Condorcet methods
88-433: 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 First-preference plurality ( FPP ) also known as single-member district plurality ( SMDP )—often shortened simply to plurality —is
176-515: 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
264-406: 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
352-727: A hung parliament . An example of this was the 2010–2015 coalition government in the United Kingdom , which was composed of the Conservative Party and the Liberal Democrats . The Conservatives won the most seats of any single party in the 2010 election, but fell short of an absolute majority. However, by combining with the Liberal Democrats a solid majority in the House of Commons was created. This
440-424: A single-winner voting rule. Voters typically mark one candidate as their favorite, and the candidate with the largest number of first-preference marks (a plurality ) is elected, regardless of whether they have over half of all votes (a majority ). It is sometimes called first-past-the-post (FPTP) in reference to gambling on horse races (where bettors would guess which horse they thought would be first past
528-623: A "Parliament full of second-choices who no one really wanted but didn't really object to either." However, FPP often results in strategic voting , which has prevented extreme left- and right-wing parties from gaining parliamentary seats, as opposed to proportional representation . This also implies that strategic voting is necessary to keep extremists from gaining seats, which often fails to materialize in practice for multiple reasons. In comparison, many other systems encourage voters to rank other candidates and thereby not (or at least less often to) have to strategically compromise on their first choice at
616-475: 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
704-425: A contributory factor in the country adopting the apartheid system after the 1948 general election in that country. Leblang and Chan found that a country's electoral system is the most important predictor of a country's involvement in war, according to three different measures: (1) when a country was the first to enter a war; (2) when it joined a multinational coalition in an ongoing war; and (3) how long it stayed in
792-518: A geographical base, parties that are small UK-wide can still do very well". On the other hand, minor parties that do not concentrate their vote usually end up getting a much lower proportion of seats than votes, as they lose most of the seats they contest and 'waste' most of their votes. The ERS also says that in FPP elections using many separate districts "small parties without a geographical base find it hard to win seats". Make Votes Matter said that in
880-403: 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,
968-415: 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 =
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#17327725646071056-542: A government without being the largest party. The use of proportional representation (PR) may enable smaller parties to become decisive in the country's legislature and gain leverage they would not otherwise enjoy, although this can be somewhat mitigated by a large enough electoral threshold . They argue that FPP generally reduces this possibility, except where parties have a strong regional basis. A journalist at Haaretz noted that Israel's highly proportional Knesset "affords great power to relatively small parties, forcing
1144-448: 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
1232-430: A majority of seats just requires receiving more than half the vote in more than half the districts—even if the other party receives all the votes cast in the other districts—so just over a quarter of the vote is theoretically enough to win a majority in the legislature. With enough candidates splitting the vote in a district, the total number of votes needed to win can be made arbitrarily small . Under first-past-the-post,
1320-615: A majority of the votes cast in Canada only three times since 1921: in 1940 , 1958 and 1984 . In the United Kingdom, 19 of the 24 general elections since 1922 have produced a single-party majority government. In all but two of them ( 1931 and 1935 ), the leading party did not take a majority of the votes across the UK. In some cases, this can lead to a party receiving the plurality or even majority of total votes yet still failing to gain
1408-485: 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
1496-598: 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,
1584-507: A minor party in protest at its policies, since to do so would likely only help the major party's main rival. Rather than curtailing extreme voices, FPP today empowers the (relatively) extreme voices of the Labour and Conservative party memberships." For example, the electoral system of Hungary , a mixed system dominated by FPP have seen Fidesz (right-wing, populist party) win 135 seats in the 2022 Hungarian parliamentary election and has remained
1672-472: A plurality of legislative seats. This results in a situation called a majority reversal or electoral inversion . Famous examples of the second-place party (in votes nationally) winning a majority of seats include the elections in Ghana in 2012 , New Zealand in 1978 and 1981 , and the United Kingdom in 1951 . Famous examples of the second placed party (in votes nationally) winning a plurality of seats include
1760-620: A powerful electoral incentive for large parties to target similar segments of voters with similar policies. The effect of this reduces political diversity in a country because the larger parties are incentivized to coalesce around similar policies. The ACE Electoral Knowledge Network describes India's use of FPTP as a "legacy of British colonialism". Duverger's law is an idea in political science which says that constituencies that use first-past-the-post methods will lead to two-party systems , given enough time. Economist Jeffrey Sachs explains: The main reason for America's majoritarian character
1848-498: A principle known in political science as Duverger's Law . Smaller parties are trampled in first-past-the-post elections. However, most countries with first-past-the-post elections have multiparty legislatures (albeit with two parties larger than the others), the United States being the major exception. There is a counter-argument to Duverger's Law, that while on the national level a plurality system may encourage two parties, in
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#17327725646071936-756: A public election in 1840 by his son Rowland for the Adelaide City Council in Australia. STV saw its first national use in Denmark in 1855, and was reinvented several times in the 19th century. 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
2024-451: 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
2112-490: A significant number of safe seats , where a representative is sheltered from any but the most dramatic change in voting behavior. In the UK, the Electoral Reform Society estimates that more than half the seats can be considered as safe. It has been claimed that members involved in the 2009 expenses scandal were significantly more likely to hold a safe seat. The House of Commons of England originated in
2200-548: A small party may draw votes and seats away from a larger party that it is more similar to, and therefore give an advantage to one it is less similar to. For example, in the 2000 United States presidential election , the left-leaning Ralph Nader drew more votes from the left-leaning Al Gore , resulting in Nader spoiling the election for the Democrats. According to the political pressure group Make Votes Matter , FPTP creates
2288-453: A system based on plurality voting spread over many separate districts is that the larger parties, and parties with more geographically concentrated support, gain a disproportionately large share of seats, while smaller parties with more evenly distributed support gain a disproportionately small share. This is because in doing this they win many seats and do not 'waste' many votes in other areas. As voting patterns are similar in about two-thirds of
2376-582: A tendency for Independentista voters to support Populares candidates. This phenomenon is responsible for some Popular victories, even though the Estadistas have the most voters on the island, and is so widely recognised that Puerto Ricans sometimes call the Independentistas who vote for the Populares "melons", because that fruit is green on the outside but red on the inside (in reference to
2464-466: A vote could be considered as wasted . FPP wastes fewer votes when it is used in two-party contests. But waste of votes and minority governments are more likely when large groups of voters vote for three, four or more parties as in Canadian elections. Canada uses FPP and only two of the last seven federal Canadian elections ( 2011 and 2015 ) produced single-party majority governments. In none of them did
2552-412: A war after becoming a party to it. When the people are fairly represented in parliament, more of those groups who may object to any potential war have access to the political power necessary to prevent it. In a proportional democracy, war and other major decisions generally requires the consent of the majority. The British human rights campaigner Peter Tatchell , and others, have argued that Britain entered
2640-483: 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,
2728-445: Is a government by one or more governing parties that hold an absolute majority of seats in a legislature . Such a government can consist of one party that holds a majority on its own, or be a coalition government of multiple parties. This is as opposed to a minority government , where the government doesn't have a majority, and needs to cooperate with opposition parties to get legislation passed. A government majority determines
First-past-the-post voting - Misplaced Pages Continue
2816-466: 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
2904-402: Is a prospect of a change in representation, leaving safer areas excluded from participation in an active campaign. Political parties operate by targeting districts, directing their activists and policy proposals toward those areas considered to be marginal, where each additional vote has more value. This feature of FPTP has often been used by its supporters in contrast to proportional systems. In
2992-469: 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
3080-407: Is related to kingmakers in that the lesser-known candidates may encourage their supporters to rank the other candidates a certain way. Supporters of electoral reform generally see this as a positive development, and claim that alternatives certain to FPP will encourage less negative and more positive campaigning, as candidates will have to appeal to a wider group of people. Opinions are split on whether
3168-402: 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
3256-494: Is that a portion of the electorate (2.7%) voted for Ralph Nader of the Green Party , and exit polls indicated that more of them would have preferred Gore (45%) to Bush (27%). The election was ultimately determined by the results from Florida , where Bush prevailed over Gore by a margin of only 537 votes (0.009%), which was far exceeded by the 97488 (1.635%) votes cast for Nader in that state. In Puerto Rico , there has been
3344-408: Is the electoral system for Congress. Members of Congress are elected in single-member districts according to the "first-past-the-post" (FPTP) principle, meaning that the candidate with the plurality of votes is the winner of the congressional seat. The losing party or parties win no representation at all. The first-past-the-post election tends to produce a small number of major parties, perhaps just two,
3432-400: 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
3520-696: The 2017 general election , "the Green Party, Liberal Democrats and UKIP (minor, non-regional parties) received 11% of votes between them, yet they shared just 2% of seats", and in the 2015 general election , "[t]he same three parties received almost a quarter of all the votes cast, yet these parties shared just 1.5% of seats." According to Make Votes Matter, in the 2015 UK general election UKIP came in third in terms of number of votes (3.9 million/12.6%), but gained only one seat in Parliament, resulting in one seat per 3.9 million votes. The Conservatives on
3608-507: The 151 seats in the House of Representatives at a federal election (this has happened three times, in 1975 , in 1996 and 2013 ). The largest majority government in Australia was elected in 1975, when the Coalition won 71.65% of the seats in a landslide victory . In electoral systems where one party usually wins a majority of seats on their own, such as first past the post , coalitions are rare, but may happen when an election returns
First-past-the-post voting - Misplaced Pages Continue
3696-431: The 1970s , where the first round selects two major contenders who go on to receive the overwhelming majority of votes. [REDACTED] Suppose that Tennessee is holding an election on the location of its capital . The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are: The preferences of each region's voters are: In FPTP, only
3784-414: The 20th century, many countries that previously used FPP have abandoned it in favor of other electoral systems, including the former British colonies of Australia and New Zealand . Most U.S. states still officially retain FPP for most elections. However, the combination of partisan primaries with the two-party system mean the country has effectively used a variation on the two-round system since
3872-564: The Condorcet and Borda count methods, which were respectively reinvented in the 18th century by the Marquis de Condorcet and Jean-Charles de Borda . More serious investigation into electoral systems came in the late 18th century, when several thinkers independently proposed systems of proportional representation to elect legislatures. The single transferable vote in particular was invented in 1819 by Thomas Wright Hill , and first used in
3960-480: The Iraq War primarily because of the political effects of FPP and that proportional representation would have prevented Britain's involvement in the war. To a greater extent than many others, the first-past-the-post method encourages "tactical voting". Voters have an incentive to vote for a candidate who they predict is more likely to win, as opposed to their preferred candidate who may be unlikely to win and for whom
4048-650: The Middle Ages as an assembly representing the gentry of the counties and cities of the Kingdom, each of which elected either one or two members of parliament (MPs) by block plurality voting . Starting in the 19th century, electoral reform advocates pushed to replace these multi-member constituencies with single-member districts. Elections to the Canadian House of Commons have always been conducted with FPP. The United States broke away from British rule in
4136-434: The absence of) of party primaries maybe strengthen or weaken this effect. In general, FPP has no mechanism that would benefit more moderate candidates and many supporters of FPP defend it electing the largest and most unified (even if more polarizing) minority over a more consensual majority supported candidate. Allowing people into parliament who did not finish first in their district was described by David Cameron as creating
4224-559: The aftermath of strong election performances. The term "majority government" may also be used for a stable long-term coalition of two or more parties to form an absolute majority. One example of such an electoral coalition is in Australia , where the Liberal and National parties have run as an electoral bloc, known simply as the Coalition , for decades. The Coalition is the only party or coalition in Australia to have won at least 90 of
4312-453: The alternative vote (better known as instant runoff voting outside the UK) achieves this better than other systems. Supporters and opponents of FPP often argue whether FPP advantages or disadvantages extremist parties. Among single-winner systems, FPP suffers from the center squeeze phenomenon , where more moderate candidates are squeezed out by more extreme ones. However, the different types (or
4400-592: The balance of power. A government is not a majority government if it only has a majority when counting parties outside the government that have a confidence agreement with it. A majority government is usually assured of having its legislation passed and rarely if ever, has to fear being defeated in parliament, a state also known as a working majority . In contrast, a minority government must constantly bargain for support from other parties in order to pass legislation and avoid being defeated on motions of no confidence . Single-party majority governments tend to be formed in
4488-461: 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
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#17327725646074576-441: 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
4664-407: 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
4752-416: The country in question in circumstances where the government's legislative agenda has broad public support, albeit potentially divided across party lines, or at least benefits society as a whole. However handing a legislative voting majority to a government which lacks popular support can be problematic where said government's policies favor only that fraction of the electorate that supported it, particularly if
4840-472: 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
4928-486: 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
5016-436: The districts, it is more likely that a single party will hold a majority of legislative seats under FPP than happens in a proportional system, and under FPP it is rare to elect a majority government that actually has the support of a majority of voters. Because FPP permits many wasted votes , an election under FPP is more easily gerrymandered. Through gerrymandering , electoral areas are designed deliberately to unfairly increase
5104-399: The election a center squeeze . By contrast, both Condorcet methods and score voting would return Nashville (the capital of Tennessee). Perhaps the most striking effect of FPP is the fact that the number of a party's seats in a legislature has nothing to do with its vote count in an election, only in how those votes were geographically distributed. This has been a target of criticism for
5192-629: The elections in Canada in 2019 and 2021 as well as in Japan in 2003 . Even when a party wins more than half the votes in an almost purely two-party-competition, it is possible for the runner-up to win a majority of seats. This happened in Saint Vincent and the Grenadines in 1966 , 1998 , and 2020 and in Belize in 1993 . Even with only two parties and equally-sized constituencies, winning
5280-407: The electorate divides on tribal, religious, or urban–rural lines. There is also the perceived issue of unfair coalitions where a smaller party can form a coalition with other smaller parties and form a government, without a clear mandate as was the case in the 2009 Israeli legislative election where the leading party Kadima , was unable to form a coalition so Likud , a smaller party, managed to form
5368-538: The finishing post). In social choice , FPP is generally treated as a degenerate variant of ranked voting , where voters rank the candidates, but only the first preference matters. As a result, FPP is usually implemented with a choose-one ballot , where voters place a single bubble next to their favorite candidate. FPP has been used to elect the British House of Commons since the Middle Ages . Throughout
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#17327725646075456-429: 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
5544-418: 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
5632-407: The first preferences matter. As such, the votes would be counted as 42% for Memphis, 26% for Nashville, 17% for Knoxville, and 15% for Chattanooga. Since Memphis has the most votes, it would win a FPTP election, even though it is far from the center of the state and a majority of voters would prefer Nashville . Similarly, instant-runoff voting would elect Knoxville , the easternmost city. This makes
5720-401: 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
5808-435: The government to give in to political blackmail and to reach compromises"; Tony Blair , defending FPP, argued that other systems give small parties the balance of power, and influence disproportionate to their votes. The concept of kingmakers is adjacent to how Winston Churchill criticized the alternative vote system as "determined by the most worthless votes given for the most worthless candidates." meaning that votes for
5896-480: The individual constituencies supermajorities will lead to the vote fracturing. It has been suggested that the distortions in geographical representation provide incentives for parties to ignore the interests of areas in which they are too weak to stand much chance of gaining representation, leading to governments that do not govern in the national interest. Further, during election campaigns the campaigning activity of parties tends to focus on marginal seats where there
5984-479: 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
6072-587: The largest party in Hungary since 2010 by changing the electoral system to mostly use FPP instead of the previous mixed system using mostly the two-round system . Since 2010, Fidesz has implemented other anti-democratic reforms that now mean the European Parliament no longer qualifies Hungary as a full democracy. Electoral reform campaigners have argued that the use of FPP in South Africa was
6160-514: The late 18th century, and its constitution provides for an electoral college to elect its president. Despite original intentions to the contrary, by the mid-19th century this college had transformed into a de facto use of FPP for each state's presidential election. This further morphed through the introduction of the party primary , which made American elections into a two-round system in practice. Non-plurality voting systems have been devised since at least 1299, when Ramon Llull came up with both
6248-524: The latter, smaller parties act as 'kingmakers' in coalitions as they have greater bargaining power and therefore, arguably, their influence on policy is disproportional to their parliamentary size- this is largely avoided in FPP systems where majorities are generally achieved. FPP often produces governments which have legislative voting majorities, thus providing such governments the legislative power necessary to implement their electoral manifesto commitments during their term in office. This may be beneficial for
6336-500: The leading party receive a majority of the votes. The position is sometimes summarized, in an extreme form, as "all votes for anyone other than the runner-up are votes for the winner." This is because votes for these other candidates deny potential support from the second-placed candidate, who might otherwise have won. Following the extremely close 2000 U.S. presidential election , some supporters of Democratic candidate Al Gore believed one reason he lost to Republican George W. Bush
6424-403: The least supported candidates may change the outcome of the election between the most supported candidates. In this case however, this is a feature of the alternative vote, since those votes would have otherwise been wasted (and in some sense this makes every vote count, as opposed to FPP), and this effect is only possible when no candidate receives an outright majority of first preference votes. it
6512-428: The method, many arguing that a fundamental requirement of an election system is to accurately represent the views of voters. FPP often creates "false majorities" by over-representing larger parties (giving a majority of the parliamentary/legislative seats to a party that did not receive a majority of the votes) while under-representing smaller ones. In Canada, majority governments have been formed due to one party winning
6600-410: The north of England. This pattern hides the large number of votes for the non-dominant party. Parties can find themselves without elected politicians in significant parts of the country, heightening feelings of regionalism. Party supporters (who may nevertheless be a significant minority) in those sections of the country are unrepresented. In the 2019 Canadian federal election Conservatives won 98% of
6688-410: The number of seats won by one party by redrawing the map such that one party has a small number of districts in which it has an overwhelming majority of votes (whether due to policy, demographics which tend to favor one party, or other reasons), and many districts where it is at a smaller disadvantage. The British Electoral Reform Society (ERS) says that regional parties benefit from this system. "With
6776-470: The number required for victory. For example, in the UK general election of 2005 , 52% of votes were cast for losing candidates and 18% were excess votes—a total of 70% "wasted" votes. On this basis a large majority of votes may play no part in determining the outcome. This winner-takes-all system may be one of the reasons why "voter participation tends to be lower in countries with FPP than elsewhere." The effect of
6864-584: The other hand received one seat per 34,000 votes. The winner-takes-all nature of FPP leads to distorted patterns of representation, since it exaggerates the correlation between party support and geography. For example, in the UK the Conservative Party represents most of the rural seats in England, and most of the south of England, while the Labour Party represents most of the English cities and most of
6952-585: The party colors). Because voters have to predict who the top two candidates will be, results can be significantly distorted: Proponents of other voting methods in single-member districts argue that these would reduce the need for tactical voting and reduce the spoiler effect . Examples include preferential voting systems, such as instant runoff voting , as well as the two-round system of runoffs and less tested methods such as approval voting and Condorcet methods . Wasted votes are seen as those cast for losing candidates, and for winning candidates in excess of
7040-420: 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
7128-428: 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,
7216-439: 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
7304-501: 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,
7392-541: 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
7480-553: The same time. On the other hand, the Constitution Society published a report in April 2019 stating that, "[in certain circumstances] FPP can ... abet extreme politics , since should a radical faction gain control of one of the major political parties, FPP works to preserve that party's position. ...This is because the psychological effect of the plurality system disincentivises a major party's supporters from voting for
7568-656: The seats in Alberta and Saskatchewan with only 68% of the vote. The lack of non-Conservative representation gives the appearance of greater Conservative support than actually exists. Similarly, in Canada's 2021 elections, the Conservative Party won 88% of the seats in Alberta with only 55% of the vote, and won 100% of the seats in Saskatchewan with only 59% of the vote. First-past-the-post within geographical areas tends to deliver (particularly to larger parties)
7656-428: 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
7744-490: 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: Majority government A majority government
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