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Home > Range voting


 

Range voting, or average voting, or cardinal ratings is a voting system used for single or multiple-seat elections. It is also used on the web - for rating movies ( Internet Movie Database), comments ( Kuro5hin), and many other things.

1 Voting

For each candidate, each voter expresses the utility of that candidate's election to them in the form of a number. In "pure" range voting, each voter may give any candidate any real number, but as the potential for tactical voting is huge, most systems use some bounds. For example, each voter might give a real number between -1 and 1, or an integer between 1 and 10.

Range voting in which only two different votes may be submitted (0 and 1, for example) is equivalent to approval voting.

Range voting satisfies the monotonicity criterion.

2 Counting the Votes

The scores for each candidate are summed, and the candidates with the highest sums are declared the winners.

Another method of counting is to find the median score of each candidate, and elect the candidate with the highest median score.

3 Example

Imagine an election for the capital of Tennessee, a state in the United States that is over 500 miles east-to-west, and only 110 miles north-to-south. In this vote, the candidates for the capital are Memphis, Nashville, Chattanooga, and Knoxville. The population breakdown by metro area is as follows:


If the voters cast their ballot based strictly on geographic proximity, the voters' sincere preferences might be as follows:


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

26% of voters (close to Nashville)

  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis

15% of voters (close to Chattanooga)

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

Suppose that voters were told to grant 1 to 4 points to each city such that their most liked choice(s) got 4 points, and least liked choice(s) got 1 point.

City Memphis Nashville Chattanooga Knoxville Total
Memphis 168 (42 * 4) 26 15 17 226
Nashville 126 (42 * 3) 104 (26 * 4) 30 (15 * 2) 34 (17 * 2) 294
Chattanooga 84 (42 * 2) 78 (26 * 3) 60 (15 * 4) 51 (17 * 3) 273
Knoxville 42 52 (26 * 2) 45 (15 * 3) 68 (17 * 4) 207

Nashville wins.

4 Strategy

In general, the optimal strategy for range voting is to vote it identically to approval voting, so that all candidates are given either the maximum score or the minimum score. For more detailed strategies, see 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.

5 See also

Voting systems

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