[EM] Schulze Method shortcut

John john.r.moser at gmail.com
Thu Aug 9 11:12:28 PDT 2018

There is a theory that later-no-harm is not desirable, and satisfying
participation proper may not be desirable either by similar logic.

I'm not certain about Mono-Add-Top.  Alternative smith fails monotonicity;
although by adding a ballot that ranks X strictly above all candidates, X
(winner) would necessarily have a larger plurality first-vote than Y.  If Y
is in the Smith set already, it has fewer plurality first-votes than X, and
retains this going down the rounds, so ranking X first should keep it ahead
of Y in the elimination order.

You can add a ballot that ranks only X and removes candidate Z from the
Smith set, strengthening Y and causing Y to defeat X.  To me, this seems
unlikely; or, rather, it seems unlikely to matter in practice.  You'll find
that X has to be strong enough with voters to be in the running anyway, so
your best bet is to vote—and if you keep casting ballots that rank X above
everyone else, X is eventually going to become the majority winner.  These
are anomalies along the way.

On Thu, Aug 9, 2018 at 1:51 PM Kevin Venzke <stepjak at yahoo.fr> wrote:

> 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 my
> opinion, probably can't.
> I don't think it's worth worrying about Participation too much. Satisfying
> Participation seems to greatly
> constrain what kinds of logic a method can use. And the people who
> advocate methods that satisfy Participation
> probably aren't so dedicated to that aspect in particular.
> Kevin
> 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:
> Hi,
> 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
> Hallo,
> > 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.
> http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf
> Markus Schulze
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