# Utility

Though often used in voting theory to refer to cardinal utility i.e. rated method utility, it can also be used for discussing ordinal utility i.e. ranked-preference utility.

An example would be (using a preference-approval):

51: A>B|

49: B|>A

A majority prefer A over B, but are willing to support either of the two, whereas a minority both prefer and only support B. Therefore, ordinal utility says A is best, while rated utility says B is best.

In the two-candidate case, the two approaches differ; cardinal/rated utility says that the candidate who makes voters net-happier should win (if everyone measured their happiness on a scale), whereas ranked/ordinal utility requires majority rule, which can be thought of as at least satisfying the majority criterion.

Self-referential Smith-efficient Condorcet methods that always elect the utilitarian (rated utility) winner in the two-candidate case will be Approval voting or Score voting. For majority rule, the equivalent is Smith-efficient Condorcet methods.

Note that in the two-candidate case, voters using rated utilities can exaggerate the difference in utility between the candidates to derive majority rule, whole voters using ranked utilities can (in the limit) approximate rates utility by using a probability proportional to their personal difference in utility between the two candidates to decide whether to vote for their preferred candidate of the two, or not vote. Example:

100,001: A:1 B:0.8

100,000: A:0 B:1

If the A>B voters give B a 0, they can make A have more points, i.e

majority rule..

. And if the A>B voters use a 20% probability of voting Aand 80% f>r voo voting A=B, then in the limit, A will have ab20t 80,000 votes and B 100,00n 8 a 20,000 vote margin in favor of B, thus effectively simulating the rated utility margin.