[EM] Schulze Method shortcut

Kevin Venzke stepjak at yahoo.fr
Thu Aug 9 10:49:31 PDT 2018

 Note that Condorcet methods aren't necessarily Smith-efficient. (For example, plain minmax methods, or"Condorcet//Approval".) At least one Condorcet method satisfies mono-add-top, but Smith methods, in myopinion, probably can't.
I don't think it's worth worrying about Participation too much. Satisfying Participation seems to greatlyconstrain what kinds of logic a method can use. And the people who advocate methods that satisfy Participationprobably aren't so dedicated to that aspect in particular.

    Le jeudi 9 août 2018 à 12:13:12 UTC−5, John <john.r.moser at gmail.com> a écrit :  

On Thu, Aug 9, 2018 at 12:43 PM Arthur Wist <arthur.wist at gmail.com> wrote:


I suspect you didn't receive the below email since Markus Schulze
elected to not copy you onto his response. I've decided to thus foward
it to you.

Kind regards,

Arthur Wist

---------- Forwarded message ----------
From: Markus Schulze <markus.schulze8 at gmail.com>
Date: 7 August 2018 at 18:41
Subject: Re: [EM] Schulze Method shortcut
To: election-methods at electorama.com


> The Schulze method elects from the Schwartz set using a beatpath
> algorithm.  The usual explanation is incredibly complex, and complexity is
> undesirable but often necessary.  Would this method be equivalent?
>    1. Eliminate all candidates not in the Schwartz set.
>    2. If there is one candidate left, elect that candidate.
>    3. Exclude the pairwise race with the smallest win margin.
>    4. Repeat.
> Tideman's Alternative Schwartz is this, except #3 eliminates the candidate
> with the fewest first-rank votes.  I am leaning toward Tideman's
> Alternative Schwartz or Smith for their simplicity and resistance to
> tactical voting and nomination.

(1) The best possible election method according to the underlying heuristic
of instant-runoff voting will always be instant-runoff voting. Therefore,
I don't think that any supporter of instant-runoff voting will be convinced
by a hybrid of Condorcet voting and instant-runoff voting.

(2) The Schulze method satisfies monotonicity and reversal symmetry.
Instant-runoff voting and Tideman's alternative methods violate
monotonicity and reversal symmetry. Therefore, monotonicity and
reversal symmetry cannot be used anymore as arguments against
instant-runoff voting.

IRV tends to squeeze out candidates with weak first-rank votes but strong second-rank votes. 
(3) Promoting a hybrid of Condorcet voting and instant-runoff voting
will make the audience believe that there is a fundamental problem
when there is no Condorcet winner and that every possible way to solve
a situation without a Condorcet winner necessarily contains arbitrary
decisions. However, election methods like the Schulze method solve
situations without a Condorcet winner in a consistent manner without
having to step outside their underlying heuristic, without having to
resort to some other method, and without having to sacrifice
compliance with important criteria.

Condorcet methods are Smith-efficient:  they identify a particularly-suitable set of candidates meeting a sort of mutual majority criteria (strong support overall) and elect from that.  When that set is exactly one candidate, it is the Condorcet candidate.
Because these attempt to identify a strong candidate instead of a "winner" (someone with a certain number of votes—the most, a majority, or a quota), they can have some difficulty finding a resolution.  That is to say:  the strongest candidate defeats all others; yet that candidate may not exist, and so you find a set of such strong candidates.
Each underlying heuristic, thus, is designed to identify a particular strong candidate—a "winner"—in a way which elects from this set of strong candidates.  They're influenced in different ways (best ranking overall versus most broad acceptance or whatnot; one method even attempts to change the fewest votes to elect the candidate "closest to being the Condorcet candidate").
This decision is, itself, an arbitrary one:  you select one of these voting systems based on how you feel about picking one of multiple eligible suitors.  Score voters would probably lean toward Schulze more than Ranked Pairs because Schulze does something more akin to finding the candidate with the best marginal utility instead of the strongest rankings.
 Any ISDA method effectively throws out non-Smith candidates.  Doing so explicitly is thus similar in theory to using any so-called Condorcet method.  Tideman's Alternative Smith, for example, might find the plurality first-rank loser (which IRV eliminates) is a strong candidate in the Smith set, and second rank on many non-Smith-first-rank ballots, thus eliminating some other Smith candidate first.  This can lead to that candidate winning.
Alternative Smith is an underlying heuristic; while any ISDA method like Schulze is effectively "eliminate all non-Schwartz candidates and apply this heuristic" because the heuristic eliminates all non-Schwartz candidates.  The same is true of Ranked Pairs and other ISDA methods.  Schulze and Ranked Pairs have much-more-complex heuristics than Alternative Smith.

(4) "I am leaning toward Tideman's Alternative Schwartz or Smith
for their simplicity and resistance to tactical voting and nomination."
I don't see why Tideman's alternative methods are supposed to be more
resistant to tactical voting and nomination.

It inherits that from IRV.

Markus Schulze

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