[EM] Where the best Condorcet methods (Schulze, Ranked Pairs, River etc.) differ (Toby Pereira)

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[EM] Where the best Condorcet methods (Schulze, Ranked Pairs, River etc.) differ (Toby Pereira)

Forest Simmons
If the Smith set is a cycle of three, then the methods you mention give the same result as long as the defeat strength is measured the same way. (You knew that)

Not all of these satisfy Independence from Pareto Dominated Alternatives.  I doubt that would make a difference in any known public election from the past, but  all else being equal, it is a difference that could make a difference.

Simplicity of explanation and implementation, along with heuristic appeal, and other selling points may be more important than any other distinction among the methods you mention.  

For me the easiest to sell formulation of Schulze is in the form of "beat-path." But that is probably just the mathematician in me appreciating an elegant way of creating a transitive relation with minimal violence to the intransitive relation on which it is based.

Thanks for asking this question!



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Re: [EM] Where the best Condorcet methods (Schulze, Ranked Pairs, River etc.) differ (Toby Pereira)

Toby Pereira
Thank you for this response, Forest. I was reminded of this subject again when I re-encountered Jameson Quinn's work on Voter Satisfaction Efficiency the other day. According to his simulations, to be found here https://electionscience.github.io/vse-sim/VSE/ ranked pairs performs quite a bit better than the Schulze method. This surprises me since I wouldn't expect much difference in practice (as I put in the original post of this discussion). I'm not sure if Jameson still reads the stuff on this mailing list, but it would be interesting to know what caused the difference.

Toby


On Wednesday, 4 March 2020, 17:45:08 GMT, Forest Simmons <[hidden email]> wrote:


If the Smith set is a cycle of three, then the methods you mention give the same result as long as the defeat strength is measured the same way. (You knew that)

Not all of these satisfy Independence from Pareto Dominated Alternatives.  I doubt that would make a difference in any known public election from the past, but  all else being equal, it is a difference that could make a difference.

Simplicity of explanation and implementation, along with heuristic appeal, and other selling points may be more important than any other distinction among the methods you mention.  

For me the easiest to sell formulation of Schulze is in the form of "beat-path." But that is probably just the mathematician in me appreciating an elegant way of creating a transitive relation with minimal violence to the intransitive relation on which it is based.

Thanks for asking this question!


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Re: [EM] Where the best Condorcet methods (Schulze, Ranked Pairs, River etc.) differ (Toby Pereira)

robert bristow-johnson


> On May 29, 2020 3:46 PM Toby Pereira <[hidden email]> wrote:
>
>
> Thank you for this response, Forest. I was reminded of this subject again when I re-encountered Jameson Quinn's work on Voter Satisfaction Efficiency the other day. According to his simulations, to be found here https://electionscience.github.io/vse-sim/VSE/ ranked pairs performs quite a bit better than the Schulze method. This surprises me since I wouldn't expect much difference in practice (as I put in the original post of this discussion). I'm not sure if Jameson still reads the stuff on this mailing list, but it would be interesting to know what caused the difference.
>

>
>
> On Wednesday, 4 March 2020, 17:45:08 GMT, Forest Simmons <[hidden email]> wrote:
>
>
> If the Smith set is a cycle of three, then the methods you mention give the same result as long as the defeat strength is measured the same way. (You knew that)
>
> Not all of these satisfy Independence from Pareto Dominated Alternatives. I doubt that would make a difference in any known public election from the past, but all else being equal, it is a difference that could make a difference.
>
> Simplicity of explanation and implementation, along with heuristic appeal, and other selling points may be more important than any other distinction among the methods you mention.
>
> For me the easiest to sell formulation of Schulze is in the form of "beat-path." But that is probably just the mathematician in me appreciating an elegant way of creating a transitive relation with minimal violence to the intransitive relation on which it is based.
>

For me, the easiest sell is what makes for simpler and easy-to-understand legal language, since cycles will be exceedingly rare and a cycle bigger than Rock-Paper-Scissors will almost certainly never happen.  And RP and Schulze and River elect the same candidate for the Condorcet case and the 3-candidate Smith set.

Now that is different than the STV-BTR, which I am actively plugging for lawmakers here in Vermont.  In the case of Rock-Paper-Scissors, STV-BTR will elect the candidate with the most votes in the semifinal round.  But I am finding that the language for STV-BTR is far easier to sell than even RP.

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