Range voting, or average voting, or cardinal ratings is a voting system used for single or multiple-seat elections. A real world examples of its use is Kuro5hin.
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.
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.
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.