Utility: Difference between revisions
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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 https://www.reddit.com/r/EndFPTP/comments/acw8fs/mock_ballot_who_do_you_think_should_win_in_this/<nowiki/> for an example. |
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 https://www.reddit.com/r/EndFPTP/comments/acw8fs/mock_ballot_who_do_you_think_should_win_in_this/<nowiki/> for an example. |
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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. |
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