3-2-1 voting: Difference between revisions

In '''3-2-1 voting''', voters may '''rate each candidate “Good”, “OK”, or “Bad”'''. (Alternately, they may rate one candidate "Good" and leave the rest blank;, inwhich thiswill casecause theirthe chosen candidate's predeclared ratingsrest of thetheir othersballot areto usedbe to fillfilled in the blanksautomatically.[[#Footnote_.C2.B9:_Blank_ratings|¹]]) The tallying process has three steps:

* Find '''3 Semifinalistssemifinalists''': the candidates with the '''most “good”''' ratings.[[#Footnote_.C2.B2:_rules_for_the_third_semifinalist|²]]

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

In this method, each candidate can pre-rate other candidates "OK", "conditionally OK", or "bad". If they do not explicitly pre-rate, they are considered to pre-rate all others "conditionally OK". Once all pre-ratings have been submitted, all "conditionally OK" pre-ratings are turned to "Bad" if the pre-rating coming from the other waycandidate is "Bad", and to "OK" otherwise. For example, if candidate A pre-rates candidate B "conditionally OK" and B pre-rates A "bad", A's pre-rating of B turns to "bad"; if A pre-rates B "conditionally OK" and B pre-rates A "OK" or "conditionally OK", A's pre-rating of B turns to "OK". Candidate pre-ratings are public information.

When a voter leaves a candidate X blank/unrated, and rates exactly one other candidate Y as "Good", that counts as rating X as "OK" if Y pre-rated X "OK". Otherwise, it counts as rating X "Bad". Implicit OKs in this sense are counted as lower than explicit OKs in stepthe 3final round of the tally.

For example, if I rated only Aurelio "good" and left Beth and Chung blank; and Aurelio pre-rated Beth as "OK" and Chung as "Bad", then I'd count as giving those ratings. If I'd also rated AmyDana "good", then my blank rating for Beth would count as "bad", no matter what AmyDana and Aurelio said.

This method 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 [[w:Condorcet_paradox#Likelihood_of_the_paradox|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.

In terms of summability, this can be done in one of two ways. TheyThe method can work with one count that is O(N²) summable, or with two consecutive tallies that are each O(N) summable (one for "3-2" and the second for "1"). The latter could make this feasible to run even on older ballot machines; though full counts of the second step might involve some configuration and a couple of passes over the ballots, in many cases the "3-2" tallies would make it obvious who wins the "1" step, so voters would not have to be kept in suspense as the second step proceeded.

In order toTo be usable for US presidential elections, a voting method should be able to work as an interstate compact alongside other methods. Such an interstate compact would have at most the following steps:

In order forFor a voting method to work with this, it must have a feasible way to work with steps 2, 3, and 4.

'''Step 2''': "raw totals in some format": many voting methods exist, and many of them require different information from the ballots for summability. One reasonable lowest common denominator would be that all states must publish the rating or ranking levels available, and the raw tallies — the number of times each candidate is rated or ranked at each level. This is far less information than would be required to find a winner under IRV or Condorcet, but it is enough for 3-2-1, when combined with the following steps. It is also information that naturally would always be available from states using simpler methods such as plurality or approval.

'''Step 4''': In order to add to provide national totals, each state's final totals should be in the form of a point method - that is, approval, score, or bordaBorda ballots, normalized so that each vote is in the range 0-1. This is not an endorsement of approval, score, or bordaBorda as voting methods; it's simply because these point methods are the only methods natively compatible with ballots from states still using plurality.

'''Step 3''': So a state using 3-2-1 must be able to look at the raw tallies from other states, and provide final local tallies, such that the following properties are satisfied: