# [EM] Schulze Method shortcut

Markus Schulze markus.schulze8 at gmail.com
Tue Aug 7 09:41:01 PDT 2018

```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.

(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.

(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.

Markus Schulze

```