Preference Approval Sorted Margins

  • Re: Least-bad Single-winner Ranking Method?

    Among Condorcet methods, I'm most happy with Approval Sorted Margins. It's simple and resolves in a sensible way.

    I used to maintain that page a lot but haven't had time recently.

    Lately I like to think of the method as Preference Approval Sorted Margins. I feel like it's less confusing for voters if any ranking above Reject is interpreted as some level of acceptance for that candidate winning, but that there is a higher preference for certain candidates.

    Let's say you have 6 tiers of approval. The top 3 tiers, A, B, and C, are preferred. Tiers D and E are approved (tolerable / acceptable). Tier F is disapproved/Reject. Rank can be inferred from rating.

    This gives the same degree of expression as 4 levels of ranking with a preference cutoff. In general, any ranking with M levels with a preference cutoff is equivalent to 2M - 2 levels with top (M-1) ranks preferred, next (M-2) ranks approved, bottom rejected.

    Voters are instructed to give a rating of A, B, or C to their preferred candidate, ratings D or E to candidates they can tolerate, and F to those they reject completely.

    Count pairwise preferences and total preference, and total approval.

    Seed an initial ranking by sorting in descending order of total preference, breaking ties with descending order of total approval. There's some room for argument on further tie-breakers, but that should do for now.

    Then search the entire seeded ranking for the pair that is out of order pairwise, with minimum preference margin (breaking ties with minimum approval margin, etc.). Swap that pair. Then repeat until the sequence is in pairwise order.

    This process is symmetric and biased toward higher preference. It is intuitive to voters. It is Condorcet compliant, Smith efficient, and clone resistant. It is not completely burial resistant, but it is more resistant to chicken dilemma and burial than other methods (if an "ally" is a strategic threat, put them in the approved but not preferred slot).

    As described in the Electowiki page, this method is optimal in that it disrupts the overall preference rating as minimally as possible.

  • Can you add a procedure section to the electowiki page? There are a few sections which talk about this but they all add a ton of justification. I just want the procedure.

  • @Keith-Edmonds There is python code in , and it is also described in section

    The general procedure for PASM is,

    Tabulate total preference and pairwise scores.

    Seed initial candidate ranking by sorting in descending order of total preference.

    Repeat until the candidate ranking has no pairwise out-of-order candidates:

    Find all pairwise out of order pairs. (i.e. A(Y, X) > A(X, Y), for candidate X earlier than Y)
    Select the pair with minimum preference margin (i.e., P(X) - P(Y) is minimal for all such pairs
    Swap those candidates in the ordering.

    The winner is the first candidate in the resulting sequence.

  • I am not sure I understand and I think that says something. If somebody who spends time looking into this stuff can't understand it in under 30seconds then it is likely not viable with the masses.

  • @Keith-Edmonds Could you be more specific about what you don't understand?

    Do you understand tabulating total preference? If not, if you are using scores 0 to 5, with 3 and higher preferred, then total preference score is the sum of all ballots 3 and higher. If you are using A, B, and C for preferred votes, total preference is all ballots scoring A, B, or C, and total approved is all ballots scoring A-E, excluding F.

    Do you understand the pairwise array? If not, that is a matrix A[i,j], with rows and columns corresponding to the candidates. A[i,j] is incremented by 1 for every ballot that rates candidate i higher than candidate j.

    Do you understand putting the candidates in an initial ranking, seeded by preference score? If not, start with a sequence of all the candidates. Then sort them in descending order by their total preference score, above.

    Do you understand pairwise out of order? If not, consider each pair of candidates as you go through the candidate ranking, with X coming earlier (i.e. higher ranking) than Y. Pairwise out of order means that in the pairwise contest between X and Y, Y gets more ballots higher than X.

    Do you understand preference margin? If not, what that means is the difference between candidate X's total preference score and candidate Y's total preference score.

    I'm not sure what else might not be clear here. I guess I assumed that someone who spends time looking into this stuff would have familiarity with the terminology commonly used with Condorcet methods. I've explained this before to people completely unfamiliar with voting methods, and they could follow what I was saying.

  • @Ted-Stern said in Preference Approval Sorted Margins:

    Could you be more specific about what you don't understand?

    I have not spent a lot of time with Ranked or Condorset methods. I really only browsed it for 30 seconds. I am sure I could figure it out if I put in the time. My point was that if you want it to catch on you need to have a very clear layperson explanation.

  • @Keith-Edmonds I'm kind of disappointed. I was replying to a thread about ranked methods. In this forum, I would have thought that anyone interested in ranked methods would know the basics of Condorcet. At the very least, I was not writing with the expectation that my method would "catch on" with the public, but rather that readers of this forum would consider it and discuss it. Promotion is a completely different matter. As far catching on with the public, I think Approval has the best shot at that, since you can explain it in 10 seconds: Vote for every candidate you approve of.

    The ASM page has links to Condorcet, which you can read up on.

  • @Ted-Stern said in Preference Approval Sorted Margins:

    I would have thought that anyone interested in ranked methods would know the basics of Condorcet.

    I have no interest in Ranked methods. Sorry

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