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

robert bristow-johnson rbj at audioimagination.com
Mon May 20 21:06:48 PDT 2019

---------------------------- Original Message ----------------------------

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

From: "Kevin Venzke" <stepjak at yahoo.fr>

Date: Mon, May 20, 2019 6:48 pm

To: election-methods at lists.electorama.com

"robert bristow-johnson" <rbj at audioimagination.com>


> 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?
But this is not
about 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 for
WV.  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 if
we'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 one
vote for both makes no difference in the defeat strength.  but it makes a difference for WV.
> 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 either
candidate, 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?

> 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.
r b-j
> Le lundi 20 mai 2019 à 16:06:32 UTC−5, robert bristow-johnson <rbj at audioimagination.com> a écrit :





> So this would be about Tideman Ranked-Pairs, or Schulze, or some other Condorcet-compliant method.


> It doesn't make much difference if the measure of Defeat Strength is Margins (supporting votes minus opposing votes), but what if Winning Votes is the measure of Defeat Strength in either RP or Schulze?  How should a pair of candidates that are equally-ranked on a ballot be counted? 
Do you count it (as a winning vote) for *both* candidates?  For neither candidate?  (I dislike the idea of a half-vote for both candidates.  And I hate the idea of not allowing equal-ranking in a Condorcet RCV election.)

> What is the right way to do this?  It seems the most consistent might be to count an equally-ranked votes for **neither** candidate, since we consider unranked candidates as tied for last place on the ballot, and we would *not* count those as votes.


> But what do you guys think?  If we allow for equal-ranking in a Condorcet-compliant RCV, how do we deal with it in terms of vote totals?



r b-j                         rbj at audioimagination.com

"Imagination is more important than knowledge."

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