Utility: Difference between revisions
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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.
== Two-candidate case ==
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|majority rule]], which can be thought of as at least satisfying the [[Majority criterion|majority criterion]].
[[Self-referential Smith-efficient Condorcet method|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,
100,001: A:1 B:0.8
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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. <br />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 <ref>{{Cite web|url=https://www.reddit.com/r/EndFPTP/comments/acw8fs/mock_ballot_who_do_you_think_should_win_in_this/|title=r/EndFPTP - Mock ballot: who do you think should win in this election, and why?|website=reddit|language=en-US|access-date=2020-05-11}}<
== Ballot types ==
There are two ways to derive ranked ballots using ordinal utility. The first is for a voter to ask themselves "who are the candidates I would want to win if I could choose the winner myself?" This is equivalent to asking who you would honestly vote for in [[FPTP]], and it shows who your 1st choice(s) are. If you then remove them from consideration and repeat the question, you find your 2nd choices, etc. The second way is for a voter to ask themselves, for every possible [[head-to-head matchup]], who they'd prefer. The [[Copeland]] ranking shows the voter's ranking of the candidates. This is arguably one way to justify [[Smith-efficient]] [[Condorcet methods]]: if, for an individual voter, the best candidate(s) are the ones from the smallest group that win all head-to-head matchups against all other candidates based only on that voter's judgment, then why not for society? Similar reasoning shows why [[Score voting]] can be justified using rated utilities in head-to-head matchups to quantify harm or benefit done to the voter.
== Notes ==
One notable contrast between ordinal and cardinal utility is that with ordinal, one voter can shift their preference to make a good majority-preferred candidate become a bad minority-preferred candidate, whereas with cardinal utility, there is a degree of damage i.e. it is not too bad a thing to elect a candidate with slightly less utility than the utilitarian winner.
=== Additive nature ===
Many forms of utility are mostly additive i.e. it's not the voters' individual preferences that are of utmost importance, but rather the values produced by adding them up. For example, a candidate given 5 points when voters had rated ballots on a scale of 0 to 5 could've been given 1 point by 5 voters or 5 points by 1 voter.
Likewise, with [[pairwise preference]]<nowiki/>s, if candidate A has 5 votes against B's 4 in the A vs B matchup, this could be equivalent to 5 voters ranking A 1st and B 2nd, or 5 voters ranking A 2nd-to-last and B last.
== Utility vs utility ==
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