Definitions 1-4 Flashcards
3 preference relations of consumers?
1) Complete (ie. x must be weakly preferred to y or other way round, must be able to weakly rank all options ITO preference)
2) Reflexive (ie. x is weakly preferred to x (is at least as good as itself))
3) Transitive (if a is preferred to b and b to c then a is preferred to c)
What is convexity of a set?
A convex set is a set of points such that, given any two points A and B within the set, the line which joins them lies entirely within the set.
What is the Samuelson rule?
Samuelson rule states that for socially efficient provision of public goods, MRS1+MRS2+…+MRSn=MRT
What happens when there is competitive eq in public and private goods situ?
CE will not, in general, be PE since MRS are unlikely to add to 1
See
groves clarke mechanism L7 p3
Explain the 4 axioms of voting rules?
1) Universal domain (all possible preference selections are allowed)
2) Anonymity (the identity of each voter is irrelevant to the outcome of the vote)
3) Neutrality (if the ranking of 2 alternatives is reversed for all voters, then the social ranking is reversed)
4) Positive responsiveness (For a preferences profile, if some voters change their votes in favour of one alternative, and the rest do not change their vote, then the social ranking does not reverse in the other direction)
What is May’s Theorem?
An aggregation rule satisfies the 4 axioms U, A, N and PR if and only if it is the majority (plurality) rule
What is the majority rule?
Voters vote for their most favoured outcome and the one that gets the most votes wins
2 advantages of Majority rule?
satisfies May’s theorem
easy to use
2 advantages of Majority rule?
1) not very democratic; ignores lots of information
2) Lots of wasted votes (UK 2005 election, 52% votes were for losing candidates)
3) open to manipulation
(also only considers SPPs)
(see notes L8 p1s2)
Explain what plurality with run-off is? Pro of it?
If no candidate gets an absolute majority (ie. above 50%) in first stage, then all but top 2Cs are eliminated; there is then comparison between them again to decide the winner
Minimises the problem of wasted votes
3 problems with plurality with run-off?
1) open to manipulation still
2) is not monotonic (ie. one may win sub elections and lose grand elections)
3) See point one in notes
What is sequential run off?
Sequential voting rounds, each time eliminating the lowest voted outcome IF there is no abs. majority formed; if no majority is formed each round it continues until last round 1v1 and there will be an abs majority
2 advantages of sequential run-off?
Less manipulable (not immune to it tho) can encourage voters to vote for marginal (ie. unpopular) Cs
2 problems with SRF?
not monotonic
‘spoiler’ effect (if several close political candidates, vote-splitting may occur -> overall winner actually being a big distance from others!)
What is the Condorcet paradox?
Collective preferences can be irrational even when individual preferences are rational
