Glossary

The following is a partial list of terms used throughout this site. To see a definition and discussion, simply roll your mouse over the phrase. Clicking the link will go to the page where the term is described in more detail. Typically the first mention on a given page of any of these phrases is linked to the glossary in this way.

• Approval VotingThis system is the most basic extension of traditional plurality. Rather than selecting a single candidate, voters simply select one or more candidates of which they “approve,” in effect voting as many times as they want, but only once for each candidate. The winner is the candidate who receives the most votes, pure and simple.
• BordaThe Borda method is a means of giving different numbers of “points” to various candidates, so that one can choose one candidate as their distinct first choice but still lend support to others. Typically, a ranked ballot is used, with the voter’s first choice being given the greatest number of points, and each subsequent candidate receiving one fewer. The winner is the candidate with the most points.
• CondorcetThe general term for any election method that uses ranked ballots and has, as it's first princple, the Condorcet Criterion: any candidate which beats every other candidate individually must win the election. Any Condorcet method must come along with an ambiguity resolution procedure for cases in which there is no winner by this first criterion.
• Condorcet CriterionAny candidate that would defeat every other candidate in a one-on-one runoff must win the election. This is simply a restatement of majority rule.
• Condorcet MatrixThe typical way of representing the votes of a Condorcet election are in a matrix. For example, the following might be the result of a Condorcet election between three candidates. Each number corresponds to the number of voters who chose the candidate for that row over the candidate for that column. In this case, Bob Jones is the Condorcet winner, John Hennessy second place.

  	John Hennessy	Bob Jones	Tiger Woods
  John Hennessy		27	98
  Bob Jones	73		52
  Tiger Woods	2	48

• Condorcet's ParadoxThis paradox is that in some situations it is impossible to obey majority rule in an election. The situation in which paradox can arise is what is called a majority rule cycle. This is when, according to the result of the election, there is a cycle of candidates, each beating the next in a runoff. Imagine the simplest case: there are three candidates: A, B, and C. A majority rule cycle occurs when A defeats B, B defeats C, and C defeats A. This is a paradox because to install any one of these three candidates defies majority rule, since there exists another candidate which the majority prefers.
• honestA vote is called "honest" if it reflects the true preference of the voter, even if it is apparent to the voter that voting differently will produce a more preferred result.
• IllocutionaryThis is term applied to the act of voting, meaning that it consists of two distinct and often conflicting actions: an act of power (attempting to cause your most preferred possible candidate to win), and an act of speech (saying that you approve of the candidate you select).
• Instant RunoffThis election method is based on the principle of being able to initially vote for your preferred choice, and then transfer your vote to more viable candidates if your first choice cannot win. Like Condorcet methods, IRV begins with a ranked ballot. Initially, all first choices are tallied, and if one candidate wins a majority, they win. If no candidate has the majority, then the candidate with the least votes is eliminated from all ballots (wherever that candidate was the first choice, the second choice becomes the new first choice) and the process begins again. It is called "instant" in comparison to other election systems where a series of "runoffs" are held, reducing the pool of candidates each time. In instant runoff, the voters need not return to the polls, since these runoffs can be performed instantly using ranked ballots.
• MinimaxThis is an ambiguity resolution system in which the winner is the candidate whose worst defeat is best. Intuitively, the idea is to pick the candidate who was most nearly a Condorcet winner in the sense that even their worst defeat was closest to being a victory.
• monotonicityThis is technical term referring to the property that expressing your preference for a particular candidate should increase that candidates chance of winning. It is fairly obvious why this should be the case.
• PluralityThis is the voting system currently used for most American elections. Each voter chooses only one candidate, and the winner is the candidate with the most votes.
• ranked ballotA ballot on which a vote consists in ranking the candidates in order of preference.
• Ranked PairsIn this ambiguity resolution system, all pairwise defeats are ranked in terms of strength. The defeats are then examined from strongest to weakest. The strongest defeat is “locked in” but ranking the winner above the loser. Each defeat is then examined, and if it does not violate any previous decisions, it is also locked in. This is a bit subtle. The intuition is that we should regard each defeat as sufficient cause to rank the winner above the loser, but since this cannot be done for defeats, we at least ensure that it is done for the defeats of strongest margin.
• Rock-Paper-Scissors thought experimentI propose the following thought experiment of an example in which a majority rule cycle can occur.
  • Every citizen is given a card with “rock,” “paper,” or “scissors” written on it. Exactly one third of the citizens have each type.
  • The government conducts will choose to "play" one of the three moves.
  • Anyone voter who is beaten (rock beats scissors, scissors beats paper, paper beats rock) by the government must pay extra taxes; anyone who wins receives a tax rebate; anyone with the same move as the government is unaffected.
  By varying the proportions of voters with each type of card, various interesting results can be obtained. As a basic example, if one third of the population has each, there is a majority rule cycle: two-third of voters prefer rock to paper, another two thirds prefer paper to scissors, and yet another two thirds prefer scissors to rock.
• Smith SetThe Smith set is the set of candidates on which a Condorcet ambiguity resolution procedure acts. It is formed by finding the smallest group of candidates such that each candidate in the set defeats each candidate not in the set. This is the natural second step of the Condorcet process, since all ambiguity lies exclusively within this set.
• strategicA vote is called "strategic," "tactical," or "pragmatic" if it does not reflect the voter's true preference, but is rather an attempt by the voter to secure the best possible outcome, given the voter's prediction of how other voters will act.