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
• PnPass and vote nay
• PyPass and vote yes
• FnFail and vote nay
• FyFail 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
no
yes
yes
yes
no
no
no
yes
Py Py Py
PyPyPn
PyPnPy
FyFnFn
PnPyPy
FnFyFn
FnFnFy
FnFnFn
i j k
3
i
yes
no
j
j
no
yes
yes
no
i j
Py Py
Py Pn
Pn Py
Fn Fy
k
k
k
k
no
yes
yes
yes
no
no
no
yes
Py Py Py
PyPyPn
PyPnPy
FyFnFn
PnPyPy
FnFyFn
FnFnFy
FnFnFn
i j k
4
i
yes
no
j
j
Py
i
Pn
no
yes
yes
no
i j
Py Py
Py Pn
Pn Py
Fn Fy
k
k
k
k
no
yes
yes
yes
no
no
no
yes
Py Py Py
PyPyPn
PyPnPy
FyFnFn
PnPyPy
FnFyFn
FnFnFy
FnFnFn
i j k
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 8020
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
9
Chauncey Depews 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

1. Amendment to the proposal vs Proposal
2. 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
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
12
Depew amend. Vs CA 65 35Depew amend. Vs SQ
6535 (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
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
15
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment nay 67 130 197
totals 199 227 426
16
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment 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
17
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment 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
18
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment 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 .
19
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment nay 67 130 197
totals 199 227 426
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
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment nay 67 130 197
totals 199 227 426
21
Southerners (yzx) All southerners repr. (105
democrats and 11 republicans) and some
Northerners (2 Democrats and 12 Repubblicans)
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment nay 67 130 197
totals 199 227 426
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)
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment nay 67 130 197
totals 199 227 426
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)
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 97 229
Voting Powell Amendment nay 67 130 197
totals 199 227 426
24
Voting Final passage Voting Final passage Voting Final passage Voting Final passage
Voting Powell Amendment yea nay Totals
Voting Powell Amendment yea 132 Powellians 78D. 54 R. xyz 97R.against aid 49 R. zxy 48 R. zxy 229
Voting Powell Amendment nay 67 S. Aiders 42D. 25R. yxz 130 Southerners 107D. 23R. yzx 197
totals 199 227 426
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)
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
27
Node III (sincere voting)
y z
Powellians, xyz 132
School aiders, yxz 67
Southerners, yzx 130
Republican against aid, zxy
Republican against aid, zyx 97
totals 329 97
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 billat 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)
x y
Powellians, xyz 132
School aiders, yxz 67
Southerners, yzx 130
Republican against aid, zxy
Republican against aid, zyx 97
totals 229 197
31
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
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)
R. Holding zyx Vote non strat. R. Holding zyx Vote non strat. R. Holding zyx Vote strat. R. Holding zyx Vote 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
35
Node III (strategic voting of Powellians)
y z
Powellians, xyz 132
School aiders, yxz 67
Southerners, yzx 130
Republican against aid, zxy
Republican against aid, zyx 97
totals 329 97
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.