Range voting
Encyclopedia
Range voting is a voting system
for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.
A form of range voting was apparently used in some elections in Ancient Sparta by measuring how loudly the crowd shouted for different candidates; rough modern-day equivalents include the use of clapometers in some television shows and the judging processes of some athletic competitions. Approval voting
can be considered to be range voting with only two levels: approved (1) and disapproved (0).
; that is, each voter rates each candidate with a number within a specified range, such as 0 to 99 or 1 to 5. All candidates should be rated, unlike cumulative voting
where voters are not permitted to provide scores for more than some number of candidates. The scores for each candidate are summed, and the candidate with the highest sum is the winner. If voters are explicitly allowed to abstain from rating certain candidates, as opposed to implicitly giving the lowest number of points to unrated candidates, then a candidate's score would be the average rating from voters who did rate this candidate.
In some competitions subject to judges' scores, a truncated mean
is used to remove extreme scores. For example, range voting with truncated means is used in figure skating competitions to avoid the results of the third skater affecting the relative positions of two skaters who have already finished their performances (the independence of irrelevant alternatives
), using truncation to mitigate biases of some judges who have ulterior motives to score some competitors too high or low.
Another method of counting ratings ballots is to find the median
score of each candidate, and elect the candidate with the highest median score. This method is also referred to as Majority Judgment
. It could have the effect of reducing the incentive to exaggerate. A potential disadvantage is that multiway exact ties for winner may become common, although a method exists in Majority Judgment to break such ties. In conventional range voting, these ties would be extremely rare. Another consequence of using medians is that adding an "all-zero ballot"
can alter the election winner, which is arguably a disadvantage.
Range voting in which only two different votes may be submitted (0 and 1, for example) is equivalent to approval voting
. As with approval voting, range voters must weigh the adverse impact on their favorite candidate of ranking other candidates highly.
rate competitors on a numeric scale, although the fact that judges' ratings are public makes it less likely for them to engage in blatant tactical voting
. Range voting is common for things where there is no single winner: for instance on the Web
, sites allow users to rate items such as movies (Internet Movie Database
), comments, recipes, and many other things.
Dotmocracy
is an established paper-based group facilitation method that invites participants to brainstorm
ideas and then vote on a range of agreement for each idea in order to recognize which ideas have the most collective agreement.
Range voting has been used informally by various amateur clubs to make decisions such as meeting dates, event themes or what books to read.
Nashville, the capital in real life, likewise wins in the example. However, if voters from Knoxville and Chattanooga were to rate Nashville as 0 and/or both sets of voters were to rate Chattanooga as 10, the winner would be Chattanooga over Nashville by 508 to 428. This would be a better outcome for the voters in those cities than what they would get if they were to reflect their true preferences, and is considered to be an instance of tactical voting. Such tactical voting would be less effective if the ballots were counted using median scores.
Range voting satisfies the monotonicity criterion
, i.e. raising your vote's score for a candidate can never hurt their chances of winning. Also, in range voting, casting a sincere vote can never result in a worse election winner (from your point of view) than if you had simply abstained from voting. Range voting passes the favorite betrayal criterion, meaning that it never gives voters an incentive to rate their favorite candidate lower than a candidate they like less. Range voting advocates contend that this is a good property, because it leads to higher average voter satisfaction when voters are honest, and still gives voters the choice to strategically lower their scores for less preferred candidates if they choose.
Range voting is independent of clones
in the sense that if there is a set of candidates such that every voter gives the same rating to every candidate in this set, then the probability that the winner is in this set is independent of how many candidates are in the set.
In summary, range voting satisfies the monotonicity criterion
, the favorite betrayal criterion, the participation criterion
, the consistency criterion
, independence of irrelevant alternatives
, resolvability criterion
, and reversal symmetry
. It is immune to cloning, except for the obvious specific case in which a candidate with clones ties, instead of achieving a unique win. It does not satisfy either the Condorcet criterion
(i.e. is not a Condorcet method
) or the Condorcet loser criterion
, although with all-strategic voters and perfect information the Condorcet winner is a Nash equilibrium
. It does not satisfy the majority criterion
, but it satisfies a weakened form of it: a majority can force their choice to win, although they might not exercise that capability. It does not satisfy the later-no-harm criterion
, meaning that giving a positive rating to a less preferred candidate can cause a more preferred candidate to lose.
As it satisfies the criteria of a deterministic voting system, with non-imposition, non-dictatorship, monotonicity, and independence of irrelevant alternatives, it may appear that it violates Arrow's impossibility theorem
. The reason that range voting is not regarded as a counter-example to Arrow's theorem is that it is a cardinal voting system, while the "universality" criterion of Arrow's theorem effectively restricts that result to ordinal voting systems.
strategy, and a voter would want to give his least and most favorite candidates a minimum and a maximum score, respectively. If one candidate's backers engaged in this tactic and other candidates' backers cast sincere rankings for the full range of candidates, then the tactical voters would have a significant advantage over the rest of the electorate. When the population is large and there are two obvious and distinct front-runners, tactical voters seeking to maximize their influence on the result would give a maximum rating to their preferred candidate, and a minimum rating to the other front-runner; these voters would then give minimum and maximum scores to all other candidates so as to maximize expected utility.
However, there are examples in which voting maximum and minimum scores for all candidates is not optimal. Exit poll experiments have shown that voters tend to vote more sincerely for candidates they perceive have no chance of winning. Thus range voting may yield higher support for third party and independent candidates, unless those candidates become viable, than other common voting methods, creating what has been called the "nursery effect".
Range voting advocates argue that range voting systems (including approval voting) give no reason to ever dishonestly rank a less-preferred candidate over a more-preferred one in 3-candidate elections. However, detractors respond that it provides motivation to rank a less-preferred and more-preferred candidate equally or near-equally (i.e., both 0-1 or both 98-99). This could lead to undemocratic results if different segments of the population used strategy at significantly different rates.
, now endorses range voting. No elected official in the United States is known to endorse range voting.
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.
A form of range voting was apparently used in some elections in Ancient Sparta by measuring how loudly the crowd shouted for different candidates; rough modern-day equivalents include the use of clapometers in some television shows and the judging processes of some athletic competitions. Approval voting
Approval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
can be considered to be range voting with only two levels: approved (1) and disapproved (0).
Voting system
Range voting uses a ratings ballotRatings ballot
A ratings ballot is a ballot on which candidates are rated on a cardinal scale. For example candidates in an election could be rated from 0 to 99 or from -5 to 5 or from 1 to 10...
; that is, each voter rates each candidate with a number within a specified range, such as 0 to 99 or 1 to 5. All candidates should be rated, unlike cumulative voting
Cumulative voting
Cumulative voting is a multiple-winner voting system intended to promote more proportional representation than winner-take-all elections.- History :...
where voters are not permitted to provide scores for more than some number of candidates. The scores for each candidate are summed, and the candidate with the highest sum is the winner. If voters are explicitly allowed to abstain from rating certain candidates, as opposed to implicitly giving the lowest number of points to unrated candidates, then a candidate's score would be the average rating from voters who did rate this candidate.
In some competitions subject to judges' scores, a truncated mean
Truncated mean
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both.For...
is used to remove extreme scores. For example, range voting with truncated means is used in figure skating competitions to avoid the results of the third skater affecting the relative positions of two skaters who have already finished their performances (the independence of irrelevant alternatives
Independence of irrelevant alternatives
Independence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....
), using truncation to mitigate biases of some judges who have ulterior motives to score some competitors too high or low.
Another method of counting ratings ballots is to find the median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
score of each candidate, and elect the candidate with the highest median score. This method is also referred to as Majority Judgment
Majority Judgment
Majority Judgment is a single-winner voting system proposed by Michel Balinski and Rida Laraki. Voters freely grade each candidate in one of several named ranks, for instance from "excellent" to "bad", and the candidate with the highest median grade is the winner. If more than one candidate has the...
. It could have the effect of reducing the incentive to exaggerate. A potential disadvantage is that multiway exact ties for winner may become common, although a method exists in Majority Judgment to break such ties. In conventional range voting, these ties would be extremely rare. Another consequence of using medians is that adding an "all-zero ballot"
can alter the election winner, which is arguably a disadvantage.
Range voting in which only two different votes may be submitted (0 and 1, for example) is equivalent to approval voting
Approval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
. As with approval voting, range voters must weigh the adverse impact on their favorite candidate of ranking other candidates highly.
Alternative use
The range voting concept has been used in non-political contexts also. Sports such as gymnasticsGymnastics
Gymnastics is a sport involving performance of exercises requiring physical strength, flexibility, agility, coordination, and balance. Internationally, all of the gymnastic sports are governed by the Fédération Internationale de Gymnastique with each country having its own national governing body...
rate competitors on a numeric scale, although the fact that judges' ratings are public makes it less likely for them to engage in blatant tactical voting
Tactical voting
In voting systems, tactical voting occurs, in elections with more than two viable candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome.It has been shown by the Gibbard-Satterthwaite theorem that any voting method which is...
. Range voting is common for things where there is no single winner: for instance on the Web
World Wide Web
The World Wide Web is a system of interlinked hypertext documents accessed via the Internet...
, sites allow users to rate items such as movies (Internet Movie Database
Internet Movie Database
Internet Movie Database is an online database of information related to movies, television shows, actors, production crew personnel, video games and fictional characters featured in visual entertainment media. It is one of the most popular online entertainment destinations, with over 100 million...
), comments, recipes, and many other things.
Dotmocracy
Dotmocracy
Dotmocracy is an established facilitation method for collecting and recognizing levels of agreement on written statements among a large number of people...
is an established paper-based group facilitation method that invites participants to brainstorm
Brainstorm
Brainstorm generally refers to brainstorming, a group or individual creativity exercise.Brainstorm may also refer to:-Film:* Brainstorm , directed by Douglas Trumbull* Brainstorm , directed by William Conrad...
ideas and then vote on a range of agreement for each idea in order to recognize which ideas have the most collective agreement.
Range voting has been used informally by various amateur clubs to make decisions such as meeting dates, event themes or what books to read.
Example
Suppose that voters each decided to grant from 0 to 10 points to each city such that their most liked choice got 10 points, and least liked choice got 0 points, with the intermediate choices getting an amount proportional to their relative distance.| Voter from/ City Choice |
Memphis | Nashville | Chattanooga | Knoxville | Total |
|---|---|---|---|---|---|
| Memphis | 420 (42 * 10) | 0 (26 * 0) | 0 (15 * 0) | 0 (17 * 0) | 420 |
| Nashville | 168 (42 * 4) | 260 (26 * 10) | 90 (15 * 6) | 85 (17 * 5) | 603 |
| Chattanooga | 84 (42 * 2) | 104 (26 * 4) | 150 (15 * 10) | 119 (17 * 7) | 457 |
| Knoxville | 0 (42 * 0) | 52 (26 * 2) | 90 (15 * 6) | 170 (17 * 10) | 312 |
Nashville, the capital in real life, likewise wins in the example. However, if voters from Knoxville and Chattanooga were to rate Nashville as 0 and/or both sets of voters were to rate Chattanooga as 10, the winner would be Chattanooga over Nashville by 508 to 428. This would be a better outcome for the voters in those cities than what they would get if they were to reflect their true preferences, and is considered to be an instance of tactical voting. Such tactical voting would be less effective if the ballots were counted using median scores.
Properties
Range voting allows voters to express preferences of varying strengths.Range voting satisfies the monotonicity criterion
Monotonicity criterion
The monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...
, i.e. raising your vote's score for a candidate can never hurt their chances of winning. Also, in range voting, casting a sincere vote can never result in a worse election winner (from your point of view) than if you had simply abstained from voting. Range voting passes the favorite betrayal criterion, meaning that it never gives voters an incentive to rate their favorite candidate lower than a candidate they like less. Range voting advocates contend that this is a good property, because it leads to higher average voter satisfaction when voters are honest, and still gives voters the choice to strategically lower their scores for less preferred candidates if they choose.
Range voting is independent of clones
Strategic nomination
Strategic nomination is the manipulation of an election through its candidate set...
in the sense that if there is a set of candidates such that every voter gives the same rating to every candidate in this set, then the probability that the winner is in this set is independent of how many candidates are in the set.
In summary, range voting satisfies the monotonicity criterion
Monotonicity criterion
The monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...
, the favorite betrayal criterion, the participation criterion
Participation criterion
The participation criterion is a voting system criterion. It is also known as the "no show paradox". It has been defined as follows:* In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing...
, the consistency criterion
Consistency criterion
A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative...
, independence of irrelevant alternatives
Independence of irrelevant alternatives
Independence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....
, resolvability criterion
Resolvability criterion
Resolvability criterion can refer to any voting system criterion that ensures a low possibility of tie votes.#Nicolaus Tideman's version of the criterion demands that if and only if for every winner in a result, a vote exists, such that when added, makes that winner unique.#Douglas R...
, and reversal symmetry
Reversal symmetry
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, the Kemeny-Young method, and the Schulze method...
. It is immune to cloning, except for the obvious specific case in which a candidate with clones ties, instead of achieving a unique win. It does not satisfy either the Condorcet criterion
Condorcet criterion
The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...
(i.e. is not a Condorcet method
Condorcet method
A Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...
) or the Condorcet loser criterion
Condorcet loser criterion
In single-winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion....
, although with all-strategic voters and perfect information the Condorcet winner is a Nash equilibrium
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
. It does not satisfy the majority criterion
Majority criterion
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....
, but it satisfies a weakened form of it: a majority can force their choice to win, although they might not exercise that capability. It does not satisfy the later-no-harm criterion
Later-no-harm criterion
The later-no-harm 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 cannot cause a more preferred candidate to lose.- Complying methods :Single...
, meaning that giving a positive rating to a less preferred candidate can cause a more preferred candidate to lose.
As it satisfies the criteria of a deterministic voting system, with non-imposition, non-dictatorship, monotonicity, and independence of irrelevant alternatives, it may appear that it violates Arrow's impossibility theorem
Arrow's impossibility theorem
In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives , no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a...
. The reason that range voting is not regarded as a counter-example to Arrow's theorem is that it is a cardinal voting system, while the "universality" criterion of Arrow's theorem effectively restricts that result to ordinal voting systems.
Strategy
In most cases, ideal range voting strategy for well-informed voters is identical to ideal approval votingApproval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
strategy, and a voter would want to give his least and most favorite candidates a minimum and a maximum score, respectively. If one candidate's backers engaged in this tactic and other candidates' backers cast sincere rankings for the full range of candidates, then the tactical voters would have a significant advantage over the rest of the electorate. When the population is large and there are two obvious and distinct front-runners, tactical voters seeking to maximize their influence on the result would give a maximum rating to their preferred candidate, and a minimum rating to the other front-runner; these voters would then give minimum and maximum scores to all other candidates so as to maximize expected utility.
However, there are examples in which voting maximum and minimum scores for all candidates is not optimal. Exit poll experiments have shown that voters tend to vote more sincerely for candidates they perceive have no chance of winning. Thus range voting may yield higher support for third party and independent candidates, unless those candidates become viable, than other common voting methods, creating what has been called the "nursery effect".
Range voting advocates argue that range voting systems (including approval voting) give no reason to ever dishonestly rank a less-preferred candidate over a more-preferred one in 3-candidate elections. However, detractors respond that it provides motivation to rank a less-preferred and more-preferred candidate equally or near-equally (i.e., both 0-1 or both 98-99). This could lead to undemocratic results if different segments of the population used strategy at significantly different rates.
Advocacy
Range voting is advocated online by the election reform sites RangeVote.com, The Center for Election Science, and the Center for Range Voting. Guy Ottewell, who helped develop the system of approval votingApproval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
, now endorses range voting. No elected official in the United States is known to endorse range voting.
See also
- List of democracy and elections-related topics
- Consensus decision-makingConsensus decision-makingConsensus decision-making is a group decision making process that seeks the consent, not necessarily the agreement, of participants and the resolution of objections. Consensus is defined by Merriam-Webster as, first, general agreement, and second, group solidarity of belief or sentiment. It has its...
- Decision makingDecision makingDecision making can be regarded as the mental processes resulting in the selection of a course of action among several alternative scenarios. Every decision making process produces a final choice. The output can be an action or an opinion of choice.- Overview :Human performance in decision terms...
- DemocracyDemocracyDemocracy is generally defined as a form of government in which all adult citizens have an equal say in the decisions that affect their lives. Ideally, this includes equal participation in the proposal, development and passage of legislation into law...
- Relative Utilitarianism
- Hot or NotHot or NotHot or Not is a rating site that allows users to rate the attractiveness of photos submitted voluntarily by others. The site also offers a match making engine called 'Meet Me' and an extended profile feature called 'HOTLISTS'. It is owned by Avid Life Media....
— a real world example
External links
- The Center for Range Voting and its simplified introductory homepage
- The Center for Election Science includes an article on Range Voting
- RangeVote includes a user-friendly presentation on range voting
- Voting In Sanity includes a comprehensive description of the benefits of score voting
- Range voting discussion list at Yahoo Groups
- Discussion list on Google Groups
- FairVote criticism of approval, range voting, and Condorcet methods
- Mock 2008 U.S. Presidential Election using range voting
- Vote! web application that implements Range Voting, you can create your own ballots or vote in a few sample polls.
- Simulation of various voting models for close elections Article by Brian Olson.