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=== Electoral systems === {{main|Electoral system|Social choice function}} There are many electoral methods. The purpose of an election may be to choose one person, such as a president, or a group, such as a committee or a parliament. In electing a parliament, either each of many small constituencies can elect a single representative, as in Britain; or each of a lesser number of multi-member constituencies may elect two or more representatives, as in Ireland; or multi-member districts and some single-member districts can be used; or the entire country can be treated as one "at-large" district, as in The Netherlands.[[File: Swiss voting material.jpg|thumb|left|In [[Voting in Switzerland|Switzerland]], without the need to register, every citizen receives at home the [[ballot papers]] and information brochure for each voting (and can send it by post). Switzerland has a [[direct democracy]] system and votes (and elections) are organized about four times a year; here, to [[Bern#Politics|Berne]]'s citizens in November 2008 about 5 national, 2 cantonal, 4 municipal referendums, and 2 elections (government and parliament of the City of Berne) to take care of at the same time.]] Different [[voting system]]s use different [[ballot]] designs. Some ballots allow only one choice to be selected (single X voting); others allow ranking or selecting multiple options ([[Ranked ballots]]). Different voting systems allow each voter to cast a different number of votes - only one (single voting as in [[First-past-the-post voting]], [[Single non-transferable voting]] and [[Single transferable voting]]); as many as are being elected in a multiple-member district (multiple voting as used in [[Plurality block voting]]; more than one but fewer than are being elected in a multiple-member district ([[Limited voting]]). Most allow a voter to put just one vote on each candidate, but others allow a voter's votes to be piled on to one candidate. Different voting systems require different levels of support to be elected. [[Plurality voting]] ([[First-past-the-post voting]]) elects the candidate with more votes than any other single candidate. It does not require the winner to achieve a voting majority, to have more than half of the total votes cast. In [[First-past-the-post voting]], when more than two candidates run, the winner commonly has less than half of the vote, as few as 18 percent was recorded in 2014 in Toronto.<ref>{{Cite web |title=Councillor Toronto Election 2014 Poll By Poll Results |url=https://www.toronto.ca/wp-content/uploads/2017/08/9021-election-2014-councillor-poll-by-poll-results.pdf |website=City of Toronto}}</ref> In [[Instant-runoff voting]], a candidate must have a majority of votes to be elected, although presence of exhausted votes may mean that the majority at time of final count is not majority of votes cast. In STV, any candidate who takes quota (usually set at much less than half of the votes) is elected; others without quota (but with more votes than any other single candidate) may be declared elected as well. Side effects of [[First-past-the-post voting]] include a [[wasted vote|waste of votes]] due to [[vote splitting]], a [[two-party system]] and [[political polarization]] due to electing candidates that do not support [[centrism]]. To understand why a race using [[First-past-the-post voting]] tends to favor less-centric candidates, consider a simple lab experiment where students in a class vote for their favorite marble. If five marbles are assigned names and are placed "up for election", and if three of them are green, one is red, and one is blue, then a green marble will rarely win the election. The reason for the green's lack of success is vote splitting. The three green marbles will split the votes of those who prefer green. In fact, in this analogy, the only way that a green marble is likely to win is if more than three-fifths of the voters prefer green. If the same number of people prefer green as those who prefer red and blue, that is to say, if one-third of the voters prefer green, one-third prefer blue, and one-third prefer red, then each green marble will only get one-ninth of the vote, if the green marbles each take same number of votes, while the red and blue marbles will each get one-third, putting the green marbles at a serious disadvantage. If the experiment is repeated with other colors, the color that is in the majority (if the majority is split among multiple choices) will still rarely win. In other words, from a purely mathematical perspective, a single-winner system tends to favor a winner that is different from the majority, if the majority runs multiple candidates, and if the minority group runs just one candidate. This minority rule success can also result if multiple winners are elected and voters cast multiple votes ([[Plurality block voting]]). But even if the majority is split among multiple candidates, proportionate results can still be produced if votes can be transferred, as under STV, or if multiple winners are elected and each voter has just one vote. Alternatives to First-past-the-post voting include [[approval voting]], [[two-round system|two-round]], [[proportional representation]], and [[instant-runoff voting]]. With [[approval voting]], voters are encouraged to vote for as many candidates as they approve of, so the winner is much more likely to be any one of the five marbles because people who prefer green will be able to vote for every one of the green marbles. With two-round elections, the field of candidates is thinned prior to the second round of voting. In most cases, the winner must receive a [[Majority rule|majority]] of the votes, which is more than half. If no candidate obtains a majority in the first round, then the two candidates with the most significant plurality run again for the second round of voting. Variants exist regarding these two points: the requirement for being elected at the first round is sometimes less than 50%, and the rules for participation in the runoff may vary. With single-round ranked voting, such as instant-runoff voting system as used in some elections in Australia and the United States, voters rank each candidate in order of preference (1,2,3,4 etc.). Votes are distributed to each candidate according to the first preferences. If no single candidate has 50% of the vote, then the candidate with the fewest votes is excluded and their votes are redistributed according to the voter's nominated order of preference. The process repeats itself until a candidate has 50% or more votes. The system is designed to produce the same result as an [[exhaustive ballot]] but using only a single round of voting. Ranked voting is also used in a PR format. PR-STV is used in Australia, Ireland and Malta. Quota is calculated. In say a four-seat constituency, quota (if [[Droop quota]] is used) is 20 percent of the valid vote plus 1. Every candidate with quota (of 1st preferences alone or combination of first preferences and later preferences) will be elected. If a candidate has more than a quota and seats are yet to be filled, his/her surplus will be distributed to the other candidates in proportion to all of that candidate's 2nd preferences, in line with secondary preferences marked on the vote if any. If there are still candidates to be elected and no surplus votes to be transferred, the least-popular is eliminated, as above in AV or IRV, and the process continues until four candidates have reached a quota or are declared elected when the field of candidates is thinned to the number of remaining open seats. In the [[Quota Borda system|Quota Borda System]] (QBS),<ref name=":0">{{Cite book |last=Emerson |first=Peter |url=https://www.worldcat.org/oclc/948558369 |title=From Majority Rule to Inclusive Politics: Electing a Power-Sharing Coalition |date=2016 |isbn=978-3-319-23500-4 |edition=1st |location=Cham |oclc=948558369 |publisher=Springer International Publishing}}</ref> the voters also cast their preferences, 1,2,3,4... as they wish. In the analysis, all 1st preferences are counted; all 2nd preferences are counted; after these preferences have been translated into points per the rules of a [[Borda count#Modified Borda count|Modified Borda Count]] (MBC), the candidates' points are also counted. Seats are awarded to any candidates with a quota of 1st preferences; to any pair of candidates with two quotas of 1st/2nd preferences; and if seats are still to be filled, to those candidates with the highest MBC scores. In a voting system that uses ''multiple votes'' ([[Plurality block voting]]), the voter can vote for any subset of the running candidates. So, a voter might vote for Alice, Bob, and Charlie, rejecting Daniel and Emily. [[Approval voting]] uses such multiple votes. In a voting system that uses a ''ranked vote'', the voter ranks the candidates in order of preference. For example, they might mark a preference for Bob in the first place, then Emily, then Alice, then Daniel, and finally Charlie. [[Ranked voting systems]], such as those used in Australia and Ireland, use a ranked vote. In a voting system that uses a ''scored vote'' (or ''range vote''), the voter gives each alternative a number between one and ten (the upper and lower bounds may vary). See [[cardinal voting systems]]. Some "multiple-winner" systems such as the Single Non-Transferable Vote, SNTV, used in Afghanistan and Vanuatu give a single vote or one vote per elector per available position. STV uses single ranked votes; block voting ([[Plurality-at-large voting]]) are often used for [[at-large]] positions such as on some city councils. Finally, the Condorcet rule is used (sometimes) in decision-making. The voters or elected representatives cast their preferences on one, some, or all options, 1,2,3,4... as in PR-STV or QBS. In the analysis, option A is compared to option B, and if A is more popular than B, then A wins this pairing. Next, A is compared with option C, then D, and so on. Likewise, B is compared with C, D, etc. The option which wins the most pairings, (if there is one), is the Condorcet winner.'''β'''
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