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Anti-plurality Voting
Anti-plurality voting describes an electoral system in which each voter votes ''against'' a single candidate, and the candidate with the fewest votes against wins. Anti-plurality voting is an example of a positional voting method. Example In this electoral system, each voter marks a vote against his or her fourth preference. In this case, it would be a tie between Nashville and Chattanooga, both receiving zero votes. If the tie is to be resolved with anti-plurality voting as well, Nashville would win, as it has less second-to-last place votes (32%) than Chattanooga (42%). Ties could also be resolved through a second subsequent runoff election. Characteristics As can be seen from the example, in the absence of tactical voting, this system tends to favor middle-of-the-road candidates. However, it is very sensitive to tactical voting, as any candidate perceived beforehand as a potential winner will attract more countervotes from partisans of their opponents. This creates the ...
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Electoral 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, nonprofit organizations and informal organisations. These rules govern all aspects of the voting process: when elections occur, Suffrage, who is allowed to vote, Nomination rules, who can stand as a candidate, Voting method, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on Campaign finance, 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. Some electoral systems elect a single winner to a unique position, such as prime minister, president or governor, while others elect multiple winners, such as membe ...
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Positional Voting Method
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 (Eurovision Song Contest) or it may form a mathematical sequence such as an arithmetic progression (Borda count), a geometric one (positional number system) or a harmonic one ( Nauru/Dowdall method). 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. Positional voting should be distinguished from score voting: in the former, the score that each voter g ...
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Runoff Election
The two-round system (TRS or 2RS), sometimes called ballotage, top-two runoff, or two-round plurality, is a single-winner electoral system which aims to elect a member who has support of the majority of voters. The two-round system involves one or two rounds of choose-one voting, where the voter marks a single favorite candidate in each round. If no one has a majority of votes in the first round, the two candidates with the most votes in the first round move on to a second election (a second round of voting). The two-round system is in the family of plurality voting systems that also includes single-round plurality (FPP). Like instant-runoff (ranked-choice) voting and first past the post, it elects one winner. The two-round system first emerged in France and has since become the most common single-winner electoral system worldwide. Despite this, runoff-based rules like the two-round system and RCV have faced criticism from social choice theorists as a result of their suscep ...
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Tactical Voting
Strategic or tactical voting is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results. Gibbard's theorem shows that no voting system has a single "always-best" strategy, i.e. one that always maximizes a voter's satisfaction with the result, regardless of other voters' ballots. This implies all voting systems can sometimes encourage voters to strategize. However, weaker guarantees can be shown under stronger conditions. Examples include one-dimensional preferences (where the median rule is strategyproof) and dichotomous preferences (where approval or score voting are strategyproof). With large electoral districts, party list methods tend to be difficult to manipulate in the absence of an electoral threshold. However, biased apportionment methods can create opportunities for strategic voting, as can small electoral districts (e.g. those used most often with the single transferable vote). Proporti ...
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Monotonicity Criterion
Electoral system criteria In social choice, the negative response, 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 (or wins because of increased opposition). In other words, increasing (decreasing) a candidate's ranking or rating causes that candidate to lose (win), respectively. Electoral systems that do not exhibit perversity are sometimes said to satisfy the monotonicity criterion.D R Woodall"Monotonicity and Single-Seat Election Rules" '' Voting matters'', Issue 6, 1996 Perversity is often described by social choice theorists as an exceptionally severe kind of electoral pathology, as such rules can have "backwards" responses to voters' opinions, where popularity causes defeat while unpopularity leads to a win. Similar rules treat the well-being of some voters as "less than worthless". These issues have led to constitutional prohibitions on such systems as violating ...
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Participation Criterion
The participation criterion is a voting system criterion that says candidates should never lose an election as a result of receiving too many votes in support. More formally, it says that adding more voters who prefer ''Alice'' to ''Bob'' should not cause ''Alice'' to lose the election to ''Bob''. Voting systems that fail the participation criterion exhibit the no-show paradox, where a voter is effectively disenfranchised by the electoral system because turning out to vote could make the result worse for them; such voters are sometimes referred to as having negative vote weights, particularly in the context of German constitutional law, where courts have ruled such a possibility violates the principle of one man, one vote. Positional methods and score voting satisfy the participation criterion. All deterministic voting rules that satisfy pairwise majority-rule can fail in situations involving four-way cyclic ties, though such scenarios are empirically rare, and the random ...
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Consistency Criterion
A voting system satisfies join-consistency (also called the reinforcement criterion) if combining two sets of votes, both electing ''A'' over ''B'', always results in a combined electorate that ranks ''A'' over ''B''. It is a stronger form of the participation criterion. Systems that fail the consistency criterion (such as instant-runoff voting or Condorcet method, Condorcet methods) are susceptible to the multiple-district paradox, a Pathological (mathematics), pathological behavior where a candidate can win an election without carrying even a single precinct. Conversely, it can be seen as allowing for a particularly egregious kind of gerrymander: it is possible to draw boundaries in such a way that a candidate who wins the overall election fails to carry even a single electoral district. Rules susceptible to the multiple-districts paradox include all Condorcet methods and Instant-runoff voting, instant-runoff (or ranked-choice) voting. Rules that are not susceptible to it includ ...
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Condorcet Loser Criterion
In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion but does not imply the Condorcet winner criterion. A voting system complying with the Condorcet loser criterion will never allow a ''Condorcet loser'' to win. A Condorcet loser is a candidate who can be defeated in a head-to-head competition against each other candidate.https://arxiv.org/pdf/1801.05911 "We say that an alternative is a Condorcet loser if it would be defeated by every other alternative in a kind of one-on-one contest that takes place in a sequential pairwise voting with a fixed agenda4.– Condorcet loser criterion (CLC), ..we say that a social choice procedure satisfies the Condorcet loser criterion (CLC) provided that a Condorcet loser is never among the social choices." (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in di ...
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Independence Of Irrelevant Alternatives Criterion
In social choice theory and politics, a spoiler effect happens when a losing candidate affects the results of an election simply by participating. Voting rules that are not affected by spoilers are said to be spoilerproof. The frequency and severity of spoiler effects depends substantially on the voting method. Instant-runoff voting (IRV), the two-round system (TRS), and especially first-past-the-post (FPP) without winnowing or primary elections are highly sensitive to spoilers (though IRV and TRS less so in some circumstances), and all three rules are affected by center-squeeze and vote splitting. Majority-rule (or Condorcet) methods are only rarely affected by spoilers, which are limited to rare situations called cyclic ties.. "This is a kind of stability property of Condorcet winners: you cannot dislodge a Condorcet winner ''A'' by adding a new candidate ''B'' to the election if A beats B in a head-to-head majority vote. For example, although the 2000 U.S. Presidential El ...
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Independence Of Clones Criterion
In social choice theory, the independence of (irrelevant) clones criterion says that adding a ''clone'', i.e. a new candidate very similar to an already-existing candidate, should not spoil the results. It can be considered a weak form of the independence of irrelevant alternatives (IIA) criterion that nevertheless is failed by a number of voting rules. A method that passes the criterion is said to be clone independent. A group of candidates are called clones if they are always ranked together, placed side-by-side, by every voter; no voter ranks any of the non-clone candidates between or equal to the clones. In other words, the process of ''cloning'' a candidate involves taking an existing candidate ''C'', then replacing them with several candidates ''C1'', ''C2..''. who are slotted into the original ballots in the spot where ''C'' previously was, with the clones being arranged in any order. If a set of clones contains at least two candidates, the criterion requires that deleti ...
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Reversal Symmetry
The reversal symmetry criterion is a voting system criterion which says that if every voter's opinions on each of the candidates is perfectly reversed (i.e. they rank candidates in order from worst to best), the outcome of the election should be reversed as well, i.e. the first- and last-place finishers should switch places. In other words, the results of the election should not depend arbitrarily on whether voters rank candidates from best to worst (and then select the best candidate), or whether we ask them to rank candidates from worst to best (and then select the least-bad candidate). Another, equivalent way to motivate the criterion is to say that a voting system should never elect the worst candidate, according to the method itself (as doing so suggests the method is, in some sense, self-contradictory). The worst candidate can be identified by reversing all ballots (to rank candidates from worst-to-best) and then running the algorithm to find a single worst candidate. Sit ...
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Plurality Voting
Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other (that is, receive a plurality) are elected. Under single-winner plurality voting, and in systems based on single-member districts, plurality voting is called single member istrictplurality (SMP), which is widely known as " first-past-the-post". In SMP/FPTP the leading candidate, whether or not they have a majority of votes, is elected. There are several versions of plurality voting for multi-member district. The system that elects multiple winners at once with the plurality rule and where each voter casts as many X votes as the number of seats 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 more than one vote but fewer than the number of seats to fill in a multi-seat district is known as limited voting. A semi-prop ...
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