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# Rational foresight - PowerPoint PPT Presentation

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.

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• 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:

• Pn=Pass and vote nay

• Py=Pass and vote yes

• Fn=Fail and vote nay

• 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°: i

2°: j

3°: k

yes

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Py

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PyPyPn

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PnPyPy

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FnFnFy

FnFnFn

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PyPyPn

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FyFnFn

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FnFnFn

yes

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• 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.

• 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.

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.

• Amendment to the proposal vs Proposal

• Proposal vs Status quo

Depew amendment

yes

Senate

yes

Senate

Status Quo

no

propose amend.

original

Const.proposal

Senate

yes

No (original

Const.proposal

Depew

Not

propose amend.

Status Quo

no

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

• 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

I

H

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History

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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 …

Powellians (xyz) 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 .

Political group (60% D. 40% R.)

Northern urban, big cities from midwest and north Atlantic

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 .

School aiders: (yxz) 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.

19% Democrats who followed the party leadership

Some Republicans (24) from states like Maine, Colorado etc.who preffered school aid to a gesture for blacks

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

Southerners (yzx): 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;

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

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)

Two political groups: zxy or zyx ; The could have voted sincerely (and having zxy) or strategically (and having zyx)

1) YN (zxy) Repubblicans against aid but symbolically pro black (49)

2) YN (zyx) Repubblicans against aid and indifferent to black issues.(48)

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

H

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y

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Node I (sincere voting) strategically?

History 3 (that did not take place) strategically?

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• 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) 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 II (strategic voting of R. against aid) 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)

History 2 (the real one) 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)

H

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y

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History

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Puzzle 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)

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

Node I (strategic voting of Powellians) 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 III (strategic voting of Powellians) 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)

History 3 (in case Powellians had voted strategically 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))

H

x

y

I

H

H

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History

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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

H

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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:

• By producing legislative outcomes

• 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 herestetician

When 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.