A  Glossary for  Democracy

Condorcet candidate. The Condorcet candidate is the one who could beat each of the others in separate pair-wise contests. Majorities of voters prefer him or her to each of the other candidates. Condorcet winner. The Condorcet candidate in a multi-candidate election is the candidate, if one exists, who could beat each of the others in separate pairwise contests,i.e., is preferred to each of the others candidates by a majority. Condorcet winner.

Condorcet completion method. Condorcet completion method is a voting system that chooses the Condorcet candidate, if one exists, and specifies a contingency rule if one does not due to a voting cycle.

Condorcet efficiency. The Condorcet efficiency of a voting procedure is the proportion or percentage of a class of elections (for which a Condorcet candidate exists) in which the voting system chooses the Condorcet candidate as winner.

Correlation. The correlation between two random variables is a statistical measure of the tendency of the two variables to vary together.

Dimension of a spatial model. The dimension of a spatial model denotes the number of coordinates designated in each point in space. Each such coordinate may be intended to represent the position of a participant (voter or candidate) on a specific issue or characteristic.

Impartial culture. An impartial culture is a model of an electorate in which all preference orders (for a set of candidates) are equally likely.

Insincere voting. A voter's ballot is insincere if his reported preference order differs from his true preference order.

Kemeny distance. The Kemeny distance between two preference orders is the number of adjacent pairwise switches needed to convert one preference order to the other.

Monotonicity. A voting system violates monotonicity if a voter can raise a candidate in the social ordering by lowering that candidate in his individual ordering.

Multi-candidate. A multi-candidate election is an election in which there are three or more candidates.

Normal distribution. The normal (or Gaussian or bell-shaped) distribution of probability specifies that probability follow the density
f (x) = (1/σ '2p) exp[ - (x - μ)/2σ?]
Where σ (sigma)?= the standard deviation, and μ = the mean.

Polarized society. A polarized society is an electorate in which two or more (usually disparate) preference orders predominate. Such a society with exactly two dominating preference orders is called a dual culture.

Random society. A random society is a model for an electorate in which, for each voter, candidate utilities are drawn independently from a uniform distribution. = an impartial culture?

Relative dispersion. In a spatial model of voting, the relative dispersion of candidates to voters is the ratio of the standard deviation of the candidates' positions to that of the voters. [See figure 3 and 4]

Simulation. A simulation is an experiment run as a model of reality. The simulations in this book are computer simulations, i.e., are run on a computer using mathematical models. They are also stochastic, that is they involve input generated to follow probability distributions.

Social utility. The social utility of a candidate is the total (alternatively, the average) utility of the candidate over all voters. Will Merrill OK this?

Social-utility efficiency. The social utility efficiency of a voting system is the normalized ratio between the expected social utilities of the candidate selected by the system and the candidate maximizing social utility.

Squeeze effect. The squeeze effect refers to the reduction in electoral success of a candidate when, in a spatial model, nearby candidates draw support away from the focal candidate.

Standard deviation. Standard deviation is a measure of the variation of a random variable; namely, the square root of the average squared deviation of the mean.

Strategic voting. Strategic voting involves any decision by the voter in marking his ballot intended to improve the outcome from his point of view. [ In addition to insincere voting, it includes, under approval voting for example, expansion or truncation used to optimize a voter's effect on the outcome. ]

Transitivity. A voter's preference order is said to be transitive if whenever the voter prefers A over B and B over C, he also prefers A over C. A similar definition applies to a social preference ordering.

Mandate, the authority and instructions that votes convey from voters to winners.

Criterion Definitions

Condorcet winner criterion: If there is an alternative X which could obtain a majority of votes in pairwise contests against every other alternative, a voting rule should choose X as the winner.

Majority criterion: If a majority of voters [1 out of every 2] have an alternative X as their first choice, a voting rule should choose X.

Monotonicity criterion: If X is a winner under a voting rule, and one or more voters change their preferences in a way favorable to X (without changing the order in which they prefer any other alternatives), then X should still be a winner.

Pareto criterion: If every voter prefers as alternative X to an alternative Y, a voting rule should not produce Y as a winner.

Definitions used in electing multi-seat legislatures

Coalitions: A ruling coalition of legislators must continue to agree on policies or else risk a collapse of government that requires a new election. A working coalition may form simply to pass a particular bill and then disappear.

Cumulative-vote plurality gives each voter as many votes as there are offices to be filled. He may give all of his votes to one candidate or spread them out among several candidates. The first strategy is always better than the latter.

Multi-seat districts:

Non-dominated strategy:

Proportional representation (PR): Most European parlemants have used PR since early in the 20th century. Such constitutions help small parties to earn some representation - giving them a voice, but rarely power, in their legislatures.

Single-seat districts:

Single Transferable Vote (STV): In its multi-winner form, Hare's STV becomes a bit more complicated.

Weighted Votes:

Recommended social-choice glossaries on the web: Blake Cretney's, Lorrie Faith Crannor's, legislative terminology,

There are definitions of particular voting rules in some chapters. The chapter on single-winner elections for example has a whole page of rivals to the Condorcet rules.

Searching for more? This discipline is fractured by many synonyms. Even its title varies; some call it public choice; others prefer social choice. The table below has many terms that can help you find similar web sites.

You will find most of these terms include topics other than formulas for calculating winners from ballots. Searching for voting systems will bring you most often to sites that sell voting equipment. So will election systems and ballot systems. Tally rules include tallies of things other than votes. Voting rules seems least ambiguous.

Election chapters' terms for electing, nominating or selecting a:
1) chairperson, chair, chairman, chairmen, chairwoman, chairwomen; president, prime minister, judge;
2) representative, minister, delegate;
3) council, legislature, parliament, house of commons, senate, congress, house of representatives, assembly, meeting, convention, board of directors, sub committee;

Legislation chapters' terms to enact, set, pass, fund or budget:
1) policies, laws, rules;
2) projects, grants, earmarks, proposals;
3) budgets, agencies;