Score voting

Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 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. Range voting was used in all public elections in Ancient Sparta in the form of measuring how loud the crowd shouted for different candidates. Approval voting can be considered to be range voting with only 2 levels (approved (1) and disapproved (0)).

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.

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 Judgement. 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 Judgement to break such ties. In conventional range voting, these ties would be extremely rare. Another problem with medians is that adding an "all-zero ballot" can alter the election winner.

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.

Alternative use

The range voting concept has been used in non-political contexts also, Sports such as gymnastics 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.

Range voting has been used informally by various amateur clubs to determine dates and venues for events like seasonal dinners. In one variant, any club member who wants to propose a date/time or restaurant writes it down on a whiteboard. All other members can each vote once for each new option; either by adding +1 to the total (in favour), casting no vote (neutral), or by subtracting one from the total (disapproval). At the end of the season, the club goes to the restaurant with the most votes, at the date and time with the most votes.

Example

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:

• Memphis, the largest city, but far from the others (42% of voters)
• Nashville, near the center of the state (26% of voters)
• Chattanooga, somewhat east (15% of voters)
• Knoxville, far to the northeast (17% of voters)

The preferences of each region's voters are:

42% of voters Far-West	26% of voters Center	15% of voters Center-East	17% of voters Far-East
Memphis Nashville Chattanooga Knoxville	Nashville Chattanooga Knoxville Memphis	Chattanooga Knoxville Nashville Memphis	Knoxville Chattanooga Nashville Memphis

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.

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 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 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.

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

In most cases, ideal range voting strategy for well-informed voters is identical 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.

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 the strategic voting encouraged by a Range system is less dishonest than that encouraged by other systems, as Range voting systems (including Approval voting), unlike any possible ordinal voting systems, 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 still provides motivation to rank a less-preferred and more-preferred candidate equally or near-equally (ie, both 0-1 or both 99-100). This could lead to undemocratic results if different segments of the population used strategy at significantly different rates.

Advocacy

Guy Ottewell, who helped develop the system of approval voting, now endorses range voting. No elected official in the United States is known to endorse range voting.

Range voting is advocated online by the election reform sites rangevote.com and rangevoting.org. These sites argue that strategy is less of a problem in Range voting than in other systems, and also point to computer simulations which show that it produces lower Bayesian regret (that is, greater overall utility) than other methods. This result holds across any of a number of assumptions about the distribution of voter preferences, but does depend on the more debatable assumption that different systems lead to similar amounts of strategic voting. Even if the latter assumption is relaxed (that is, comparing Range Voting's worst case, with strategic voters, against other systems' best cases, with honest voters), Range Voting is still the only simulated system to prove always superior to the Plurality voting system.

Center for Range Voting

The Center for Range Voting was founded in 2005 by Warren D. Smith and Jan Kok. It operates a web site and a mailing list. The Center is notable as a source for information about Range voting, simulations and analysis of voting systems, and arguments about instant-runoff voting.

See also

• List of democracy and elections-related topics
• Consensus decision-making
• Decision making
• Democracy
• Hot or Not — a real world example
• Majoritarianism (Majority rule)
• Minoritarianism

External links

• The Center for Range Voting and its simplified introductory homepage
• RangeVote includes a user-friendly presentation on range 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.
• Mechanic, Michael (2007-01-02). "The verdict is in: our voting system is a loser". Mother Jones. The Foundation for National Progress. Retrieved 2008-02-04. {{cite news}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)