w11 social choice theory Flashcards
social choice theory
what are voting rules used for
they are used to find the best ranking given a set of individual rankings according to a measure,
theres a lot of voting rules so you need to figure otu which one is best for your situation
what do we look for in a fair vote
treat all voters equally
neutrality, no bias in wording
monotonicity, a winning candidate cannot lose by gaining votes and vise versa
what is majority voting
every one votes for their best candidate
candidates are ranked via number of votes they recieve and ties are broken randomly or pre defined way
what are the advantages of majority rule
voter equality, candidate equality, monotone
what is mays theorem
Among all possible two-candidate voting systems that never result in a tie, majority rule is the only one that is anonymous, neutral, and monotone.
what is condorcet method
a candidtate is a winner if they defeat every other candidate in a one on one contest via majority rule
what is the condorcet voting paradox
with three or more candidates there are elections where the condorcet method has no winners
what is condorcet consistency
a desierable property, where if a condorcet winner exists (not always garunteed) it should be selected top in the aggregate ranking
voting rules that follow this property are called condorcet methods and are condorcet consistent
why is voting manulation bad
elections will not refelct the true will of societiy
Aggregation rules are designed with certain social welfare criteria in mind.
Misrepresentation of preferences results in a suboptimal choice w.r.t. these criteria.
what is the borda count voting system
scores are assigned to each candidate
from 0 for lowest to (# of candidates -1) for the highest
the final score is the sum of each score for the canddiate
then they are ranked highest to lowest
what are the pros and cons of the borda count
satifyies the monotonocity criterion,
does not satisfy the independce of irrelevant alternatives
does not satisfy the condorcet criteron
what is the independence of irrelevant alternatives
the social preferences between candidates a & B depend only on the individual preferences betwen a & b
The social preference between two candidates (e.g., A and B) should depend only on how individuals rank A versus B. The presence, absence, or ranking of other candidates (irrelevant alternatives) should not affect the outcome of the comparison between A and B.
Example:
Suppose voters rank three candidates (A, B, and C):
Voter 1: A > B > C
Voter 2: B > A > C
Voter 3: A > B > C
If A is socially preferred to B, introducing or removing C from consideration should not change the outcome. That is, the comparison between A and B should remain the same regardless of whether C is in the race
what is black rule voting rule
variation of borda rule,
select condorcet winner if one exists
else use borda count
gaurneteed to be condorcet consistent
what is copelands method voting rule
each candiates score is based on its pairwise victories minus its losses
they are ranked according to the score highest to lowest
gaurunteed condorcet consistent
what is arrows impossibility theorem
with three or more candidates there will enver be a voting system that will satisfty
unainimity where if every voter prefers A over B then the group prefers A over B
indepenednece of irrelevant alternatives
non dictatorship - no single voter possesses the power to always determine the groups preferences
