[EM] Condorcet methods - should the cycle order always determine the result order? (Toby Pereira)

[Juho Laatu]

On 06 Nov 2014, at 03:28, Toby Pereira <tdp201b at yahoo.co.uk> wrote:

> Yes, you're right that some methods that fail independence of clones do so far more spectacularly than others. And also what you say about my example where A, B and C might be candidates of the same party but might just happen to be ranked adjacently. But I suppose that's the problem of ranked ballots - that there is no single non-arbitrary method of deciding a winner. And that is one advantage of approval/score. You would get very little disagreement about how to find the winner.

I think also other ballot formats, like rated ballots, have some similar problems, i.e. there is no one clear answer to the question what is the ideal way to decide who the winner should be. We could discuss about average score vs. sum of scores, or average score vs. not many low scorings. I agree that it is typically easy to find the agreement in approval/score since the basic summing of the approvals/scores is so obvious first choice.

The problem is also on the real life side in the sense that there are different kind of electons with different needs. Therefore different methods may be ideal (or closest to ideal) for different needs.

Also the strategy questions play a role in the sense that often, even if we wanted to use ratings, we are forced to use rankings because of the risk of excessive strategic voting in competitive environments. A nicer way to explain this is to say that ranked methods give exactly one vote to every voter (in the pairwise comparisons). From this nice equality point of view it is quite possible to find ideal explanations for ranked methods on who should win.

One problem with ranked methods (and especially the Condorcet family) is that the methods try to be very strategy free (and they indeed are), and this sets some limitations to the design. For example it is a natural thought that the number of losses (to different candidates) would be a rather nice measure of popularity, but we can't usually use that criterion since it typically makes the methods vulnerable to clones. I gave one ideal winner explanation to minmax(margins). It focused on worst losses and told that this may be a useful measure of amount of opposition after the election. We could also say that a useful measure of opposition is the number of voters who would like to change the winner to any other candidate, not to some specific candidate. But that explanation is thus ruled out because the strategy and clone related concerns. We must satisfy with comparing the worst losses and contemplate if that is a natural way to measure who should win in our elections.

> That and you get a clear order with an easy-to-digest way of seeing how close it was - total approvals or score (or average score). I do think these things are worth considering in a method. For a Condorcet system, the minimax system has an advantage over most others in that you can put the finishing positions of all the candidates, as well as a meaningful number by them (the number of extra ballots required to make them a winner). Dodgson is the same, so that makes me wonder - which other Condorcet methods are like this? I almost think it's worth being a named criterion in its own right. Candidate result scorable or something.

Yes, being able to display the results and/or distance to winning the race in an easy to understand way is a good target that could be formulated as a criterion. It may be a true problem of many Condorcet methods that displaying the pairwise comparison values in a matrix or in a cyclic graph is too complex. It may also be difficult to give clear numbers even to experts on how close each candidate is to winning the race. Meadia wants to tell people about the race, also online while waiting for the final results, with clear numbers if possible. (I welcome input here. What can we say about the distance to winning the race in different Condorcet methods?)

As you can already guess, I also don't like very much the idea of forcing the potentially cyclic results into a linear order in some way that "breaks the loops" since that approach easily gives a distorted impression of the relative position of the candidates (the score / minmax ordered results are however ok). This expression, "breaking the loops" (that do exist, are natural, and should not be hidden) actually points out quite well what is wrong in the artificial linearization of the group opinions (also with respect to finding the best winner, not just with respect to giving nice histograms to media).

Juho


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