[EM] Schulze Method shortcut

[Pareto Man]

Hi Markus,

I would appreciate any feedback you can give on this game I adapted from
Nicky Case.  https://paretoman.github.io/ballot/log.html

What method would you call this?  It isn't exactly Schulze beatpath.  I
would describe it as pair elimination.

Paretoman

On Thu, Aug 9, 2018 at 2:12 PM, John <john.r.moser at gmail.com> wrote:

> 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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