Cardinal Ratings

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.

Voting

Cardinal Ratings uses a ratings ballot; that is, each voter rates each candidate with a number. In "pure Cardinal Ratings", each voter may give any candidate any real number, but as the potential for tactical voting is huge, most systems use upper and lower bounds. For example, each voter might give a real number between -1 and 1, or an integer between 1 and 10.

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

Cardinal Ratings satisfies the monotonicity criterion.

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.

Example

Tennessee's four cities are spread throughout the state

Imagine that Tennessee is having an election 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 these four cities, and that everyone wants to live as near the capital as possible.

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, near the center of Tennessee
• Knoxville, with 17% of the voters
• Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this:

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

Strategy

In general, the optimal strategy for Cardinal Ratings 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.

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