3-2-1 voting: Difference between revisions

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In 3-2-1 voting, voters may rate each candidate “Good”, ~~“Acceptable”~~, or ~~“Rejected”~~. It has three steps:

In 3-2-1 voting, voters may rate each candidate “Good”, “OK”, or “Bad”. It has three steps:

* Find 3 Semifinalists: the candidates with the most “good” ratings. ~~(If this is a partisan election, no two semifinalists may come from the same party).~~

* Find 3 Semifinalists: the candidates with the most “good” ratings.

* Find 2 Finalists: the semifinalists with the fewest ~~rejections~~.

* Find 2 Finalists: the semifinalists with the fewest "bad" ratings.

* Find 1 winner: the finalist who is rated above the other on more ballots.

There are two extra qualifications for semifinalists: their "good" ratings should be more than anyone else in their party (that is, only one semifinalist per party), and at least 15% of the electorate. Usually all three semifinalists will easily pass these qualifications naturally, but if only 2 of them do, you can just treat them as finalists and skip step 2.

== Motivation for each step ==

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It satisfies the [[mutual majority criterion]] as long as any member of the mutual majority set of candidates is among the 3 semifinalists. In practice, this is almost guaranteed to be the case.

Steps 1 and 3 satisfy the [[later no-harm criterion]]. Thus, the only strategic reason not to add any "~~acceptable~~" ratings would be if your favorite was one of the two most-rejected semifinalists but also was able to beat the least-rejected semifinalist in step 3. This combination of weak and strong is unlikely to happen in real life, and even less likely to be predictable enough a priori to be a basis for strategy.

Steps 1 and 3 satisfy the [[later no-harm criterion]]. Thus, the only strategic reason not to add any "OK" ratings would be if your favorite was one of the two most-rejected semifinalists but also was able to beat the least-rejected semifinalist in step 3. This combination of weak and strong is unlikely to happen in real life, and even less likely to be predictable enough a priori to be a basis for strategy.

This system fails the [[favorite betrayal criterion]], in that in steps 1 or 2 it could in theory be necessary to rate your favorite below "Good" in order to leave room for a more-viable compromise candidate to be a semifinalist or finalist. However, in order for that to be a worthwhile strategy, the compromise would have to do better in a pairwise race against the other finalist, but have a worse chance of becoming a semifinalist or finalist under your honest vote. This combination of strength in one context and weakness in another is akin to a Condorcet cycle, and like such cycles, it may be rare in real-world elections, and even rarer that it is predictable enough a priori to make a favorite-betrayal strategy feasible.

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! Candidate

! "Good" ratings

! "~~Acceptable~~" ratings

! "OK" ratings

! "Bad" ratings

! 2-way score

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! Faction size

! "Good" candidates

! "~~Acceptable~~" candidates

! "OK" candidates

! "Bad" candidates

|-

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