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In social choice theory, anonymity, sometimes called symmetry, is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different voters. In other words, the rule returns the same outcome (whatever this outcome may be) if the vector of votes is permuted arbitrarily. [1] [2]
Most voting rules are anonymous by design. For example, plurality voting is anonymous, since only counts the number of votes received by each candidates, regardless of who cast these votes. Similarly, the utilitarian rule and egalitarian rule are both anonymous, since the only consider the set of utilities, regardless of who these utilities belong to.
All rules using a secret ballot are anonymous, since they do not know which voter cast which vote. But the opposite is not true: a committee can use non-secret ballot, and still use an anonymous voting rule.
Weighted voting rules are non-anonymous, as they give some voters a higher weight than others, for example, due to their expertise or entitlement.
Another example of a non-anonymous voting rule is plurality voting with the additional rule that, in case of a tie, the option preferred by the chair is selected.
Approval voting is an electoral system in which voters can select any number of candidates instead of selecting only one.
Plurality voting refers to electoral systems in which a candidate who polls more than any other is elected. In systems based on single-member districts, it elects just one member per district and may also be referred to as first-past-the-post (FPTP), single-member plurality (SMP/SMDP), or single-choice (choose-one) voting. A system that elects multiple winners elected at once with the plurality rule and where each voter casts multiple X votes in a multi-seat district is referred to as plurality block voting. A semi-proportional system that elects multiple winners elected at once with the plurality rule and where each voter casts just one vote in a multi-seat district is known as single non-transferable voting.
The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian result, not a simple-plurality result as under first past the post. Under the two-round election system, the election process usually proceeds to a second round only if in the first round no candidate received an absolute majority of votes cast, or some other lower prescribed percentage. Under the two-round system, usually only the two candidates who received the most votes in the first round, or only those candidates who received above a prescribed proportion of the votes, are candidates in the second round. Other candidates are excluded from the second round.
The single transferable vote (STV), sometimes known as proportional ranked choice voting (P-RCV), is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate preferences if their preferred candidate is eliminated or elected with surplus votes, so that their vote is used to elect someone they prefer over others in the running. STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another. Formally, STV satisfies a fairness criterion known as proportionality for solid coalitions.
Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for a candidate or party other than their sincere preference to prevent an undesirable outcome. For example, in a simple plurality election, a voter might gain a better outcome by voting for a less preferred but more generally popular candidate.
In social choice theory and politics, the spoiler effect refers to a situation where the entry of a losing candidate affects the results of an election. A voting system that is not affected by spoilers satisfies independence of irrelevant alternatives or independence of spoilers.
Arrow's impossibility theorem is a celebrated result and key impossibility theorem in social choice theory. It shows that no ranked voting rule can produce a logically coherent ranking in elections with more than two candidates. Specifically, no such rule can satisfy a key criterion of decision theory, called independence of irrelevant alternatives: that its choice between and should not depend on the quality of a third, unrelated outcome .
Voting is a method by which a group, such as a meeting or an electorate, convenes together for the purpose of making a collective decision or expressing an opinion usually following discussions, debates or election campaigns. Democracies elect holders of high office by voting. Residents of a jurisdiction represented by an elected official are called "constituents", and the constituents who choose to cast a ballot for their chosen candidate are called "voters." There are different systems for collecting votes, but while many of the systems used in decision-making can also be used as electoral systems, any which cater to proportional representation can only be used in elections.
Coombs' method or the Coombs rule is a ranked voting system which uses a ballot counting method for ranked voting created by Clyde Coombs. Coombs' method can be thought of as a cross between instant-runoff voting and anti-plurality voting.
The Gibbard–Satterthwaite theorem is a theorem in voting theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner, and states that for every voting rule of this form, at least one of the following three things must hold:
Social choice theory or social choice is a branch of economics that analyzes mechanisms and procedures for collective decisions. Social choice incorporates insights from welfare economics, mathematics, and political science to find the best ways to combine individual opinions, preferences, or beliefs into a single coherent measure of well-being.
Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is never worth more. A valid progression of points or weightings may be chosen at will or it may form a mathematical sequence such as an arithmetic progression, a geometric one or a harmonic one. The set of weightings employed in an election heavily influences the rank ordering of the candidates. The steeper the initial decline in preference values with descending rank, the more polarised and less consensual the positional voting system becomes.
Instant-runoff voting (IRV), also known as plurality with elimination or plurality loser, is a ranked-choice voting system that modifies plurality by repeatedly eliminating the last-place winner until only one candidate is left. In the United Kingdom, it is generally called the alternative vote (AV). In the United States, IRV is often referred to as ranked-choice voting (RCV), by way of conflation with ranked voting systems in general.
An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.
Rated voting refers to any electoral system which allows the voter to give each candidate an independent evaluation, typically a rating or grade. These are also referred to as cardinal, evaluative, or graded voting systems. Cardinal methods and ordinal methods are the two modern categories of voting systems.
The term ranked voting, also known as preferential voting or ranked-choice voting, pertains to any voting system where voters indicate a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally.
A major branch of social choice theory is devoted to the comparison of electoral systems, otherwise known as social choice functions. Viewed from the perspective of political science, electoral systems are rules for conducting elections and determining winners from the ballots cast. From the perspective of economics, mathematics, and philosophy, a social choice function is a mathematical function that determines how a society should make choices, given a collection of individual preferences.
In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold:
Fractional approval voting is an electoral system using approval ballots, in which the outcome is fractional: for each alternative j there is a fraction pj between 0 and 1, such that the sum of pj is 1. It can be seen as a generalization of approval voting: in the latter, one candidate wins and the other candidates lose. The fractions pj can be interpreted in various ways, depending on the setting. Examples are:
In social choice theory, Neutrality is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different candidates. In other words, if the vector of candidates is permuted arbitrarily, then the returned result is permuted in the same way.