User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
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* This is because, when every voter casts a Score voting-style ballot (i.e. they score each candidate the same in all of their matchups), the Score winner will be the CW. In fact, it is possible to mathematically determine how secure a "rated CW" (the CW according to rated pairwise) is in avoiding being in a cycle (having a pairwise defeat) by looking at their pairwise margins against every other candidate. In other words, if using a score scale of 0 to 5, if the rated CW's weakest pairwise victory has a 6-point margin when every voter votes Score-style, then even if one of the voters now switches to cast a non-Score-style ballot (i.e. they increase their pairwise power in at least one matchup beyond what Score voting would allow), the most this can do is make the rated CW have only a 1-point margin victory. |
* This is because, when every voter casts a Score voting-style ballot (i.e. they score each candidate the same in all of their matchups), the Score winner will be the CW. In fact, it is possible to mathematically determine how secure a "rated CW" (the CW according to rated pairwise) is in avoiding being in a cycle (having a pairwise defeat) by looking at their pairwise margins against every other candidate. In other words, if using a score scale of 0 to 5, if the rated CW's weakest pairwise victory has a 6-point margin when every voter votes Score-style, then even if one of the voters now switches to cast a non-Score-style ballot (i.e. they increase their pairwise power in at least one matchup beyond what Score voting would allow), the most this can do is make the rated CW have only a 1-point margin victory. |
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* It's also worth considering who can viably be in the Smith set, depending on how voters pairwise-rate the candidates. If only a few of the voters casts a non-Score ballot, then this can only plausibly mean candidates whose utilities are very close to the Score winner can be in the Smith set along with the Score winner, since candidates whose utilities are significantly lower can't make up their large margin of loss to the higher-utility candidates with the help of only a few voters maximizing their pairwise support for these candidates. So there can be some value to analyzing the rated utilities/Score voting result or ranking ([[order of finish]]) of the candidates when analyzing how the [[Smith set ranking]] produced by rated pairwise ballots will look like. |
* It's also worth considering who can viably be in the Smith set, depending on how voters pairwise-rate the candidates. If only a few of the voters casts a non-Score ballot, then this can only plausibly mean candidates whose utilities are very close to the Score winner can be in the Smith set along with the Score winner, since candidates whose utilities are significantly lower can't make up their large margin of loss to the higher-utility candidates with the help of only a few voters maximizing their pairwise support for these candidates. So there can be some value to analyzing the rated utilities/Score voting result or ranking ([[order of finish]]) of the candidates when analyzing how the [[Smith set ranking]] produced by rated pairwise ballots will look like. |
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A voter's rated pairwise preference can be partially expressed as a ranked preference augmented with margins. So, for example, A 30%>B 50%>C 100%>D 100% (which could also be written as A 0.3>B..., or A 40% to 10%>B 80% to 30%, etc.) would indicate the voter gave a 30% margin to A>B, a 50% margin to B>C (implying, by transitivity, that they gave at least a 50% margin to A>C as well), etc. This doesn't tell you how the voter scored matchups involving candidates who are more than one rank apart, however. |
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=== Connection between Condorcet, Smith set, and Asset === |
=== Connection between Condorcet, Smith set, and Asset === |
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