Part 2: Individual To Social Preferences Flashcards
(34 cards)
Political institutions are not neutral. If they were neutral, what would be the effect on economic policy
No effect
2 key challenges of turning individual preferences into social preferences
Aggregation problem
Agency problem
Aggregation problem
Whether majority preference be applied
Agency problem
Information problem - does political process (voting) ensure majority preference will be achieved
Stable match
When no unmatched partner each prefers the other to their partner (not mutually profitable to break away)
E.g a married couple, NEITHER wants to join up with someone from another pair to make them mutally better off.
Stable roommate problem with 4 agents
Pick from other 3 in order.
Look at table pg 16:
A) is a room with Henry and Mary, and a second room with Peter and Jack stable?
B) a room with M+P, and room with J+H
C) room with M+J and room with P+H
Not stable, as Mary would prefer to be with Peter, as well as Peter prefer to be with Mary than Jack. Thus Mary and Peter are the blocking pair (mutually profitable: thus unstable)
B)
Not stable as Henry would prefer to be with Peter than Jack, and Peter would rather be with henry than Mary.
Thus Henry and Peter are blocking pair, deviation is mutually profitable: thus unstable!
C) stable as even though not all got first choices, no mutually profitable deviation
Arrow’s impossibility theorem
No mechanism is able to aggregate consistently i.e satisfy all 5 properties , thus political institutions cannot be neutral
Hence why called impossibility theorem
So no system that aggregates individual preferences consistently and satisfies 5 properties
What are the 5 properties for social welfare function
Unrestricted domain
Rationality
Unanimity
Independence of irrelevant alternatives (IIA)
Non-dictatorship
3 policy options Ω = [A, B, C]
Each individuals has preferences which are complete and transitive and strict: Meaning.
Completeness: either A>B or B>A
Transitivity: if A>B and B>C, A>C
Strict: no indifference
What is the mapping of individual prerences into social preference called
Social welfare function (SWF)
So explain the first 4 properties SWF needs to satisfy
Unrestricted domain (universality) - consider all preferences
Rationality (complete and transitive) (agenda-setting voting method violates!)
Unanimity i.e if everyone agrees A>B policy, SWF preference should prefer A>B
Independence of irrelevant alternatives: if we are trying to figure out whether society prefers A to B, what people think of C shouldn’t matter (irrelevant - just concentrate on issue at stake) (Borda count can violate this!)
Sad result Arrow’s impossibility theorem of SWF satisfying all 4 properties:
If satisfies all 4, it must be a dictatorship (i.e the SWF only accounts for the same certain individual’s preferences, ignoring anyone elses’)
So to avoid dictatorship, we can ignore other of the 4 properties
a) if we violate unrestricted domain what does this mean
b) example of violating rationality
c) when can unanimity be violated
d) example of violating IIA
violating unrestricted domain means ignoring some individuals preferences
b) condorcet paradox in pair-wise majority voting - completeness and transitivity violated, hence why have to solve other ways to break tie e.g voting agenda , which reduces legitimacy of outcome!
c) if fixed social preferences (regardless of individiual preferences)
d) borda count
Which one is the strongest property
IIA , since assuming IIA mean we ignores cardinal aspect of preferences, only ordinal pair-wise.
E.g if 100 policy options, and A and B ranked 45 and 47, you near indifferent between them.
However if ranked 1 and 100, you probably like A a lot more. IIA treats the 2 cases as the same
So this stuff looked at aggregation problem.
Now look at voting rules. What is a condorcet winner
Policy that beats any other feasible policy in a pair-wise vote
Condorcet paradox:
Some voting rules can fail to produce a clear cut winner
Condorcet paradox ice cream example pg37
pg 38 ice cream example of concordet winner
no clear winner in a pairwise
3 citizens with the following preferences:
A>B>C;
B >C>A;
C>A>B
Cycling outcome - there is no social transitivity!
A vs B: A wins
B vs C: B wins
C vs A: C wins
concorcet paradox! no clear winnerh
When there is a cycling outcome i.e no transivity;
What do agents have an incentive to do
agents may not truthfully reveal their preference since a cycle, so vote strategically to get next best
So we have chocolate vanilla or strawberry. How many strong preferences (no indifferences) ordering possibilities are there
b) as a result, how many possible socieites
6
b) 6 x 6 x 6 = 216 possible societies (since 3 agents)
when would the cyclical outcome (condorcet paradox) occur
If one of the alternatives is ranked once first by one voter, 2nd by another voter, and 3rd by the last voter
(like 3 citizens with the following preferences:
A>B>C;
B >C>A;
C>A>B)
given 6 strong preference orderings, and 216 possible societies, how many times will lead to a cycle?
b) what can we conclude; what is the probability of a condorcet cycle (not finding a winner)
12
b) 12/216 societies we get a cycle! so condorcet voting (pairwise comparisons) mostly works to find a clear winner!
probability of not finding a winner is 12/216 x 100 = 5.56%
(we see how this probability changes with the number of alternatives and voters!)
What does probability of finding a condorcet cycle (no clear winner) changes with (2)
And state the relationship with them
Number of alternatives (policy options - only had 3 in example) POSITIVE REL
Number of voters - POSITIVE REL
