[EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on ballot?

[Kevin Venzke]

 Hi Robert,
I'll add a bit below but the long story made short is that under WV, you traditionally don't add any tally to the pairwise matrix for a single ballot's tied rankings, no matter whether the equality is implicit or explicit.
Also, the conventional wisdom is that voters don't want to create strong defeats among the candidates they like. So if you had different treatment for implicit or explicit equality, you might if anything want to add the tally for ties among truncated candidates, not explicitly ranked candidates. (But I don't actually think you should do that.)

    Le lundi 20 mai 2019 à 23:06:57 UTC−5, robert bristow-johnson <rbj at audioimagination.com> a écrit :  ---------------------------- Original Message ----------------------------
>> Hi Robert,
>> In a WV method you can't trace beatpaths through a loss.
>I agree with that (but i don't think it speaks to the point).  You **can** include a tie in a beatpath, no?  And, if it's >RP with WV instead of margins, a tie can be used in the ranking graph, no?
Generally no... With RP in particular I can't imagine it, because you are locking defeats in descending order of strength. Even if you assign a defeat strength to a tie, there is no way to say in which direction it can be locked.
I wonder if you're thinking of the Schwartz set which has kind of a tricky definition. To be in the Schwartz set you need a path of wins to those candidates that have such a path to you. So you don't need a path to everyone. Tied contests can help you, but you don't actually trace through them.

>But this is notabout ties in the vote totals.  This is about whether we count ties on an individual ballot toward vote totals or do not count them.

>> So if A defeats B you can only trace from A to B, and the strength of the defeat is equal to the number of voters who preferred A>B.
>Only forWV.  For Margins, the strength of the defeat is the number of voters who prefer A>B minus the number >of voters who prefer B>A.  Now for Margins, that net margin is unchanged if we count equal ranks as votes for both or votes for neither.
>But it **does** make a difference ifwe're measuring defeat strength using WV.

>> (If you added half a vote to A in the case of an equal ranking between A and B, this gives the same effect as margins, assuming you applied this rule everywhere.)
>for Margins, adding half a vote (to both A and B) or no vote to either or onevote for both makes no difference in the defeat strength.  but it makes a difference for WV.
What I mean is that if you always add half votes for (both types of) equality under WV, the method will give the same result as margins.

>> Normally these methods do not show a difference based on whether an equal ranking was explicit, vs. implied via truncation.


>If we don't count equal ranking as votes for eithercandidate, you're correct.  But if we *do* count equal ranked >(active ranking, higher than unranked), there is a difference for WV.  If two candidates were equally ranked (and >not unranked), that WV is in the beatpath.  It could end up counting in the net beatpath score, no?
If you used such a rule then yes. But typically there is no concept of ranked vs. unranked.

>> I would say this is mostly because explicit vs. implicit ranking isn't really native/inherent to the idea of Condorcet. >>But I'd suggest also because a distinction in treatment doesn't help the voter. A "half vote" treatment turns equal >>ranking into a "neither here nor there"strategy, where ranking your favorite candidates equal-top is prima facie >>not optimal regardless of your priorities.

>This last statement I can't figure out.
Compare this with the concept of giving half-approvals under Approval. In most scenarios it's not possible to calculate that giving a candidate half an approval is strategically optimal. Similarly if you use a treatment of equal ranking such that a vote for A=B is simply midway, in effect, between voting A>B and B>A, then you should imagine that one of A>B or B>A must be a better vote than equality. I see this as a loss because ordinarily WV comes quite close to meeting the principle that you can rank your true favorite candidate equal-top with your compromise choice without thereby making the compromise choice lose to somebody worse.
Kevin

  
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