User:Homunq/voting rule

A voting rule (sometimes called election method or voting method) is the abstract logical procedure by which a winner or winners of an election or referendum is determined. In mathematical terms, it is a function, whose domain (input) consists of the information from the validly-cast ballots, and whose range (output) is a winner or winners. It is thus a key component of an electoral system; however, unlike an electoral system, a voting rule does not address practical matters such as implementation, technology, timing, managing authority, voter and candidate eligibility, etc.

The study of voting rules is a branch of mathematics known as social choice theory. In this field, many more voting rules have been proposed and studied than have ever formed part of any actual polity's electoral system. Social choice theory often uses game theory to study the incentives created by different voting rules, or mathematical proofs to show whether they meet various abstractly-defined voting criteria. An important set of results in voting theory are impossibility results such as Arrow's impossibility theorem, which show that no rule can simultaneously meet certain sets of desirable criteria.

One of the most commonly-used voting rules is the plurality voting system, in which each voter can vote for just one candidate, and the candidate with the most votes wins. However, social theorists prefer other rules over plurality. Another kind of rule that is commonly used in the electoral systems of parliamentary democracies are proportional representation rules, which elect multiple winners at once in a way intended to represent the various ideological or partisan groups of voters in proportion to their size. Some electoral systems also involve composite voting rules that require multiple rounds of elections, such as runoffs or primaries.