ps 171b ucla exam 1

transitive

not a cycle, there is a clear winner

not transitive

there is a cycle and no clear winner

condorcet’s paradox

when majority rule creates a cycle (not transitive) in which there is no clear winner, the agenda setter can get any outcome they want

rationality requires

completeness and transitivity

completeness requires that

its possible to rank any two alternatives in the choice set (prefer or indifferent)

intransitive is

irrational

framing effects

can explain intransitive individual preferences

utility functions can

resolve framing paradoxes

majority rule can

lead to intransitive social preferences even when individuals have transitive preferences

preferences over uncertain choices are induced by

beliefs about likelihoods of given outcomes given each choice

why can’t utility be used socially?

people may incorrectly report their utility level, “willingness to pay” can indicate intensity of preference but may lead to inequality

turn to voting when

we want to avoid interpersonal comparisons of utility in collective choice

backward induction

used in strategic voting, does not remove the power from an agenda setter if they expect it

condorcet winner

an alternative that wins a majority against all other alternatives

weak condorcet winner

does not lose a majority against any other alternative (can tie with another)

axiom a of may’s axioms

anonymity - outcome must be the same if two votes are switched (equal weight)

axiom n of may’s axioms

neutrality - treat both alternatives the same, if everyone voted the opposite way then the decision would be opposite

axiom t of may’s axioms

fragile ties - if there is a profile that produces a tie and we change one abstention to a yes that is sufficient to change the decision to a yes (ties must be easily broken)

may’s theorem

the best way to decide between two alternatives is majority rule

axiom m of may’s axioms

monotonicity - alt to fragile ties, if we start with a tie or a yes and replace an abstention or a nay to a yes then it is a yes

arrow’s impossibility theorem

no method of producing a social preference ordering can be guaranteed to meet basic fairness and practicality requirements, no social choice procedure can satisfy all six axioms

arrow’s axioms several choices

ordering 3 or more alternatives

arrow’s axioms transitivity

if a>b and b>c then a>c

arrow’s axioms unrestricted domain

procedure works for all preference profiles

arrow’s axioms pareto principle

if every individual prefers a to b then society does not prefer b to a

arrow’s axioms independence of irrelevant alternatives (iia)

in deciding between a and b, the preferences between a and c & b and c do not matter, plurality voting violates this bc of spoilers

arrow’s axioms no dictator

there is no single person who’s preference always determines the social ordering no matter the preferences of others

plurality winner

whoever has the highest share of votes in a plurality voting scenario, not always the condorcet winner

spoiler

non-winning candidate who, if they had dropped out of the race, would have changed the plurality winner