Utility

From electowiki

Utility broadly means satisfaction.

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

The points are roughly A 100,000, B 180,000, so there is a rated utility margin of 80,000 points in favor of B.

If, for cardinal utility, the A>B voters give B a 0, they can make A have slightly more points, i.e. majority rule. And if, in majority rule, the A>B voters use a 20% probability of voting A>B and 80% for voting A=B (i.e. a 20% probability of picking A and a 80% probability of not voting for either candidate), then in the limit, A will have ~20,000 votes and B ~100,000, which is an 80,000 vote margin in favor of B, thus effectively simulating the rated utility margin.
Another consideration is whether there should be a "satisfaction threshold" at which point increasing someone's utility matters less. For example, between a candidate who gives 100% utility to 60% of the voters and a candidate who gives 51% utility to all voters, some would consider the latter candidate better, despite them giving less cardinal utility., because all voters get significant utility from them, while 49% of voters get nothing from the first candidate. See https://www.reddit.com/r/EndFPTP/comments/acw8fs/mock_ballot_who_do_you_think_should_win_in_this/ for an example.