) as just after the civil war, during the so called Reconstruction Era.

Sequence of voting

1. Amendment to the proposal vs Proposal2. Proposal vs Status quo

Senate

Depew

propose amend.

Not propose amend.

Status Quo

yes

No (originalConst.proposal

Senateyes

no

Senate yes

no

Depew amendment

Status Quo

originalConst.proposal

Status Quo

Preference ordering after the Depew killer amendment

Preference ordering

Northern Dem. (25)

Southern Dem. (35)



1° Depew amendment

C.A. Depew amendment

Depew amendment


Status Quo Status quo C.A.

3° Status Quo Depew amendment

C.A. Status Quo

Depew amend. Vs CA = 65: 35Depew amend. Vs SQ= 65:35 (not enough..not 2/3)

CA Vs. SQ = 80 : 20 ( more than 2/3); There is a cycle

Preference ordering

Northern Dem. (25)

Southern Dem. (35)



1° Depew amendment

C.A. Depew amendment

Depew amendment


Status Quo Status quo C.A.

3° Status Quo Depew amendment

C.A. Status Quo

Powell amendment story (1956)• Democratic leadership sponsored a bill that

authorized the distribution of federal funds to the states for the purpose of building schools (alternative y)

• Powell, black representative from Harlem, proposed as amendment that “grants could be given only to states with school open to all children without regard to race in conformity with the requirements of U.S. Supreme court decisions. (alternative x)

• Status quo= z

x y

x zy z

H

H H

History 1 2 3 4

I

II III

Voting Final passage

Voting Powell Amendment

yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426



yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426

Who voted YY (as in the final passage no strategic voting is possibile) can have the following preference ordering : xyz , xzy , yxz. However if they voted non strategically the could not have yxz. As they do not like z also if they vote strategically yxz does not make any sense . xzy is higly unlikely for the Democrats as it means that they would have wanted school aid only with Powell amendment.YY voters has xyz preference ordering …



yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426

Powellians (xyz)

Political group (60% D. 40% R.)Northern urban, big cities from midwest and north Atlantic



yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426

Who voted NY can have as the Powellians the following preference ordering : xyz , xzy , yxz. However we can eliminate the preference ordering of Powellians ( xyz). xzy is higly unlikely for the Democrats as it means that they would have wanted school aid only with Powell amendment.NY voters has yxz preference ordering if they voted sincerly .



yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426

School aiders: (yxz)

19% Democrats who followed the party leadershipSome Republicans (24) from states like Maine, Colorado etc.who preffered school aid to a gesture for blacks



yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426

Those who voted NN could have the following preference orderings: zxy, zyx, yzx ; zxy is not possible if they vote sincerely. Conceivably the could have zxy and vote strategically. However it does not make any sense as they would have increased the chances of y against z in the final passage;NN voters can have zyx or yzx ; however if they held zyx the most convenient behaviour should have been voting strategically YN



yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426

Southerners (yzx):All southerners repr. (105 democrats and 11 republicans) and some Northerners (2 Democrats and 12 Repubblicans)



yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426

YN voters may have been either of the remaining unassigned : zxy or zyx ; The could have voted sincerely (and having zxy) or strategically (and having zyx)



yea nay Totals

yea 132 97 229

nay 67 130 197

totals 199 227 426

Two political groups: 1) YN (zxy) Repubblicans against aid but symbolically pro black (49)2) YN (zyx) Repubblicans against aid and indifferent to black issues.(48)



yea nay Totals

yea 132 Powellians78D. 54 R.

xyz

97R.against aid49 R. zxy48 R. zxy

229

nay 67 S. Aiders42D. 25R.

yxz

130 Southerners107D. 23R.

yzx

197

totals 199 227 426

What would have happened if all players had voted non strategically?

x y

x zy z

H

H H

History 1 2 3 4

I

II III

Node I (sincere voting)x y

Powellians, xyz 132

School aiders, yxz 67

Southerners, yzx 130

Republican against aid, zxy

49

Republican against aid, zyx

48

totals 181 245

Node III (sincere voting)y z

Powellians, xyz 132



Republican against aid, zxyRepublican against aid, zyx

97

totals 329 97

History 3 (that did not take place)

x y

x zy z

H

H H

History 1 2 3 4

I

II III

• If the Repubblicans with zyx preference had voted strategically in order to defeat the bill…at node I instead of voting y they could misrepresent their preferences and vote for x (just to increase the chances to defeat x in the following step)

Node I (strategic voting of R. against aid)x y

Powellians, xyz 132




97

totals 229 197

Node II (strategic voting of R. against aid)

x z

Powellians, xyz 132


Southerners, yzx


130


97

totals 199 227

History 2 (the real one)

x y

x zy z

H

H H

History 1 2 3 4

I

II III

Puzzle

• Why did the Powellians not vote strategically as if they preferred yxz instead of xyz ?

Node I (strategic voting of Powellians)R. Holding zyxVote non strat.

R. Holding zyxVote strat.

X y x y

Powellians, xyz 132 132

School aiders, yxz 67 67

Southerners, yzx 130 130


49 49


48 48

totals 49 377 97 329

Node III (strategic voting of Powellians)

y z

Powellians, xyz 132




97

totals 329 97

History 3 (in case Powellians had voted strategically)

x y

x zy z

H

H H

History 1 2 3 4

I

II III

Choosing x or y in the node I means that at the node II the strategic equivalent is z or at the node III the strategic equivalent

is y. Therefore the choice is in fact between z and y since the very beginning

x y

x zy z

H

H H

History 1 2 3 4

I

II IIIz y

Puzzle..again why did the Powellians not vote strategically as if they preferred yxz

instead of xyz ? • Problem: to explain why one set of politicians

rationally voted strategically and another set rationally voted non strategically

• 2 ways to earn credit with and future votes from people in their constituencies:

1. By producing legislative outcomes2. By taking positions supported by some

constituents• Powellians decided to take position• Rep. against aid decided to produce the best

(for them) legislative outcome

Costs of the different way can be captured by the different preference ordering (in terms

of outcome utility) of the 2 groups • R. with zyx in order to obtain their best (z) must vote

their worst• Powellians with xyz in order to obtain at most y (the

second best) had to vote against the best alternative x• Republicans were able to vote strategically at low

price; Powellians would have to pay a high price. Powell in fact obtained what he wanted: to humiliate the Democratic leadership. He was and heresteticianWhen we consider the utility outcome we always we should add the utility and the cost in terms of “image” of the behaviour that makes possible a certain outcome

Lincoln at Freeport or the best example of an heresthetical device (in the large)

• For a person who expects to lose on some decision, the fundamental heresthetical device is to divide the majority with a new alternative (preferred to the previous winning alternative). If successful, this maneuver produces a new majority coalition, composed of the old minority and a portion of the old majority that likes the new alternative better.

• Practically the heresthetician redefine the situation choice.

The Lincoln’s trap

• 2 elections (a, b) , 2 competitors (Douglas and Lincoln) :

• a) candidates for Illinois legislatures who on their turn were pledged to vote for Lincoln or Douglas for the U.S. Senate

• b) two years later presidential elections.• For both competitors ( L. and D.) a>b

The Lincoln’s trap• Main political actors 1) Democratic party that was divided between Northern D. who were weakly against slavery and Southern D. who strongly defended it.2) Republican party.Douglas was a Northern D who tried unsuccesully ( because a supreme Court’s sentence) to push back in the localities the issue of the slavery. In order to become senator in Illinois he had to win the support of Northern D. However he had also to please Southern D to win two years later the presidential nomination for the Democratic Party.

The Lincoln’s trap• Lincoln’s question during electoral debates for Illinois

legislatures:«Can the people of a United States Territory, in any lawful way,against the wish of any citizen of U.S., exclude slavery from its limits prior to the formation of a state constitution ?»If Douglas answered yes he could become senator as Illinois Democrats agree but he would have lost the support of S.Democrats for the presidential nominationIf Douglas answered no he would hurt his chances in Illinois …

The Lincoln’s trap• He answered yes and was reelected to the Senate.

However in the nominating convention in 1860 he was nominated only after Southerns withdrew in order to nominate a third candidate for themselves.

• Lincoln won the Republican nomination and was elected president by a plurality.

Rational foresight

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