[EM] Schulze Method shortcut

[Pareto Man]

Hi Markus,

I realize now that the method I was wondering about is just common old
minimax.  I am thinking it would be cool to add a Schulze beatpath.  I
guess I would do it by finding the Schwartz set like John moser suggested.

Paul

On Sat, Aug 11, 2018 at 3:09 PM, Pareto Man <paretoman1 at gmail.com> wrote:

> 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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>>
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