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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. - PowerPoint PPT Presentation
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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)
Northeastern Rep.(20)
Midwestern and Western Rep.(20)
1° Depew amendment
C.A. Depew amendment
Depew amendment
2° Constitutional Amendment (C.A.)
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)
Northeastern Rep.(20)
Midwestern and Western Rep.(20)
1° Depew amendment
C.A. Depew amendment
Depew amendment
2° Constitutional Amendment (C.A.)
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
Voting Final passage
Voting Powell Amendment
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 …
Voting Final passage
Voting Powell Amendment
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
Voting Final passage
Voting Powell Amendment
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 .
Voting Final passage
Voting Powell Amendment
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
Voting Final passage
Voting Powell Amendment
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
Voting Final passage
Voting Powell Amendment
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)
Voting Final passage
Voting Powell Amendment
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)
Voting Final passage
Voting Powell Amendment
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)
Voting Final passage
Voting Powell Amendment
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
School aiders, yxz 67
Southerners, yzx 130
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
School aiders, yxz 67
Southerners, yzx 130
Republican against aid, zxyRepublican against aid, zyx
97
totals 229 197
Node II (strategic voting of R. against aid)
x z
Powellians, xyz 132
School aiders, yxz 67
Southerners, yzx
Republican against aid, zxy
130
Republican against aid, zyx
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
Republican against aid, zxy
49 49
Republican against aid, zyx
48 48
totals 49 377 97 329
Node III (strategic voting of Powellians)
y z
Powellians, xyz 132
School aiders, yxz 67
Southerners, yzx 130
Republican against aid, zxyRepublican against aid, zyx
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.