Rating choice

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The review choice ( English Range voting ) is a voting system in which individual alternatives (candidates) with dots of a predetermined interval, are evaluated, for example, 0 to 99, 1 to 10, -5 to +5, or grades. The awarded points (grades) are then averaged. The alternative with the best average rating wins.

An evaluation election is a particularly general and expressive voting process, as a voter evaluates each candidate independently of the other applicants. At the same time, the rating choice is a very easy to understand, intuitive and paradox-free system. In particular, the evaluation of a candidate cannot affect the relative ranking of the others.

A jury evaluates many sporting disciplines by means of an evaluation choice.

Description of the voting method

The electoral winner is determined by means of evaluation voting in three steps: First, the candidates are evaluated by the voters; This is followed by the determination of the social evaluation for each candidate, i.e. H. the ratings of all voters are combined into one rating. Finally, the candidates are ranked according to their ratings.

Voting

Example of a rating ballot

Each voter evaluates all candidates independently of one another and chooses for evaluation from a scale of possible values, for example the natural numbers from 0 to 9. Numbers can be assigned multiple times and of course not every number has to be used. It is also allowed to give individual candidates no grade at all.

Candidate Results

There are different variants of the evaluation choice to determine the result for each candidate:

  • Average : Each candidate is assigned the average of the ratings given to him.
  • Total : Each candidate is assigned the total of the ratings given for him.

Note : If all voters have rated all candidates, both variants deliver the same result. The two variants only differ if not every voter rated every candidate:

  • In the average variant, undecided voters are ignored; that is, not to rate a candidate is how to give him the average score.
  • In the case of the totals variant, evaluations that are not available are not added up; That is, not to rate a candidate is like giving him a 0.

Combinations are also possible: For example, the American “Center for Range Voting” suggests the average variant, whereby all candidates whose total is less than half of the highest total achieved by a candidate are excluded. This prevents little-known candidates who are fanatically supported by their own supporters and thus presumably extremist candidates from winning the election. This is an absolute necessity when using the average variant, especially when voters, as required by law in many American elections, have the option of handwritten a candidate who does not appear on the ballot paper. Without such a (or similar) rule, someone could simply register themselves and give themselves the highest score. Since probably nobody else has this person on the ballot paper, he would also get the highest possible average and win the election.

winner

The candidate with the highest score is the winner.

If one considers the ratings given for a candidate as a measure of the satisfaction that a voter has with a candidate, then the rating election selects that candidate who represents the highest social satisfaction as the winner.

example

Consider an election with four candidates R, C, P and I and the following ratings by the 10 voters:

reviews
# of voters R. C. P I.
4th 6th 7th 10 0
3 8th 4th 2 9
2 9 10 1 2
1 10 3 3 5
cut 7.6 6.3 5.1 3.6

With the evaluation election, candidate R would win because he achieved the best average of 7.6 - even if he was rated best among all candidates by the lowest number of voters (namely only one).

Remarks :

  • Under instant run-off voting , the on average most unpopular candidate I would win, since the lower preferences are ignored in the deletion (later no harm criterion), whereby first the average most popular candidate R and then the second most popular candidate C are deleted and the votes move to I.
  • Using relative majority voting , candidate P would win because he would be the first preference out of 4 voters, while none of the other candidates out of more than 3 candidates is the first preference. With the other 6 voters, however, candidate P has only a very low reputation and would therefore lose with both Condorcet methods and the evaluation choice.
  • Using a Condorcet method , Candidate C would win as he is preferred over any other candidate out of 6 voters. However, since the 4 voters who prefer R over C clearly prefer R over C, while the 6 who prefer C over R evaluate both candidates almost identically, candidate R wins in the evaluation election.

properties

This electoral process fulfills most of the known electoral system criteria , in particular freedom from dictatorship, completeness, independence from irrelevant alternatives and the weak Pareto principle.

The evaluation choice therefore apparently violates the Arrow theorem , which rules out the existence of a ranking voting procedure that fulfills these criteria. This effect arises from the fact that the Arrow theorem only applies to ranking electoral processes (i.e. processes in which candidates are ranked by voters), but not to absolute evaluations (i.e. processes in which voters evaluate each candidate independently of the others ).

Furthermore, the evaluation choice fulfills the independence of clone alternatives, the consistency criterion, the participation criterion, the transitivity criterion, the favorite betrayal criterion, the resolvability criterion and the reversal symmetry criterion.

The Condorcet criterion, the Condorcet loser criterion and the majority criterion are not met. However, since the choice of valuation allows majorities to be weighted and expressed by how much more one prefers one option over another, while these criteria - as well as the ranking methods for which they were developed - do not take this information into account, the significance of these criteria is controversial for the evaluation choice.

The later-no-harm criterion is not fulfilled: Submitting a (lower) rating for a non-favored candidate can lead to this candidate being elected instead of the favored candidate. Suppose the voters for candidate B give 0 points to candidate A for tactical reasons, while the voters for candidate A also give points to candidate B, since B still appears to be the better option over C. Then it can be that B wins, although the A-voters, had they only voted for A, could have got their candidate A through.

Alternatives

The greatest weakness of the rating choice with average is that a few outsiders can strongly influence the result by assigning extreme values. The larger the scale, the stronger the effect. A possible consequence of this is a rating system with the smallest scale: election by approval voting. Only the point values ​​0 and 1 are possible. Critics object, however, that the advantage of the choice of assessment, namely the possibility of the individual to express his preferences in a differentiated way, is lost.

In the case of a differentiated scale, the influence of a small group of strategic voters can be absorbed by introducing a quorum . One possible form of such a quorum is a blocking clause analogous to parliamentary elections based on proportional representation . Only candidates would be considered who were supported by a specified minimum number of voters or eligible voters, e.g. B. 10% have been rated. Another possibility is to add an equal, fixed number of bad ratings as “handicaps” to each candidate and to average the overall result (ratings submitted + “handicap”).

Other ways to mitigate the influence of extreme grades are to use the median instead of the average or to work with deleted results.

literature

Web links

Individual evidence

  1. ↑ Mike Ossipoff, Warren D. Smith: Survey of Voting Methods that Avoid Favorite-Betrayal . rangevoting.org. Retrieved October 3, 2015.