Math and Politics
Plurality
candidate ranked as first choice among the most voters is the winner, awards 1 point to first place and zero points to all other places
condorcet
if the candidate can beat every other candidate in a head-to-head match-up
neutral
treats both candidates equally, if A is the winner and all votes for A were changed to all votes for B and all votes for B were changed to votes for A then B would be the winner
anonymous
treats voters equally, which voter votes for which candidate does not impact the chance for winning
simple minority
whoever gets the least amount of votes wins
dictator
winner is chosen by one particular voter
monarchy
winner is the candidate that chooses him or herself
majority
if a voter majority chooses a candidate as best than that candidate is the unique winner
simple majority
tally votes to find candidate with the most votes; if candidates have the same # of votes there is a "tie"; not a decisive method
Vote for Two
award one point to both 1st and 2nd place and 0 points to all other places
tabulated profile
calculation of all the votes per candidate
super majority
candidate must have certain proportion of the votes to win; if candidate has less than the proportion there is a "tie"
weighted voting
certain number of votes is proportioned to each voter and candidate with more than half of the votes wins
Decisive
chooses a winner; no ties
Copeland
compare each candidate head-to-head by viewing who places higher on each ballot, then determine the winner; awards one point for every win and 1/2 a point for every tie in the head-to-head competitions
almost decisive
decisive except when there is an actual tie
Anti-Plurality
0 points for last place and 1 point for every other place
profile
results of the votes of all voters
status quo
un-neutral method where if two candidates are running, if the newcomer does not win then the incumbent candidate wins
unanimity
unanimous vote is necessary for the candidate to win, otherwise there is a "tie"
May's Theorem
no social choice function satisfies all of the criteria (Decisive, Anonymous,Monotone, Neutral); the only theorem that satisfies anonymous, monotone, neutral is simple majority
Hare
elimination method; remove candidates from running by first seeing who has the least amount of 1st place votes, remove that candidate then continue this process until there is a winner
Coombs
elimination; eliminate candidates with the most last place votes, continue until there is a winner
Borda Count
given the number of candidates, the first choice gets the higher number of votes subtracting one point the lower the placement until last place which gets 0 points; candidate with the greatest number of votes is the winner
Arrow's Theorem
if a social choice function with at least three candidates satisfies Pareto and independence, then it is a dictatorship
monotonicity
if a voter profile has a certain candidate as a winner, and a vote is taken from a candidate and given to the winning candidate , the winning candidate should still win
pareto
if every voter prefers one candidate to another, then the unpreffered candidate is not the winner
anti-condorcet
if the candidate loses to every other candidate in a head-to-head match-up
Black
if there is a condorcet candidate then that candidate is a unique winner, otherwise use the borda count method
independence
minimizes the effect of 3rd party candidate within two profiles, each voter prefers one candidate to another, both profiles have the same preference for every voter, then the preferred candidate must win no matter the placement of the third candidate
all-ties
no matter how many voters vote for one candidate, all candidates are winners, so there is a "tie"
all-ties method
no matter the winner or the outcome, the result is a "tie"
parity method
one candidate gets an even number of votes the other candidate an odd number of votes; the candidate with the even number wins, otherwise it is a "tie"
