Difference between revisions of "Cardinal Ratings"

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(move to "range voting", because "cardinal ratings" describes a ballot type rather than a tally method)
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'''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.
#REDIRECT [[Range voting]]
== 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.  (See [[Median Ratings]])
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.
<TABLE BORDER=1 style="empty-cells: show">
<TD>168 (42 * 4)</TD>
<TD>126 (42 * 3)</TD>
<TD>104 (26 * 4)</TD>
<TD>30 (15 * 2)</TD>
<TD>34 (17 * 2)</TD>
<TD>84 (42 * 2)</TD>
<TD>78 (26 * 3)</TD>
<TD>60 (15 * 4)</TD>
<TD>51 (17 * 3)</TD>
<TD>52 (26 * 2)</TD>
<TD>45 (15 * 3)</TD>
<TD>68 (17 * 4)</TD>
Nashville wins.
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.
[[Category:Single-winner voting systems]]

Latest revision as of 23:20, 18 May 2005

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