Rational foresight

1. 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: • 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

2. i yes no j j no yes yes no k k k k yes no yes yes no no no yes i: j: k: Py Py Py PyPyPn PyPnPy FyFnFn PnPyPy FnFyFn FnFnFy FnFnFn

3. i yes no j j no yes yes no i: j: Py Py Py Pn Pn Py Fn Fy k k k k yes no yes yes no no no yes i: j: k: Py Py Py PyPyPn PyPnPy FyFnFn PnPyPy FnFyFn FnFnFy FnFnFn

4. i yes no j Py j i: Pn no yes yes no i: j: Py Py Py Pn Pn Py Fn Fy k k k k yes no yes yes no no no yes i: j: k: Py Py Py PyPyPn PyPnPy FyFnFn PnPyPy FnFyFn FnFnFy FnFnFn

5. 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.

6. 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.

7. 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.

8. Preference ordering before the Depew killer amendment C.A Vs SQ = 80:20

9. 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.

10. Sequence of voting • 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

11. Preference ordering after the Depew killer amendment

12. 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

13. 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

14. H x y I H H III II y z x z 3 4 History 1 2

16. 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 …

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

18. 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 .

19. School aiders: (yxz) 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

20. 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

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

22. 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)

23. 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)

25. What would have happened if all players had voted non strategically? H x y I H H III II y z x z 3 4 History 1 2

26. Node I (sincere voting)

27. Node III (sincere voting)

28. History 3 (that did not take place) H x y I H H III II y z x z 3 4 History 1 2

29. 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)

30. Node I (strategic voting of R. against aid)

31. Node II (strategic voting of R. against aid)

32. History 2 (the real one) H x y I H H III II y z x z 3 4 History 1 2

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

34. Node I (strategic voting of Powellians)

35. Node III (strategic voting of Powellians)

36. History 3 (in case Powellians had voted strategically) H x y I H H III II y z x z 3 4 History 1 2

37. 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 x y I H H y z III II y z x z 3 4 History 1 2

38. 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

39. 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

40. 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.