L17 Flashcards
Define social choice theory?
Study of systems and institutions for making collective choices, choices that affect a group of people. Often needed because need a solution that holds for everyone for practicality
Define preference aggregation?
Combining the preferences of the citizenry to obtain a social preference ordering
What is the common rule for preference aggregation?
Majority Rule:
ie. x is ranked above y only if the majority of individuals rank x above y
What is a problem with the majority rule?
Can lead to a preference circle (condorcet/voting paradox). See example)
What is a social welfare function? (SWF)
Preference aggregation mechanisms that map a profile of preference orders to a single, collective preference order
What is condition U?
Unrestricted domain condition:
the requirement that the SWF produces a social ordering for every preference profile
What is condition D?
A SWF must not be dictatorial
A SWF IS dictatorial if SWF always assumes preference order of the same one citizen
What is the Pareto condition?
Requirement that if whenever all citizens rank x above y, so does society
What is the IIA condition?
Independence of irrelevant alternatives condition:
A SWF satisfies the IIA condition if the relative social ranking of 2 alternatives only depends on their relative individual rankings
What is arrows impossibility theorem?
A theorem that shows that it is impossible for a SWF to satisfy all 4 conditions (U, D, Pareto and IIA)
What was arrows opinion on the conditions?
That Pareto and IIA conditions are basic democratic principles any SWF should follow
What is the idea behind May’s Theorem?
May showed that by dropping condition U but tightening the other 3 conditions we can arrive at a set of conditions satisfied by the majority rule alone
What is May’s Theorem?
It states that simple majority voting is the only anonymous, neutral and positively responsive SWF between 2 alternatives, when there are an odd number of votes and indecision (ties) is not allowed
TF FORMALLY:
A group decision function with an odd number of votes meets conditions A, N and PR iff it is a simple majority rule
Formally, the majority decision rule is the only binary decision rule that has the following 3 properties…?
1) Anonymity (A)
SWF produces same result for a group regardless of which citizen is giving which vote
2) Neutrality (N)
x and y must occupy the same relative social ordering in group 1 as z and w do in group 2 (see her notes)
3) Positive responsiveness (PR)
if society regards x at least as good as y in G1, and in G2 the society has the same rankings EXCEPT some citizens have moved up x in the ranking, then G2 must prefer x to y as a society
