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Encyclopedia > Range voting
The Voting series:

This series is part of the
Politics and the Election series Voting is a method of decision making where in a group such as a meeting or an electorate attempts to gauge its opinion—usually as a final step following discussions or debates. ... Image File history File links Vote_icon. ... Politics is the process by which groups make decisions. ... An election is a decision making process where people choose people to hold official offices. ...

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Range voting (also called ratings summation, average voting, cardinal ratings, 0–99 voting, or the score system or point system) 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. It is not used in any public election. However, Approval voting is range voting with only 2 levels (approved (1) and disapproved (0)) and forms of Approval voting have been used -- for example, in Venice in the 13th century. Voting is a method of decision making where in a group such as a meeting or an electorate attempts to gauge its opinion—usually as a final step following discussions or debates. ... A voting system is a means of choosing between a number of options, based on the input of a number of voters. ... For the town in France, see Ballots, Mayenne. ... There exist various methods through which the ballots cast at an election may be counted, prior to applying a voting system to obtain one or more winners. ... On an approval ballot, the voter can vote for any number of candidates. ... Bloc voting (or block voting) (also called Plurality-at-large) refers to a class of voting systems which can be used to elect several representatives from a single constituency. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... The Coombs method, created by Clyde Coombs, is a voting system used for single-winner elections in which each voter rank-orders the candidates. ... Copelands method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories. ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ... The DHondt method (equivalent to Jeffersons method) is a highest averages method for allocating seats in party-list proportional representation. ... The Droop quota is the quota most commonly used in elections held under the Single Transferable Vote (STV) system. ... Dynamically Distributed Democracy (DDD) uses a social network data structure as a means of a creating a holographic model of the voting behavior of the whole group within any subset of the population that is actively participating in the groups voting process. ... In party-list proportional representation systems, an election threshold is a clause that stipulates that a party must receive a minimum percentage of votes, either nationally or within a particular district, to get any seats in the parliament. ... The Hare quota is a formula used to calculate the minimum number, or quota, of votes required to capture a seat in some forms of single transferable vote or largest remainder method party-list proportional representation voting systems. ... The highest averages method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... Example ballot Instant runoff voting (IRV) is a voting system used for single winner elections in which voters rank candidates in order of preference. ... The Kemeny-Young method is a voting system that uses preferential ballots, a tally table, and sequence scores to identify the most popular choice, and also identify the second-most popular choice, the third-most popular choice, and so on down to the least-popular choice. ... The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... Party lists are used in elections to legislatures which use Party-list proportional representation or additional member proportional representation to designate a partys nominees in the at-large portion of the vote. ... The first-past-the-post electoral system is a voting system for single-member districts, variously called first-past-the-post (FPTP or FPP), winner-take-all, plurality voting, or relative majority. ... Preferential voting (or preference voting) is a type of ballot structure used in several electoral systems in which voters rank a list or group of candidates in order of preference. ... Proportional approval voting (PAV) is a theoretical voting system for multiple-winner elections, in which each voter can vote for as many or as few candidates as the voter chooses. ... The Sainte-Laguë method of the highest average (sometimes identified with Websters method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ... This STV ballot for the Australian Senate illustrates group voting tickets. ... In voting, a ballot paper is considered to be spoilt, void, or null if it is regarded by the election authorities to contain irregularities during vote counting, and hence cannot be recorded as a valid vote. ... A voting system is a means of choosing between a number of options, based on the input of a number of voters. ... On an approval ballot, the voter can vote for any number of candidates. ... On an approval ballot, the voter can vote for any number of candidates. ...

Contents

Voting system

Range voting uses a ratings ballot; that is, each voter rates each candidate with a number within a specified range, such as 0 to 99 or 1 to 5. Although in cumulative voting voters are not permitted to provide scores for more than some number of candidates, in range voting all candidates can be and should be rated. 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. A ratings ballot is a ballot on which candidates are rated on a cardinal scale. ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ...


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 both to mitigate biases by some judges and to avoid the results of third skaters affecting the relative positions of two skaters who have already finished their performances. A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. ...


Another method of counting ratings ballots is to find the median score of each candidate, and elect the candidate with the highest median score (see Median Ratings). A disadvantage is that with strategic voting, there may often be a multiway exact tie for winner. In conventional range voting, such ties are extremely rare. Tiebreaking schemes could be added to median-rating to overcome that objection. In probability theory and statistics, a median is a number dividing the higher half of a sample, a population, or a probability distribution from the lower half. ...


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, voters must weigh the adverse impact on their favorite candidate of ranking other candidates highly. On an approval ballot, the voter can vote for any number of candidates. ...


Alternative use

Although no electoral usage of range voting is known, other than the restricted case of Approval voting, the concept can be found in other areas. Sports such as gymnastics rate competitors on a numeric scale, although the fact that judges' ratings are public makes it unlikely for them to engage in tactical voting. On the Web, sites allow users to rate items such as movies (Internet Movie Database), comments (Kuro5hin), recipes, and many other things. Range voting is the primary voting method used and endorsed by the Libertarian Reform Caucus. [1] On an approval ballot, the voter can vote for any number of candidates. ... Gymnastics is a sport involving the performance of sequences of movements requiring physical strength, flexibility, balance and kinesthetic awareness, such as handsprings, handstands, forward rolls, aerials and tucks. ... WWWs historical logo designed by Robert Cailliau The World Wide Web (WWW or simply the Web) is a system of interlinked, hypertext documents that runs over the Internet. ... The Internet Movie Database (IMDb) is an online database of information about motion pictures, actors, movie stars, TV shows, TV stars, production crew personnel, movie pictures, cast, crew as well as video games. ... Kuro5hin (K5) (pronounced corrosion) is a community discussion website (sometimes known as an example of Commons-based peer production) focused on technology and culture. ... This article needs to be cleaned up to conform to a higher standard of quality. ...


Example

Imagine that the population of Tennessee, a state in the United States, is voting on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in one of these four cities, and that they would like the capital to be established as close to their city as possible. Image File history File links Tennessee_map_for_voting_example. ... Official language(s) English Capital Nashville Largest city Memphis Largest metro area Nashville Area  Ranked 36th  - Total 42,169 sq mi (109,247 km²)  - Width 120 miles (195 km)  - Length 440 miles (710 km)  - % water 2. ... In politics, a capital (also called capital city or political capital — although the latter phrase has a second meaning based on an alternative sense of capital) is the principal city or town associated with a countrys government. ... In politics, an electorate is the group of people entitled to vote in an election. ...


The candidates for the capital are:

  • Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
  • Nashville, with 26% of the voters
  • Knoxville, with 17% of the voters
  • Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this: For other uses, see Memphis (disambiguation). ... Nickname: Music City Location in Davidson County and the state of Tennessee Coordinates: Country United States State Tennessee Counties Davidson County Founded: 1779 Incorporated: 1806  - Mayor Bill Purcell (D) Area    - City  526. ... Nickname: The Marble City, K-Town, Big Orange Country, Knox Vegas, 865 Location within the U.S. State of Tennessee Coordinates: Cities in Tennessee Tennessee  - Mayor Bill Haslam (R) Area    - City 254. ... This article or section does not cite its references or sources. ...

42% of voters
(close to Memphis)
26% of voters
(close to Nashville)
15% of voters
(close to Chattanooga)
17% of voters
(close to Knoxville)
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis

Suppose that voters each decided to grant from 1 to 10 points to each city such that their most liked choice got 10 points, and least liked choice got 1 point, with the intermediate choices getting 5 points and 2 points.

Voter from/
City Choice
Memphis Nashville Chattanooga Knoxville Total
Memphis 420 (42 * 10) 26 (26 * 1) 15 (15 * 1) 17 (17 * 1) 478
Nashville 210 (42 * 5) 260 (26 * 10) 30 (15 * 2) 34 (17 * 2) 534
Chattanooga 84 (42 * 2) 130 (26 * 5) 150 (15 * 10) 85 (17 * 5) 449
Knoxville 42 (42 * 1) 52 (26 * 2) 75 (15 * 5) 170 (17 * 10) 339

Nashville wins. But Memphis would have won if the voters from Memphis had reduced the points they gave Nashville from 5 down to 1 and all other votes had remained the same; voters from Chattanooga or Knoxville could restore Nashville to first place over Memphis if they raised the points they gave Nashville from 2 up to 10.


Properties

Range voting allows voters to express preferences of varying strengths.


Range voting satisfies the monotonicity criterion, i.e. raising your vote's score for a candidate can never hurt his 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. A voting system is monotonic if it satisfies the monotonicity criterion, given below. ... In social choice theory, the favorite betrayal criterion (or FBC) is a voting system criterion devised by Mike Ossipoff for evaluating voting systems. ...


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. Range voting is not a Condorcet method according to the traditional definition of that term. Strategic nomination is the manipulation of an election through its candidate set (compare this to tactical voting, where the manipulation comes from the voters). ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ...


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. It does not satisfy the majority criterion. A voting system is monotonic if it satisfies the monotonicity criterion, given below. ... In social choice theory, the favorite betrayal criterion (or FBC) is a voting system criterion devised by Mike Ossipoff for evaluating voting systems. ... Statement of Criterion Adding one or more ballots that vote X over Y should never change the winner from X to Y. Complying Methods Plurality voting, Approval voting, Cardinal Ratings, Borda count, and Woodalls DAC method all pass the Participation 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 alternative being selected, an election of the entire electorate also selects that alternative. ... Independence of irrelevant alternatives (IIA) is an axiom often adopted by social scientists as a basic condition of rationality. ... The Resolvability criterion pertains to Condorcet methods where at least in those cases in which there are no pairwise ties and no pairwise defeats of equal strength, the winner must be unique. ... Reversal symmetry is a voting method criterion that is stated as follows: If a candidate A is the unique winner, and the individual preferences of each voter are inverted, then candidate A must not be elected. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... Given a vote where voters rank options in order of preference, a Condorcet loser is an option that loses all of its pairwise comparisons. ... The majority criterion is a voting system criterion, used to objectively compare voting systems. ...


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 Arrow's theorem is restricted to the processing of ordinal preferences.[1] In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. ...


Bayesian regret

Many criteria have been proposed for estimating the quality of a voting method, but Bayesian regret is arguably unique in that it represents the aggregate impact of all possible (even as yet undiscovered) criteria, in terms of average voter satisfaction. The mathematical definition of the concept is as follows:

In Bayesian statistics, "regret" is the difference between the maximum possible ideal utility and the actual utility. (Depending on the application, regret can often be more convenient to deal with than utility. This terminology has been used in a large number of papers and is not new from us.) "Social" utility is the sum of utility over all the members of some human population. For voting systems purposes, "Bayesian regret" is the expectation value of social regret. It depends on both the voting system, the number of candidates, the number of voters, and the probabilistic models of utilities, candidates, and voter behaviors. [2]

Some advocates of this yard stick make the analogy to a single person making a choice: a choice is made by assessing the pros and cons of the available options, in order to assign an overall utility value to each one; and then the one with the highest estimated value is selected. Likewise, Bayesian regret is expressed as the difference between the average voter happiness that would be produced by electing the optimum candidate, and the average voter happiness brought about by the actual winner in the specified election system. By using the voting method with the lowest Bayesian regret, a voter maximizes his expected value in the "currency" of satisfation.


Princeton math doctorate Warren D. Smith has produced arguably the most comprehensive Bayesian regret calculations to date. In his simulations, hundreds of millions of elections were conducted, using 720 different tunings of five parameters governing voter behavior. Whether voters were informed or ignorant, honest or sincere, range voting produced the lowest Bayesian regret among common voting methods, in Smith's experiment. The table below shows the results of two sample simulations.


Column A: 5 candidates, 20 voters, random utilities; Each entry averages the regrets from 4000000 simulated elections. Column B: 5 candidates, 50 voters, utilities based on 2 issues, each entry averages the regrets from 2222222 simulated elections.

Voting System Regret A Regret B
Magically elect optimum winner 0 0
Range (honest voters) 0.04941 0.05368
Borda (honest voters) 0.13055 0.10079
Approval (honest voters) 0.20575 0.16549
Condorcet-LR (honest voters) 0.22247 0.14640
IRV (honest voters) 0.32314 0.23786
Plurality (honest voters) 0.48628 0.37884
Range & Approval (strategic exaggerating voters) 0.31554 0.23101
Borda (strategic exaggerating voters) 0.70219 0.48438
Condorcet-LR (strategic exaggerating voters) 0.86287 0.58958
IRV (strategic exaggerating voters) 0.91522 0.61072
Plurality (strategic voters) 0.91522 0.61072
Elect random winner 1.50218 1.00462

Criticisms of Bayesian regret as a metric

Critics of the Bayesian regret metric argue that it is not always fair, and that its inconsistency with majoritarian systems is a flaw. Consider the following scenario, given the honest utility values of three voters for three candidates.

C1 C2 C3
V1 11 9 22
V2 13 11 25
V3 5 8 2

While it is clear that the election of candiate 3 would produce the greatest average satisfaction in this scenario, this would be at the expense of voter 3. In spite of such lop-sided scenarios, Bayesian regret adherents defend the metric, because it is possible that no voting method (apart from one which reads minds) may prevent them. Range voting advocates point out that under their system, all voters have the same ballots, with the same weight, and the same opportunity to vote strategically, thus making range voting fair.


Strategy

In general, ideal range voting strategy degrades for well-informed voters to ideal approval voting 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 is to 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. On an approval ballot, the voter can vote for any number of candidates. ...


However, there are examples in which voting maximum and minimum scores for all candidates is not optimal [3]. What has been observed to happen in exit poll experiments is 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 than other common voting methods, creating what has been called the "nursery effect," unless those candidates become viable.


Because range voting produces lower Bayesian regret than other methods, even when voters are strategic, many range voting advocates believe it is the most resistant voting method to strategic voting. In voting systems, tactical voting (or strategic voting) occurs when a voter misrepresents his or her sincere preferences in order to gain a more favorable outcome. ...


Approval voting inventor Guy Ottewell now endorses range voting [4]. No elected official in the United States is known to endorse range voting.


References

  1. ^ Arrow, Kenneth (August 1950). "A Difficulty in the Concept of Social Welfare". The Journal of Political Economy 58 (4). 

Kenneth Arrow Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ... 1950 (MCML) was a common year starting on Sunday (link will take you to calendar). ...

See also

Politics is the process and method of gaining or maintaining support for public or common action: the conduct of decision-making for groups. ... Flowchart of basic consensus decision-making process. ... Decision making is the cognitive process of selecting a course of action from among multiple alternatives. ... It has been suggested that this article or section be merged into Rating sites. ... Majoritarianism is a political philosophy or agenda which asserts that a majority (sometimes categorized by religion, language or some other identifying factor) of the population is entitled to a certain degree of primacy in society, and has the right to make decisions that affect the society. ... Majority-choice approval (MCA) is a voting system devised by Forest Simmons in April 2002 for use with three-slot ballots. ... Minoritarianism (often also called minority rule) is a political philosophy or agenda which asserts that a segment of a countrys population (sometimes categorized by religion, language or some other identifying factor) to which a minority of its citizens belong is entitled to obstruct political progress sought by a majority...

External links


  Results from FactBites:
 
Approval voting - Wikipedia, the free encyclopedia (1551 words)
Approval voting is a voting system used for elections, in which each voter can vote for as many or as few candidates as the voter chooses.
Historically, something resembling Approval voting for candidates was used in the Republic of Venice during the 13th century and for elections in 19th century England.
In this vote, the candidates for the capital are Memphis, Nashville, Chattanooga, and Knoxville.
Range voting - definition of Range voting in Encyclopedia (361 words)
Range voting, or average voting, or cardinal ratings is a voting system used for single or multiple-seat elections.
Range voting in which only two different votes may be submitted (0 and 1, for example) is equivalent to approval voting.
Range voting assumes that voters are actually expressing their personal feelings rather than doing everything they can to cause their most favored outcomes.
  More results at FactBites »

 
 

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