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Social choice and electoral systems |
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Mathematicsportal |
The Oklahoma primary electoral system was a voting system used to elect one winner from a pool of candidates using preferential voting. Voters rank candidates in order of preference, and their votes are initially allocated to their first-choice candidate. If, after this initial count, no candidate has a majority of votes cast, a mathematical formula comes into play. The system was used for primary elections in Oklahoma when it was adopted in 1925 [1] until it was ruled unconstitutional by the Supreme Court of Oklahoma in 1926. [2]
The system is a hybrid between Dowdall voting and Bucklin voting. Voters rank candidates in order of preference. Like in Bucklin voting, voting proceeds in rounds, where the first candidate to reach a majority wins. However, unlike in Bucklin, and like in Dowdall, a second-preference vote is worth half as many points as a first-preference vote; a third-preference is worth a third of a point; and so on. The first candidate whose point totals exceed half the number of voters is declared winner. [3] [1]
As actually implemented in Oklahoma, the system required voters to rank half of all candidates.
Candidate | Preference | Votes |
---|---|---|
Alice | First choices | 21 |
Second choices | 8 (25) | |
Third choices | 7 [27⅓] | |
Bob | First choices | 9 |
Second choices | 10 (14) | |
Third choices | 5 [15⅔] | |
Carol | First choices | 17 |
Second choices | 16 (25) | |
Third choices | 4 [26⅓] | |
Dave | First choices | 20 |
Second choices | 10 (25) | |
Third choices | 26 [33⅔] | |
Emma | First choices | 18 |
Second choices | 7 (21.5) | |
Third choices | 9 [24½] |
In the above example, no candidate has 25.5 points, so we add the second-preference votes: each person's number of second-preference votes is divided by two and added onto their number of first-preference votes. This new total is shown in parentheses.
None of these totals exceeds the majority figure of 26 either, so the third-preference votes are now factored in. Each candidates number of third-preference votes is divided by three and added on, shown in square brackets. At this stage, Alice, Carol, and Dave all have totals in excess of 26, but Dave's total is the highest, so he is the winner despite being ranked first by fewer people than was Alice.
The nomination for U.S. Senate of impeached former Governor Jack C. Walton is said to have "frightened" the state "into a system of preferential voting as an escape from minority nominations." In his Senate nomination, Walton received only "an extremely small per cent of the total votes cast," yet was still selected as the Democratic Party candidate, [4] and this perceived injustice led to the Oklahoma Legislature resolving to adopt a different electoral system. However, it was not until the final day of debate on the law that the workings of the system chosen were agreed upon. [5]
The decision to require voters to rank their preferences, which contrasted with most other states' procedures merely giving people the option of doing so (for that matter, only eight states used preferential voting at all), [6] was an attempt to balance the competing concerns of preventing bullet voting (people deciding to list only their first choice) and of not forcing people to give any vote to candidates they found unacceptable. The Oklahoma Senate initially wanted to give second and third preferences equal weight, but the bill was eventually amended to weight them one-half and one-third respectively, it having been decided that this was "the more equitable practice." [5]
The initial adoption of what was a highly unusual electoral system caused significant comment in the media and in academia. The law was described as "the most interesting and important primary legislation of the year" by the American Political Science Review , which identified two particular features as particularly intriguing: firstly, the requirement that voters rank a certain number of candidates, and secondly, the "improvement" of giving lower-preference votes less weight: "Here, then, appears to be something new under the sun—compulsory preferential voting for all who take the trouble to come out to the primary!" [7] However, the requirement to rank candidates was also described as "obnoxious" and unfair to people who found only one candidate acceptable. [8] [9]
In 1926, the Oklahoma Supreme Court declared the 1925 law "null and void" and ruled that it was unconstitutional to "make it mandatory upon the voter to express a second choice when three or more candidates are running for a given office and a second and third choice when more than four candidates are running for a given office in order to have his vote counted" since such a principle could not "be harmonized with the constitutional guaranties [10] that no power [should] ever interfere to prevent the free exercise of the right of suffrage." [2] [11] A writ was issued banning elections from being held under the system. [3] Subsequently, Oklahoma's brief stint of preferential voting was analysed as having been "unsatisfactory." [6]
The two-round system, also called ballotage, top-two runoff, or two-round plurality, is a single winner voting method. It is sometimes called plurality-runoff, although this term can also be used for other, closely-related systems such as ranked-choice voting or the exhaustive ballot. It falls under the class of plurality-based voting rules, together with instant-runoff and first-past-the-post (FPP). In a two-round system, both rounds are held under choose-one voting, where the voter marks a single favorite candidate. The two candidates with the most votes in the first round proceed to a second round, where all other candidates are excluded.
The single transferable vote (STV), a type of proportional ranked choice voting, is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternative preferences if their preferred candidate is eliminated or elected with surplus votes, so that their vote is used to elect someone they prefer over others in the running. STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another.
In social choice, the negative responsiveness, perversity, or additional support paradox is a pathological behavior of some voting rules, where a candidate loses as a result of having "too much support" from some voters, or wins because they had "too much opposition". In other words, increasing (decreasing) a candidate's ranking or rating causes that candidate to lose (win), contrary to common sense. Electoral systems that do not exhibit perversity are said to satisfy the positive response or monotonicitycriterion.
John Calloway Walton was an American politician and the 5th Governor of Oklahoma, serving the shortest tenure. He was impeached and removed from office shortly into his first term. A populist member of the Democratic Party, Walton previously served as the 18th Mayor of Oklahoma City between 1919 and 1923.
Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the Georgist politician James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system.
In an election, a candidate is called a majority winner or majority-preferred candidate if more than half of all voters would support them in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the majority-rule principle, because they extend the principle of majority rule to elections with multiple candidates.
Nauru elects on a national level a head of state and a legislature. Parliament has 19 members, elected for a three-year term in multi-seat constituencies. The president is elected for a three-year term by the parliament.
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is never worth more. A valid progression of points or weightings may be chosen at will or it may form a mathematical sequence such as an arithmetic progression, a geometric one or a harmonic one. The set of weightings employed in an election heavily influences the rank ordering of the candidates. The steeper the initial decline in preference values with descending rank, the more polarised and less consensual the positional voting system becomes.
Instant-runoff voting (IRV) is a ranked voting method used in single-winner elections. IRV is also known outside the US as the alternative vote (AV). Today it is in use at a national level to elect the Australian House of Representatives, the National Parliament of Papua New Guinea, the President of Ireland and President of India. In Australia it is also used for elections to the legislative assemblies of all states and territories except Tasmania and the Australian Capital Territory, and for the Tasmanian Legislative Council.
Later-no-harm is a property of some ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause a higher-ranked candidate to lose.
An election for 19 of the 60 seats in Seanad Éireann, the Senate of the Irish Free State, was held on 17 September 1925. The election was by single transferable vote, with the entire state being used in a single 19-seat contest.
Ranked-choice voting (RCV), preferential voting (PV), or the alternative vote (AV), is a multi-round elimination rule based on first-past-the-post. In academic contexts, the system is generally called instant-runoff voting (IRV) to avoid conflating it with other methods of ranked voting in general. The rule works by simulating a series of primary and runoff elections, where the last-place finisher according to a plurality vote is eliminated in each round. RCV falls under the pluralitarian family of voting methods and is most closely related to first-past-the-post and two-round rules like partisan and nonpartisan primaries.
A valence issue is a political issue where there is a broad amount of consensus among voters. As valence issues are representative of a goal or quality, voters use valence issues to evaluate a political party’s effectiveness in producing this particular goal or quality.
An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.
Ranked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked system is one that depends only on which of two candidates is preferred by a voter, and as such does not incorporate any information about intensity of preferences. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them very different properties.
A major branch of social choice theory is devoted to the comparison of electoral systems, otherwise known as social choice functions. Viewed from the perspective of political science, electoral systems are rules for conducting elections and determining winners from the ballots cast. From the perspective of economics, mathematics, and philosophy, a social choice function is a mathematical function that determines how a society should make choices, given a collection of individual preferences.
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Round-robin, pairedcomparison, or tournamentvoting methods, are a set of ranked voting systems that choose winners by comparing every pair of candidates one-on-one, similar to a round-robin tournament. In each paired matchup, we record the total number of voters who prefer each candidate in a beats matrix. Then, a majority-preferred (Condorcet) candidate is elected, if one exists. Otherwise, if there is a cyclic tie, the candidate "closest" to being a Condorcet winner is elected, based on the recorded beats matrix. How "closest" is defined varies by method.