Condorcet methods
96-603: Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results 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
192-515: A . For the Nauru system, the first preference a is worth one and the common difference d between adjacent denominators is also one. Numerous other harmonic sequences can also be used in positional voting. For example, setting a to 1 and d to 2 generates the reciprocals of all the odd numbers (1, 1/3, 1/5, 1/7, …) whereas letting a be 1/2 and d be 1/2 produces those of all the even numbers (1/2, 1/4, 1/6, 1/8, …). The harmonic variant used by
288-406: A = N , the number of candidates. The value of the first preference need not be N . It is sometimes set to N – 1 so that the last preference is worth zero. Although it is convenient for counting, the common difference need not be fixed at one since the overall ranking of the candidates is unaffected by its specific value. Hence, despite generating differing tallies, any value of a or d for
384-400: A majority bonus system to either ensure one party or coalition gains a majority in the legislature, or to give the party receiving the most votes a clear advantage in terms of the number of seats. San Marino has a modified two-round system, which sees a second round of voting featuring the top two parties or coalitions if there is no majority in the first round. The winner of the second round
480-475: A Borda count election will result in identical candidate rankings. The consecutive Borda count weightings form an arithmetic progression . Common systems for evaluating preferences, other than Borda, are typically "top-heavy". In other words, the method focuses on how many voters consider a candidate one of their "favourites". Under first-preference plurality (FPP), the most-preferred option receives 1 point while all other options receive 0 points each. This
576-506: A Senator leaves office before their eight-year term ends, the first substitute takes their place, and then the second if needed. On the other hand, in political systems with a culture of by-elections, filling vacancies under Block Voting can be harder than in other voting methods. This is because by-elections to fill a single seat in a multi-member district can be expensive. In the Philippine Senate that has staggered elections ,
672-627: A country's constitution or electoral law . Participatory rules determine candidate nomination and voter registration , in addition to the location of polling places and the availability of online voting , postal voting , and absentee voting . Other regulations include the selection of voting devices such as paper ballots , machine voting or open ballot systems , and consequently the type of vote counting systems , verification and auditing used. Electoral rules place limits on suffrage and candidacy. Most countries's electorates are characterised by universal suffrage , but there are differences on
768-579: A different system, as in contingent elections when no candidate wins a majority of the United States Electoral College . An exhaustive ballot is not limited to two rounds, but sees the last-placed candidate eliminated in each round of voting. Due to the potentially large number of rounds, this system is not used in any major popular elections, but is used to elect the Speakers of parliament in several countries and members of
864-403: A geometric progression with a common ratio of one-half ( r = 1/2). Such weightings are inherently valid for use in positional voting systems provided that a legitimate common ratio is employed. Using a common ratio of zero, this form of positional voting has weightings of 1, 0, 0, 0, … and so produces ranking outcomes identical to that for first-past-the-post or plurality voting . Alternatively,
960-415: A given rank position ( n ) is defined below; where the value of the first preference is a . w n = a 2 a + ( n − 1 ) d = a 1 + ( n − 1 ) d a , {\displaystyle w_{n}={\frac {a^{2}}{a+(n-1)d}}={\frac {a}{1+{\frac {(n-1)d}{a}}}},} where w 1 =
1056-448: A high value and all the remaining options with a common lower value. The two validity criteria for a sequence of weightings are hence satisfied. For an N -candidate ranked ballot, let the permitted number of favoured candidates per ballot be F and the two weightings be one point for these favoured candidates and zero points for those not favoured. When analytically represented using positional voting, favoured candidates must be listed in
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#17327765870881152-496: A landslide. While many criticize block voting's tendency to create landslide victories, some cite it as a strength. Since the winners of a block voting election generally represent the same slate or group of voters, there is greater agreement among those elected, potentially leading to a reduction in political gridlock . Block plurality voting, like single-winner plurality voting , is particularly vulnerable to tactical voting . Supporters of relatively unpopular third parties have
1248-562: A list of candidates put forward by a political party or alliance . There are many variations in electoral systems. The mathematical and normative study of voting rules falls under the branches of economics called social choice and mechanism design , but the question has also engendered substantial contributions from political scientists , analytic philosophers , computer scientists , and mathematicians . The field has produced several major results, including Arrow's impossibility theorem (showing that ranked voting cannot eliminate
1344-400: A majority of the vote in the first round, the second preferences of the lowest-ranked candidate are then added to the totals. This is repeated until a candidate achieves over 50% of the number of valid votes. If not all voters use all their preference votes, then the count may continue until two candidates remain, at which point the winner is the one with the most votes. A modified form of IRV is
1440-493: A majority of votes to be elected, either in a runoff election or final round of voting. This is sometimes referred to as a type of majority voting, although usually only a plurality is required in the last round, and sometimes even in the first round winners can avoid a second round without achieving a majority. In social choice theory, runoff systems are not called majority voting, as this term refers to Condorcet-methods . There are two main forms of runoff systems, one conducted in
1536-485: 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
1632-598: A method for converting sets of individual preferences (ranked ballots) into one collective and fully rank-ordered set. It is possible and legitimate for options to be tied in this resultant set; even in first place. Consider a positional voting election for choosing a single winner from three options A, B and C. No truncation or ties are permitted and a first, second and third preference is here worth 4, 2 and 1 point respectively. There are then six different ways in which each voter may rank order these options. The 100 voters cast their ranked ballots as follows: After voting closes,
1728-615: A minor party which has only nominated one candidate. Thus, block voting may look like single non-transferable voting . This system sometimes fosters the creation of an electoral alliance between political parties or groups as opposed to a coalition . This has been the case in the National Assembly of Mauritius ; the New Hampshire House of Representatives , with the election of multiple Free State Project as well as New Hampshire Liberty Alliance members; and in
1824-403: A number of features which can make it unrepresentative of the voters' intentions. Block voting regularly produces complete landslide majorities for the group of candidates with the highest level of support. Additionally, like first past the post methods, if there are many parties running and voters do not engage in tactical voting , a small cohesive group of voters, making up only a minority of
1920-534: A number of seats approximately proportional to their vote share. Other systems may be insufficiently compensatory, and this may result in overhang seats , where parties win more seats in the constituency system than they would be entitled to based on their vote share. Variations of this include the Additional Member System , and Alternative Vote Plus , in which voters cast votes for both single-member constituencies and multi-member constituencies;
2016-454: A result, some countries have leveling seats to award to parties whose seat totals are lower than their proportion of the national vote. In addition to the electoral threshold (the minimum percentage of the vote that a party must obtain to win seats), there are several different ways to allocate seats in proportional systems. There are two main types of systems: highest average and largest remainder . Highest average systems involve dividing
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#17327765870882112-451: A second one is given 10 points. The next eight consecutive preferences are awarded 8, 7, 6, 5, 4, 3, 2 and 1 point. All remaining preferences receive zero points. In positional voting, the weightings ( w ) of consecutive preferences from first to last decline monotonically with rank position ( n ). However, the rate of decline varies according to the type of progression employed. Lower preferences are more influential in election outcomes where
2208-483: A series of checkboxes, preferential block voting uses a preferential ballot . A slate of clones of the top preferred candidate will win every seat under both systems, however in preferential block voting this is instead the instant-runoff winner. In Brazil, where Senatorial elections alternate between FPTP and block voting, each main candidate is registered along with two substitutes. Votes in either election are cast and counted based on these three-candidate slates; when
2304-498: A single round of voting using ranked voting and the other using multiple elections, to successively narrow the field of candidates. Both are primarily used for single-member constituencies. Runoff can be achieved in a single election using instant-runoff voting (IRV), whereby voters rank candidates in order of preference; this system is used for parliamentary elections in Australia and Papua New Guinea . If no candidate receives
2400-414: A single round of voting. The party-list version of block voting is party block voting (PBV), also called the general ticket , which also elects members by plurality in multi-member districts. In such a system, each party puts forward a slate of candidates, a voter casts just one vote, and the party winning a plurality of votes sees its whole slate elected, winning all the seats. Plurality block voting
2496-444: A single winner is to be elected, the electoral system is winner-take all. The same can be said for elections where only one person is elected per district, since the district elections are also winner-take-all, therefore the electoral system as a whole is also usually non-proportional. Some systems where multiple winners are elected at once (in the same district) are also winner-take-all. In party block voting , voters can only vote for
2592-402: A single winner to a unique position, such as prime minister, president or governor, while others elect multiple winners, such as members of parliament or boards of directors. When electing a legislature , areas may be divided into constituencies with one or more representatives or the electorate may elect representatives as a single unit. Voters may vote directly for an individual candidate or for
2688-528: A substantial incentive to avoid wasted votes by casting all of their votes for a slate of candidates from a major party. Parties in block voting systems can also benefit from strategic nomination . Coalitions are actively hurt when they have more candidates than there are seats to fill, as vote-splitting will occur. Similarly, a coalition has a substantial incentive to nominate a full slate of candidates, as otherwise supporting voters may cast some of their remaining votes for opposing candidates. Bullet voting
2784-412: A system used in eight countries. Approval voting is a choose-all-you-like voting system which aims to increase the number of candidates that win with majority support. Voters are free to pick as many candidates as they like and each choice has equal weight, independent of the number of candidates a voter supports. The candidate with the most votes wins. A runoff system in which candidates must receive
2880-483: A worse-ranked candidate must receive fewer points than a better-ranked candidate. The classic example of a positional voting electoral system is the Borda count . Typically, for a single-winner election with N candidates, a first preference is worth N points, a second preference N – 1 points, a third preference N – 2 points and so on until the last ( N th) preference that is worth just 1 point. So, for example,
2976-466: 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
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3072-444: Is a strategy in which a voter only votes for a single candidate in an attempt to stop them being beaten by additional choices. Because the voter is essentially wasting a portion of their vote, bullet voting is only a good strategy when the voter has a strong preference for their favorite and is unsure of, and/or indifferent to, the other candidates' relative chances of winning, for example, if the voter supports an independent candidate or
3168-433: Is a type of block voting method for multi-winner elections . Each voter may cast as many votes as the number of seats to be filled. The candidates with the most votes are elected. The usual result when the candidates divide into parties is that the most-popular party in the district sees its full slate of candidates elected, even if the party does not have support of majority of the voters. The term plurality at-large
3264-627: Is another form of proportional representation. In STV, multi-member districts are used and each voter casts one vote, being a ranked ballot marked for individual candidates, rather than voting for a party list. STV is used in Malta and the Republic of Ireland . To be certain of being elected, candidates must pass a quota (the Droop quota being the most common). Candidates that pass the quota are elected. If necessary to fill seats, votes are transferred from
3360-559: Is distinct from party block voting . In a block voting election, all candidates run against each other for m number of positions, where m is commonly called the district magnitude. Each voter selects up to m candidates on the ballot. Each of the voters have m votes, and are able to cast no more than one per candidate. They cannot vote for the same candidate more than once, as is permitted in cumulative voting . Voters are permitted to cast their votes across candidates of different parties ( ticket splitting ). The m candidates with
3456-410: Is either no popular vote, or the popular vote is only one stage of the election; in these systems the final vote is usually taken by an electoral college . In several countries, such as Mauritius or Trinidad and Tobago , the post of President is elected by the legislature. In others like India , the vote is taken by an electoral college consisting of the national legislature and state legislatures. In
3552-415: Is guaranteed 35 seats in the 60-seat Grand and General Council . In Greece the party receiving the most votes was given an additional 50 seats, a system which was abolished following the 2019 elections . Primary elections are a feature of some electoral systems, either as a formal part of the electoral system or informally by choice of individual political parties as a method of selecting candidates, as
3648-416: Is higher than the voting age. A total of 21 countries have compulsory voting , although in some there is an upper age limit on enforcement of the law. Many countries also have the none of the above option on their ballot papers. In systems that use constituencies , apportionment or districting defines the area covered by each constituency. Where constituency boundaries are drawn has a strong influence on
3744-410: Is in common usage in elections for representative members of a body who are elected or appointed to represent the whole membership of the body (for example, a city, state or province, nation, club or association). Where the system is used in a territory divided into multi-member electoral districts the system is commonly referred to as "block voting" or the "bloc vote". These systems are usually based on
3840-469: Is more favourable to candidates with many first preferences than the conventional Borda count. It has been described as a system "somewhere between plurality and the Borda count, but as veering more towards plurality". Simulations show that 30% of Nauru elections would produce different outcomes if counted using standard Borda rules. The Eurovision Song Contest uses a first preference worth 12 points, while
3936-402: Is straightforward. All the preferences cast by voters are awarded the points associated with their rank position. Then, all the points for each option are tallied and the one with the most points is the winner. Where a few winners ( W ) are instead required following the count, the W highest-ranked options are selected. Positional voting is not only a means of identifying a single winner but also
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4032-485: Is the two-round system , which is the most common system used for presidential elections around the world, being used in 88 countries. It is also used in 20 countries for electing the legislature. If no candidate achieves a majority of votes in the first round of voting, a second round is held to determine the winner. In most cases the second round is limited to the top two candidates from the first round, although in some elections more than two candidates may choose to contest
4128-591: Is the case in Italy . Primary elections limit the risk of vote splitting by ensuring a single party candidate. In Argentina they are a formal part of the electoral system and take place two months before the main elections; any party receiving less than 1.5% of the vote is not permitted to contest the main elections. In the United States, there are both partisan and non-partisan primary elections . Some elections feature an indirect electoral system, whereby there
4224-1763: Is the country with the most extensive experience in plurality-at-large voting. Positions where there are multiple winners usually use plurality-at-large voting, the exception is the election for sectoral representatives in the House of Representatives . The members of the Senate and all local legislatures are elected via this method. The members of the Interim Batasang Pambansa (the parliament) were also elected under this method in 1978 . The following countries use block plurality voting (not including party block voting using plurality) in their national electoral systems: Two-round system (TRS) in single-member districts, two-round block voting (BV) in dual-member districts, and List PR (simple quota largest remainder; closed-list) in larger districts + twice 20 nationally List PR (one set of 20 reserved for women) Block plurality voting (BV) in single nationwide constituency for 16 seats; D'Hondt method (8 seats) First-past-the-post (FPTP/SMP) 14 seats + Block plurality voting 6 seats All cantons, except: First-past-the-post (FPTP/SMP) in local constituencies + Block plurality voting (BV) nationwide First-past-the-post (FPTP/SMP) in single-member districts, Block plurality voting (BV) in multi-member districts seats + Block plurality voting (BV) nationwide First-past-the-post (FPTP/SMP) in single-member districts + Block plurality voting (BV) nationwide First-past-the-post (FPTP/SMP) in single-member districts + Block plurality voting (BV) nationwide Other countries using block voting: In France ,
4320-400: Is the most top-heavy positional voting system. An alternative mathematical sequence known as a geometric progression may also be used in positional voting. Here, there is instead a common ratio r between adjacent weightings. In order to satisfy the two validity conditions, the value of r must be less than one so that weightings decrease as preferences descend in rank. Where the value of
4416-670: Is the second most common electoral system for national legislatures, with 58 countries using it for this purpose, the vast majority of which are current or former British or American colonies or territories. It is also the second most common system used for presidential elections, being used in 19 countries. In cases where there are multiple positions to be filled, most commonly in cases of multi-member constituencies, there are several types of plurality electoral systems. Under block voting (also known as multiple non-transferable vote or plurality-at-large), voters have as many votes as there are seats and can vote for any candidate, regardless of party,
4512-524: Is used in Kuwait , the Pitcairn Islands and Vanuatu . In several countries, mixed systems are used to elect the legislature. These include parallel voting (also known as mixed-member majoritarian) and mixed-member proportional representation . In non-compensatory, parallel voting systems, which are used in 20 countries, members of a legislature are elected by two different methods; part of
4608-543: The Borda count , each candidate is given a number of points equal to their rank, and the candidate with the least points wins. This system is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority. This system is used to elect the ethnic minority representatives seats in the Slovenian parliament. The Dowdall system is used in Nauru for parliamentary elections and sees voters rank
4704-529: The Coombs' method and positional voting . Among the Cardinal electoral systems , the most well known of these is range voting , where any number of candidates are scored from a set range of numbers. A very common example of range voting are the 5-star ratings used for many customer satisfaction surveys and reviews. Other cardinal systems include satisfaction approval voting , highest median rules (including
4800-480: The Netherlands , elections are carried out using 'pure' proportional representation, with the votes tallied on a national level before assigning seats to parties. However, in most cases several multi-member constituencies are used rather than a single nationwide constituency, giving an element of geographical representation; but this can result in the distribution of seats not reflecting the national vote totals. As
4896-530: The Swiss Federal Council . In some formats there may be multiple rounds held without any candidates being eliminated until a candidate achieves a majority. Positional systems like the Borda Count are ranked voting systems that assign a certain number of points to each candidate, weighted by position. The most popular such system is first-preference plurality . Another well-known variant,
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#17327765870884992-624: The United States , the president is indirectly elected using a two-stage process; a popular vote in each state elects members to the electoral college that in turn elects the President. This can result in a situation where a candidate who receives the most votes nationwide does not win the electoral college vote, as most recently happened in 2000 and 2016 . In addition to the various electoral systems currently in use for political elections, there are numerous others which have been used in
5088-602: The Vermont Senate , with the elections of Vermont Progressive Party members Tim Ashe and Anthony Pollina . Historically, similar situations arose within the multi-member constituencies in the Parliament of the United Kingdom . Block voting, or block plurality voting, is often compared with preferential block voting as both systems tend to produce landslide victories for similar candidates. Instead of
5184-404: The age at which people are allowed to vote , with the youngest being 16 and the oldest 21. People may be disenfranchised for a range of reasons, such as being a serving prisoner, being declared bankrupt, having committed certain crimes or being a serving member of the armed forces. Similar limits are placed on candidacy (also known as passive suffrage), and in many cases the age limit for candidates
5280-549: The contingent vote where voters do not rank all candidates, but have a limited number of preference votes. If no candidate has a majority in the first round, all candidates are excluded except the top two, with the highest remaining preference votes from the votes for the excluded candidates then added to the totals to determine the winner. This system is used in Sri Lankan presidential elections, with voters allowed to give three preferences. The other main form of runoff system
5376-523: The majority judgment ), and the D21 – Janeček method where voters can cast positive and negative votes. Historically, weighted voting systems were used in some countries. These allocated a greater weight to the votes of some voters than others, either indirectly by allocating more seats to certain groups (such as the Prussian three-class franchise ), or by weighting the results of the vote. The latter system
5472-417: The spoiler effect ) and Gibbard's theorem (showing it is impossible to design a straightforward voting system, i.e. one where it is always obvious to a strategic voter which ballot they should cast). The most common categorizations of electoral systems are: single-winner vs. multi-winner systems and proportional representation vs. winner-take-all systems vs. mixed systems . In all cases, where only
5568-477: The "ward system" which is a municipal adaptation of single member plurality. The sole exception is London, Ontario which has recently changed to the Alternative Vote . When Toronto was amalgamated in 1997, the new entity's first election used a similar rule. From 1871 to 1988, British Columbia had some multi-member ridings using plurality-at-large, and others elected under single member plurality , with
5664-476: The allocation of seats in the multi-member constituencies is adjusted to achieve an overall seat allocation proportional to parties' vote share by taking into account the number of seats won by parties in the single-member constituencies. Vote linkage mixed systems are also compensatory, however they usually use different mechanism than seat linkage (top-up) method of MMP and usually aren't able to achieve proportional representation. Some electoral systems feature
5760-461: The binary number system, a common ratio greater than one-half must be employed. The higher the value of r , the slower the decrease in weightings with descending rank. Although not categorised as positional voting electoral systems, some non-ranking methods can nevertheless be analysed mathematically as if they were by allocating points appropriately. Given the absence of strict monotonic ranking here, all favoured options are weighted identically with
5856-441: The binary, ternary, octal and decimal number systems use a radix R of 2, 3, 8 and 10 respectively. The value R is also the common ratio of the geometric progression going up in rank order while r is the complementary common ratio descending in rank. Therefore, r is the reciprocal of R and the r ratios are respectively 1/2, 1/3, 1/8 and 1/10 for these positional number systems when employed in positional voting. As it has
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#17327765870885952-412: The candidates. First preference votes are counted as whole numbers, the second preferences by two, third preferences by three, and so on; this continues to the lowest possible ranking. The totals for each candidate determine the winners. Proportional representation is the most widely used electoral system for national legislatures, with the parliaments of over eighty countries elected by various forms of
6048-407: The chosen progression employs a sequence of weightings that descend relatively slowly with rank position. The more slowly weightings decline, the more consensual and less polarising positional voting becomes. This figure illustrates such declines over ten preferences for the following four positional voting electoral systems: To aid comparison, the actual weightings have been normalised; namely that
6144-472: The decimal point are employed rather than fractions. (This system should not be confused with the use of sequential divisors in proportional systems such as proportional approval voting , an unrelated method.) A similar system of weighting lower-preference votes was used in the 1925 Oklahoma primary electoral system . For a four-candidate election, the Dowdall point distribution would be this: This method
6240-435: The denominators of the above fractional weightings could form an arithmetic progression instead; namely 1/1, 1/2, 1/3, 1/4 and so on down to 1/ N . This further mathematical sequence is an example of a harmonic progression . These particular descending rank-order weightings are in fact used in N -candidate positional voting elections to the Nauru parliament . For such electoral systems, the weighting ( w n ) allocated to
6336-417: The district seats. Weighted systems are still used in corporate elections, with votes weighted to reflect stock ownership. Dual-member proportional representation is a proposed system with two candidates elected in each constituency, one with the most votes and one to ensure proportionality of the combined results. Biproportional apportionment is a system where the total number of votes is used to calculate
6432-423: The election of municipal councilors takes place by majority vote plurinominal, in two rounds with panachage : In British Columbia , Canada, all local governments are elected using bloc voting for city councils and for other multi-member bodies (there called "at-large" voting). In other Canadian provinces, smaller cities are generally elected under plurality-at-large, while larger cities are generally elected under
6528-429: The first preference is a , the weighting ( w n ) awarded to a given rank position ( n ) is defined below. w n = a r n − 1 , 0 ≤ r < 1 {\displaystyle w_{n}=ar^{n-1},\qquad 0\leq r<1} For example, the sequence of consecutively halved weightings of 1, 1/2, 1/4, 1/8, … as used in the binary number system constitutes
6624-418: The first preference is set at one and the other weightings in the particular sequence are scaled by the same factor of 1/ a . The relative decline of weightings in any arithmetic progression is constant as it is not a function of the common difference d . In other words, the relative difference between adjacent weightings is fixed at 1/ N . In contrast, the value of d in a harmonic progression does affect
6720-401: The former, the score that each voter gives to each candidate is uniquely determined by the candidate's rank; in the latter, each voter is free to give any score to any candidate. In positional voting, voters complete a ranked ballot by expressing their preferences in rank order. The rank position of each voter preference is allotted a specific fixed weighting. Typically, the higher the rank of
6816-479: The island nation of Nauru is called the Dowdall system as it was devised by Nauru's Secretary for Justice (Desmond Dowdall) in 1971. Here, each voter awards the first-ranked candidate with 1 point, while the 2nd-ranked candidate receives 1 ⁄ 2 a point, the 3rd-ranked candidate receives 1 ⁄ 3 of a point, etc. When counting candidate tallies in Nauru, decimal numbers rounded to three places after
6912-419: The least successful candidates. Surplus votes held by successful candidates may also be transferred. Eventually all seats are filled by candidates who have passed the quota or there are only as many remaining candidates as the number of remaining seats. Under single non-transferable vote (SNTV) voters can vote for only one candidate, with the candidates receiving the most votes declared the winners; this system
7008-823: The likely outcome of elections in the constituency due to the geographic distribution of voters. Political parties may seek to gain an advantage during redistricting by ensuring their voter base has a majority in as many constituencies as possible, a process known as gerrymandering . Historically rotten and pocket boroughs , constituencies with unusually small populations, were used by wealthy families to gain parliamentary representation. Positional voting Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Positional voting
7104-402: The list of candidates of a single party, with the party receiving the most votes winning all seats. This is used in five countries as part of mixed systems. Plurality voting is a system in which the candidate(s) with the highest number of votes wins, with no requirement to get a majority of votes. In cases where there is a single position to be filled, it is known as first-past-the-post ; this
7200-505: The membership is elected by a plurality or majority vote in single-member constituencies and the other part by proportional representation. The results of the constituency vote have no effect on the outcome of the proportional vote. In compensatory mixed-member systems the results of the proportional vote are adjusted to balance the seats won in the constituency vote. The mixed-member proportional systems , in use in eight countries, provide enough compensatory seats to ensure that parties have
7296-414: The most votes (who may or may not obtain a majority of available votes or support from the majority of the voters) are declared elected and will fill the positions. Due to multiple voting, when a party runs more than one candidate, it is impossible to know if the party had support of as many voters as the party tally of votes (up to number of voters participating in the election) or if it had support of just
7392-486: The number of each varying from one election to the next. Other Canadian provincial legislatures have in the past used plurality-at-large or single transferable vote , but now all members of provincial legislatures are exclusively elected under single-member plurality. In Hong Kong , block voting is used for a tiny proportion of the territory's population to elect the members of the Election Committee , which
7488-451: The number of seats each party is due, followed by a calculation of the constituencies in which the seats should be awarded in order to achieve the total due to them. For proportional systems that use ranked choice voting , there are several proposals, including CPO-STV , Schulze STV and the Wright system , which are each considered to be variants of proportional representation by means of
7584-433: The number of voters equivalent to the votes received by the most popular candidate and the other candidates of that party merely received votes from subset of that group. Candidates are running in a three-member district; each of the 10,000 voters may cast three votes (but do not have to). Voters may not cast more than one vote for a single candidate. Party A has about 35% support among the electorate, Party B around 25% and
7680-453: The past, are only used in private organizations (such as electing the board members for a corporation or a student organization), or have only ever been made as proposals but not implemented. Among the Ranked systems these include Bucklin voting , the various Condorcet methods ( Copeland's , Dodgson's , Kemeny-Young , Maximal lotteries , Minimax , Nanson's , Ranked pairs , Schulze ),
7776-420: The points are respectively 4, 3, 2 and 1 for a four-candidate election. Mathematically, the point value or weighting ( w n ) associated with a given rank position ( n ) is defined below; where the weighting of the first preference is a and the common difference is d . w n = a − ( n − 1 ) d {\displaystyle w_{n}=a-(n-1)d} where
7872-428: The points awarded by the voters are then tallied and the options ranked according to the points total. Therefore, having the highest tally, option A is the winner here. Note that the election result also generates a full ranking of all the options. For positional voting, any distribution of points to the rank positions is valid, so long as the points are weakly decreasing in the rank of each candidate. In other words,
7968-439: The preference, the more points it is worth. Occasionally, it may share the same weighting as a lower-ranked preference but it is never worth fewer points. Usually, every voter is required to express a unique ordinal preference for each option on the ballot in strict descending rank order. However, a particular positional voting system may permit voters to truncate their preferences after expressing one or more of them and to leave
8064-501: The rate of its decline. The higher its value, the faster the weightings descend. Whereas the lower the value of the common ratio r for a geometric progression, the faster its weightings decline. The weightings of the digit positions in the binary number system were chosen here to highlight an example of a geometric progression in positional voting. In fact, the consecutive weightings of any digital number system can be employed since they all constitute geometric progressions. For example,
8160-541: The remaining options unranked and consequently worthless. Similarly, some other systems may limit the number of preferences that can be expressed. For example, in the Eurovision Song Contest only their top ten preferences are ranked by each country although many more than ten songs compete in the contest. Again, unranked preferences have no value. In positional voting, ranked ballots with tied options are normally considered as invalid. The counting process
8256-558: The remaining voters primarily support independent candidates. Candidates of Party A won in a landslide, even though they only received a plurality (35–37%) among the voters (10,000). This is because most parties run as many candidates as there are open seats and voters of a party usually do not split their ticket, but vote for all candidates of that party. By contrast, a single transferable vote system would likely elect 1 candidate from party A, 1 candidate from party B and 1 independent candidate in this scenario. The block voting system has
8352-469: The seat is filled up on the next scheduled election, such as in 1951, 1955 and 2001. There are alternative ways of selecting a replacement in such systems: one way is to fill any seat that becomes empty by appointing the most popular unsuccessful candidate in the last election, i.e. a countback . This was used in the City of Edmonton (Canada) following the 1905 Edmonton municipal election . The Philippines
8448-422: The second round; in these cases the second round is decided by plurality voting. Some countries use a modified form of the two-round system, such as Ecuador where a candidate in the presidential election is declared the winner if they receive 40% of the vote and are 10% ahead of their nearest rival, or Argentina (45% plus 10% ahead), where the system is known as ballotage . In some cases, a runoff may be held using
8544-661: The single transferable vote. Among the proportional voting systems that use rating are Thiele's voting rules and Phragmen's voting rule . A special case of Thiele's voting rules is Proportional Approval Voting . Some proportional systems that may be used with either ranking or rating include the Method of Equal Shares and the Expanding Approvals Rule . In addition to the specific method of electing candidates, electoral systems are also characterised by their wider rules and regulations, which are usually set out in
8640-428: The smallest radix, the rate of decline in preference weightings is slowest when using the binary number system. Although the radix R (the number of unique digits used in the number system) has to be an integer, the common ratio r for positional voting does not have to be the reciprocal of such an integer. Any value between zero and just less than one is valid. For a slower descent of weightings than that generated using
8736-486: The system. Party-list proportional representation is the single most common electoral system and is used by 80 countries, and involves voters voting for a list of candidates proposed by a party. In closed list systems voters do not have any influence over the candidates put forward by the party, but in open list systems voters are able to both vote for the party list and influence the order in which candidates will be assigned seats. In some countries, notably Israel and
8832-821: The top F rank positions in any order on each ranked ballot and the other candidates in the bottom N - F rank positions. This is essential as the weighting of each rank position is fixed and common to each and every ballot in positional voting. Unranked single-winner methods that can be analysed as positional voting electoral systems include: And unranked methods for multiple-winner elections (with W winners) include: Plurality-at-large voting Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Plurality block voting
8928-399: The voters, can elect all the open seats by merely constituting a plurality . Under block voting, a slate of clones of the top-place candidate may win every available seat. A voter does have the option to vote for candidates of different political parties if they wish, but if the largest group of voters have strong party loyalty, there is nothing the other voters or parties can do to prevent
9024-409: The votes received by each party by a divisor or vote average that represents an idealized seats-to-votes ratio , then rounding normally. In the largest remainder system, parties' vote shares are divided by an electoral quota . This usually leaves some seats unallocated, which are awarded to parties based on which parties have the largest number of "leftover" votes. Single transferable vote (STV)
9120-511: 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. Some electoral systems elect
9216-500: Was used in colonial Rhodesia for the 1962 and 1965 elections . The elections featured two voter rolls (the 'A' roll being largely European and the 'B' roll largely African); the seats of the House Assembly were divided into 50 constituency seats and 15 district seats. Although all voters could vote for both types of seats, 'A' roll votes were given greater weight for the constituency seats and 'B' roll votes greater weight for
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