 | This article needs additional citations for verification .(April 2016) |
Homogeneity is a common property for voting systems. The property is satisfied if, in any election, the result depends only on the proportion of ballots of each possible type. That is, if every ballot is replicated the same number of times, then the result should not change. [1] [2] [3]
Any voting method that counts voter preferences proportionally satisfies homogeneity, including voting methods such as Plurality voting, Two-round system, Single transferable vote, Instant Runoff Voting, Contingent vote, Coombs' method, Approval voting, Anti-plurality voting, Borda count, Range voting, Bucklin voting, Majority Judgment, Condorcet methods and others.
A voting method that determines a winner by eliminating candidates not having a fixed number of votes, rather than a proportional or a percentage of votes, may not satisfy the homogeneity criterion.
Dodgson's method does not satisfy homogeneity. [4] [5]
The following four voter preference profiles show rankings of candidates by voters that are proportional.
Profile 1
| # of voters | Preferences |
|---|---|
| 6 | A > B > C |
| 3 | B > A > C |
| 3 | C > B > A |
Profile 2
| Ratio of voters | Preferences |
|---|---|
| .5 | A > B > C |
| .25 | B > A > C |
| .25 | C > B > A |
Profile 3
| Percent of voters | Preferences |
|---|---|
| 50% | A > B > C |
| 25% | B > A > C |
| 25% | C > B > A |
Profile 4
| Fraction of voters | Preferences |
|---|---|
| A > B > C | |
| B > A > C | |
| C > B > A |
A voting method satisfying homogeneity will return the same election results for each of the four preference profiles.
A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner or Pairwise Majority Rule Winner (PMRW). The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
Arrow's impossibility theorem is a key result in social choice theory, showing that no ranking-based decision rule can satisfy the requirements of rational choice theory. Most notably, Arrow showed that no such rule can satisfy all of a certain set of seemingly simple and reasonable conditions that include independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrelated option C.
The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses.
In social choice, the negative responsiveness, perversity, or additional support paradox is a pathological behavior of some voting rules, where a candidate loses as a result of having "too much support" from some voters, or wins because they had "too much opposition". In other words, increasing (decreasing) a candidate's ranking or rating causes that candidate to lose (win). Electoral systems that do not exhibit perversity are said to satisfy the positive response or monotonicitycriterion.
A Condorcet winner is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the Condorcet winner criterion. The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates.
In social choice, a no-show paradox is a surprising behavior in some voting rules, where a candidate loses an election as a result of having too many supporters. More formally, a no-show paradox occurs when adding voters who prefer Alice to Bob causes Alice to lose the election to Bob. Voting systems without the no-show paradox are said to satisfy the participation criterion.
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
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.
Woodall'splurality criterion is a voting criterion for ranked voting. It is stated as follows:
The Kemeny–Young method is an electoral system that uses ranked ballots and pairwise comparison counts to identify the most popular choices in an election. It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice.
Later-no-harm is a property of some ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause a higher-ranked candidate to lose. It is a common property in the plurality-rule family of voting systems.
The Borda method or order of merit is a positional voting rule that gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on. Once all votes have been counted, the option or candidate or candidates with the most points is/are the winner or winners.
Instant-runoff voting (IRV) is a single-winner, multi-round elimination rule that uses ranked voting to simulate a series of runoffs with only one vote. In each round, the candidate with the fewest votes counting towards them is eliminated, and the votes are transferred to their next available preference until one of the options reaches a majority of the remaining votes. Instant runoff falls under the plurality-with-elimination family of voting methods, and is thus closely related to rules like the exhaustive ballot and two-round runoff system.
An electoral or voting system is a set of rules used to determine the results of an election. 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.
Ranked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked system is one that depends only on which of two candidates is preferred by a voter, and as such does not incorporate any information about intensity of preferences. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them very different properties. In instant-runoff voting (IRV) and the single transferable vote system (STV), lower preferences are used as contingencies and are only applied when all higher-ranked preferences on a ballot have been eliminated or when one of the higher ranked preferences has been elected and surplus votes need to be transferred.
There are a number of different criteria which can be used for voting systems in an election, including the following
The later-no-help criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to win. Voting systems that fail the later-no-help criterion are vulnerable to the tactical voting strategy called mischief voting, which can deny victory to a sincere Condorcet winner.
Computational social choice is a field at the intersection of social choice theory, theoretical computer science, and the analysis of multi-agent systems. It consists of the analysis of problems arising from the aggregation of preferences of a group of agents from a computational perspective. In particular, computational social choice is concerned with the efficient computation of outcomes of voting rules, with the computational complexity of various forms of manipulation, and issues arising from the problem of representing and eliciting preferences in combinatorial settings.
This article discusses the methods and results of comparing different electoral systems. There are two broad ways to compare voting systems:
Multiwinner, at-large, or committeevoting refers to electoral systems that elect several candidates at once. Such methods can be used to elect parliaments or committees.
