MAT 155 Dawn - Chapter 1: The Mathematics of Voting - Vocabulary Flashcards

Vocabulary flashcards covering key concepts from Chapter 1: basic elements of elections, voting methods, pairwise comparisons, and Arrow's fairness criteria.

Candidate

The person, movie, team, or other option that is the object of the voters' choice in an election.

Voter

A person casting a ballot; the number of voters can range from a few to billions.

Ballot

The device by which a voter expresses their opinion about the candidates; can be a simple single-choice ballot or a ranked (preference) ballot.

Preference ballot

A ballot in which voters rank the candidates in order of preference.

Single-choice ballot

A ballot in which the voter selects exactly one candidate.

Preference schedule

A table that lists essential information from ballots to summarize voters' preferences.

Plurality

the simplest/most common; the candidate with the highest number of votes wins and so on

Majority candidate

A candidate who receives more than half of the votes (more than total/2).

Borda Count Method

A ranking-based method where each rank earns points (last place gets 1 point, second-to-last gets 2, up to first place getting m points); the candidate with the highest total points wins.

Ranking

A order of candidates from most to least preferred on a ballot.

Plurality-with-elimination Method

eliminate the candidate(s) with the fewest first-place votes and transfer their votes to the next preference, repeating until a candidate has a majority.

Instant Runoff Voting (IRV)

Another name for the plurality-with-elimination method.

Ranked-choice voting (RCV)

Another name for the plurality-with-elimination method.

Pairwise comparisons

A method where every pair of candidates is compared; the candidate who wins more pairwise matches earns more points; the overall winner is the one with the most points.

Condorcet candidate

A candidate who beats every other candidate in all their pairwise comparisons

Condorcet winner

Another term for a candidate who defeats every other candidate in all pairwise matchups.

Majority criterion

If a candidate has a majority of the first-place votes, that candidate should win the election.

Arrow's Impossibility Theorem

No voting method can satisfy all four fairness criteria (majority, Condorcet, monotonicity, and IIA) when there are three or more candidates.

Polarizing candidate

A candidate who is loved by some voters and disliked by others, often getting strong support from a subset while being rejected by another.

Compromise candidate

A candidate who is broadly acceptable to many voters, often receiving more second- and third-place votes.

weighted voting system

votes are assigned different weights rather than each voter having an equal vote, often used to reflect varying levels of influence or importance.

motion

A formal proposal put forward for discussion and decision in a meeting or assembly.

players

individuals or groups involved in a voting process or decision-making scenario, typically with vested interests in the outcome.

weights

the numerical values assigned to votes in a weighted voting system, indicating the level of influence or importance each vote carries.

Quota

A predetermined minimum number of votes required to pass a motion or make a decision in a voting system.

Anarchy

Can’t pass motion

• have the “players”(w1 and w3) are for the motion and half (w2 and w4) are against

Gridlock

cant pass motion

• all voters are for the motion but their isnt enouph voters (40:39) —> need one more voter

how pass a motion and avoid anarchy and Gridlock

Quota can’t be too big or too small