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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 (also called Total Vote Runoff or TVR). Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
The Nanson method is based on the original work of the mathematician Edward J. Nanson in 1882. [1]
Nanson's method eliminates those choices from a Borda count tally that are at or below the average Borda count score, then the ballots are retallied as if the remaining candidates were exclusively on the ballot. This process is repeated if necessary until a single winner remains.
If a Condorcet winner exists, they will be elected. If not, (there is a Condorcet cycle) then the preference with the smallest majority will be eliminated. [1] : 214
Nanson's method can be adapted to handle incomplete ballots (including "plumping") and equal rankings ("bracketing"), though he describes two different methods to handle these cases: a theoretically correct method involving fractions of a vote, and a practical method involving whole numbers (which has the side effect of diminishing the voting power of voters who plump or bracket). [1] : 231, 235 This then allows the use of Approval-style voting for uninformed voters who merely wish to approve of some candidates and disapprove of others. [1] : 236
The method can be adapted to multi-winner elections by removing the name of a winner from the ballots and re-calculating, though this just elects the highest-ranked n candidates and does not result in proportional representation. [1] : 240
Schwartz in 1986 studied a slight variant of Nanson's rule, in which candidates less than but not equal to the average Borda count score are eliminated in each round. [2]
Candidates are voted for on ranked ballots as in the Borda count. Then, the points are tallied in a series of rounds. In each round, the candidate with the fewest points is eliminated, and the points are re-tallied as if that candidate were not on the ballot.
This method actually predates Nanson's, who notes it was already in use by the Trinity College Dialectic Society. [1] : 217
It was systematized by Joseph M. Baldwin [3] in 1926, who incorporated a more efficient matrix tabulation [4] and extended it to support incomplete ballots and equal rankings, by counting fractional points in such cases.
The two methods have been confused with each other in some literature. [2]
This system has been proposed for use in the United States under the name "Total Vote Runoff", by Edward B. Foley and Eric Maskin, as a way to fix problems with the instant-runoff method in US jurisdictions that use it, ensuring majority support of the winner and electing more broadly-acceptable candidates. [5] [6] [7] [8] [9]
The Nanson method and the Baldwin method satisfy the Condorcet criterion. [2] Because Borda always gives any existing Condorcet winner more than the average Borda points, the Condorcet winner will never be eliminated.
They do not satisfy the independence of irrelevant alternatives criterion, the monotonicity criterion, the participation criterion, the consistency criterion and the independence of clones criterion, while they do satisfy the majority criterion, the mutual majority criterion, the Condorcet loser criterion and the Smith criterion. The Nanson method satisfies and the Baldwin method violates reversal symmetry. [10]
Both the Nanson and the Baldwin methods can be run in polynomial time to obtain a single winner. For the Baldwin method, however, at each stage, there might be several candidates with lowest Borda score. In fact, it is NP-complete to decide whether a given candidate is a Baldwin winner, i.e., whether there exists an elimination sequence that leaves a given candidate uneliminated. [11]
Both methods are computationally more difficult to manipulate than Borda's method. [12]
Nanson's method was used in city elections in the U.S. town of Marquette, Michigan in the 1920s. [13] It was formerly used by the Anglican Diocese of Melbourne and in the election of members of the University Council of the University of Adelaide. It was used by the University of Melbourne until 1983.
Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added, and the candidate with the highest total is elected. It has been described by various other names including evaluative voting, utilitarian voting, interval measure voting, the point system, ratings summation, 0-99 voting, average voting and utilityvoting. It is a type of cardinal voting electoral system, and aims to implement the utilitarian social choice rule.
A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
Copeland's method is a ranked voting method based on a scoring system of pairwise "wins", "losses", and "ties". The method has a long history:
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.
An electoral system satisfies the Condorcet winner criterion if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidates – that is, a candidate preferred by more voters than any others – is the Condorcet winner, although Condorcet winners do not exist in all cases. It is sometimes simply referred to as the "Condorcet criterion", though it is very different from the "Condorcet loser criterion". Any voting method conforming to the Condorcet winner criterion is known as a Condorcet method. The Condorcet winner is the person who would win a two-candidate election against each of the other candidates in a plurality vote. For a set of candidates, the Condorcet winner is always the same regardless of the voting system in question, and can be discovered by using pairwise counting on voters' ranked preferences.
The participation criterion is a voting system criterion. Voting systems that fail the participation criterion are said to exhibit the no show paradox and allow a particularly unusual strategy of tactical voting: abstaining from an election can help a voter's preferred choice win. The criterion has been defined as follows:
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority of voters, then that candidate must win".
The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states that if there is a subset S of the candidates, such that more than half of the voters strictly prefer every member of S to every candidate outside of S, this majority voting sincerely, the winner must come from S. This is similar to but stricter than the majority criterion, where the requirement applies only to the case that S contains a single candidate. This is also stricter than the majority loser criterion, where the requirement applies only to the case that S contains all but one candidate. The mutual majority criterion is the single-winner case of the Droop proportionality criterion.
In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion but does not imply the Condorcet winner criterion.
Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, ranked pairs, Kemeny-Young method, and Schulze method. Methods that fail include Bucklin voting, instant-runoff voting and Condorcet methods that fail the Condorcet loser criterion such as Minimax.
The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. Woodall defined the criterion as "[a]dding a later preference to a ballot should not harm any candidate already listed." For example, a ranked voting method in which a voter adding a 3rd preference could reduce the likelihood of their 1st preference being selected, fails later-no-harm.
The summability criterion is a voting system criterion, used to objectively compare electoral systems. The criterion states:
The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the next-lowest gets 1 point, etc., and the highest-ranked candidate gets n − 1 points, where n is the number of candidates. Once all votes have been counted, the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.
Instant-runoff voting (IRV) is an electoral system that uses ranked voting. Its purpose is to elect the majority choice in single-member districts in which there are more than two candidates and thus help ensure majority rule. It is a single-winner version of single transferable voting. Formerly the term "instant-runoff voting" was used for what many people now call contingent voting or supplementary vote.
The majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win.
The term ranked voting, also known as preferential voting or ranked choice voting, pertains to any voting system where voters use a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally. An electoral system that utilizes ranked voting employs one of numerous counting methods to determine the winning candidate or candidates. Additionally, in some ranked voting systems, officials mandate voters to rank a specific number of candidates, sometimes all; while in others, voters may rank as many candidates as they desire.
The later-no-help criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to win. Voting systems that fail the later-no-help criterion are vulnerable to the tactical voting strategy called mischief voting, which can deny victory to a sincere Condorcet winner.
Homogeneity is a common property for voting systems. The property is satisfied if, in any election, the result depends only on the proportion of ballots of each possible type. Specifically, if every ballot is replicated the same number of times, then the result should not change.
Comparison of electoral systems is the result of comparative politics for electoral systems. Electoral systems are the rules for conducting elections, a main component of which is the algorithm for determining the winner from the ballots cast. This article discusses methods and results of comparing different electoral systems, both those that elect a unique candidate in a 'single-winner' election and those that elect a group of representatives in a multiwinner election.
STAR voting is an electoral system for single-seat elections. Variations also exist for multi-winner and proportional representation elections. The name stands for "Score then Automatic Runoff", referring to the fact that this system is a combination of score voting, to pick two finalists with the highest total scores, followed by an "automatic runoff" in which the finalist who is preferred on more ballots wins. It is a type of cardinal voting electoral system.
In each case where on a voting paper no preference is expressed as between two candidates, half a preference is to be credited to each of the two candidates … For each paper where any number, p, of candidates are placed equal with a preference ranking as first, 1/p is to be credited to each of the candidates so placed.
the way Alaska uses ranked-choice voting also caused the defeat of Begich, whom most Alaska voters preferred to Democrat Mary Peltola … A candidate popular only with the party's base would be eliminated early in a Total Vote Runoff, leaving a more broadly popular Republican to compete against a Democrat.
{{cite journal}}: Cite journal requires |journal= (help)a small but significant adjustment to the "instant runoff" method … equivalent to a candidate's Borda score, and eliminating sequentially the candidate with the lowest total votes
Begich and Peltola each get half a vote by being tied for second place on this ballot
In this respect, TVR differs from Baldwin's method, which without checking whether any candidate has more than 50% of first-place votes would immediately recalculate Borda scores