# [EM] Schulze Method shortcut

John john.r.moser at gmail.com
Thu Aug 9 10:12:53 PDT 2018

```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

> (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
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>
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