Math and Politics- Chapter 2
Terms
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- preference ballot
- expresses a preference order or preference list on the candidates
- transitive preferences
- B>D>C>A voters favor not only B to D, D to C, and C to A, but also B to C, B to A, and D to A
- vote-for-one ballot
- each voter indicates only their top choice
- profile
- a set of preference orders, one for each voter
- social choice
- a choice not merely of one voter but of the society as a whole
- Borda Count Method
- for each voter given n points to the candidate (first place=n-1, second place=n-2) tally points, and the candidate with the most points wins
- Plurality Method
- any candidate with the most first place votes is the winner
- Hare Method
- eliminate the candidates with the fewest first place votes, repeat until there is a tie for fewest first place votes
- Coombs Method
- eliminate not the candidates who are least loved, rather the candidates that are most hated
- Copeland Method
- take every pair and ask electorate who they like better (round robin tournament). For each pair of candidates assign one point for the one who wins the head-to-head match up (or 1/2 point each if its a tie) Tally points, any candidate with the most points wins
- agenda
- order in which contests are waged
- sequential agenda/managing ordering
- A B C D E (A vs. B, B vs. C, C vs. D, D vs. E)
- antiplurality method
- the candidate with the fewest last place votes is the winner, or, if there is a tie, the candidates tying for fewest last place votes are all winners
- vote-for-two method
- each candidate gets one point for every voter who ranks that candidate in either first place or second place
- instant recall method
- if one candidate has a majority of the first place votes, they are declared to be the unique winner, otherwise the candidate with the plurality of the first-place votes is eliminated and a plurality election among the remaning candidates determines the winner
- constant functions
- the output of the method (winner) does not depend on the input (ballots)
- approval ballot
- voters indicate with a yes-no response whether each candidate is acceptable to them
- cumulative voting
- every voter gets one vote that can be split as the voter chooses among any of the candidates (1/2 to A, 1/3 to B, 1/6 to C, etc.)