[EM] The rationale under the "winning votes" defeat strength measure

Thu Jun 26 04:42:20 PDT 2025

Hi all,

Thanks for all your comments, axioms and explanations! From what I see, the
justification of WV is indeed rather pragmatic and strategy-oriented, which
is quite a problem for me. I would really prefer to avoid answering
the question: "Why did your rule elect a bad candidate in this election?"
by saying "Well, because you might have been dishonest in some specific
way, and then this candidate wouldn't be so bad". I also agree with Juho
that "in large public real life Condorcet elections it is very difficult to
implement and coordinate successful malicious strategies".

For example, the second example of Chris rather convinces me to support
margins and oppose WV, than the other way around. Let's see:
46: A
44: B>C
10: C
WV elect C here, while margins elect B. In fact, if the above preferences
are honest, then B is clearly the best candidate, since he is the closest
to be the Condorcet winner. Electing A or (especially) C would be extremely
unstable - if just one voter changes his preference from A to B, the result
would switch to B under any Condorcet rule. Moreover, B has much broader
support than C (assuming that A's supporters are truly indifferent between
both). I really can't find a logical justification of electing C here if
the voters are honest.

On the other hand, if we assume that voters were strategic and the honest
opinion of the middle voters is B or B>A, then it means that a massive
number of voters colluded to vote strategically, in a situation where (1)
the result of the race between A and B was unpredictable before the
election and B had real chances to win anyway, (2) a lot of voters had a
fragile preference of either B=A or B=C, and such a "dirty" operation of B
could easily change their minds to (respectively) A>B and C>B. I just don't
see this happening in practice. I can agree that such a theoretical
possibility is bad, because violating strategyproofness generally is bad,
but there's nothing particularly worrisome for me here.

Best,
Grzegorz

czw., 26 cze 2025 o 05:57 Chris Benham <cbenhamau at yahoo.com.au> napisał(a):

>
> There is also the Non-Drastic Defense criterion, which says that if more
> than half the voters vote X above Y and  X no lower than equal-top then
> Y can't win.
>
> 46  A>C (maybe sincere is A or A>B)
> 17  B
> 17  B>C
> 20  C=B (maybe sincere is C>B)
>
> B>A  54-46,   A>C  63-37,  C>B  46-34.
>
> Here B is above A and no lower than equal-top on more than half the
> ballots, but Margins elects A.   Winning Votes elects B.
>
> Also Margins can fail Later-no-Help especially egregiously and elect the
> weakest candidate:
>
> 46  A
> 44  B>C (sincere might be B or B>A)
> 10  C
>
> Margins elects B (failing the Plurality criterion).  How does the B
> voters ranking C remotely justify switching the win from A to B??  A
> pairwise beats and positionally dominates B, and C is ranked above
> bottom on the most number of ballots.  I can't accept any method that
> elects B here.  (Or A in the previous example.)
>
> I have long since decided that resolving Condorcet top cycles by
> deciding (on some basis or another) that some pairwise defeats are
> "weaker" than others is a dead end. I vastly prefer 3 other Condorcet
> methods: Margins Sorted Approval(explicit),  Margins Sorted Approval
> (implicit), and "Benham".
>
> They all resist Burial better than Margins or Winning Votes, and Margins
> Sorted Approval is very elegant.
>
> Chris Benham
>
> On 26/06/2025 1:50 am, Kevin Venzke via Election-Methods wrote:
> > Hi Grzegorz,
> >
> >> 1. What exactly are the axioms that Condorcet rules with WV satisfy,
> but with
> >> margins do not? (I'm only aware of the Plurality criterion)
> > Very few have been articulated, but:
> >
> >> 2. I have sometimes read that WV are better to prevent strategic
> behavior of
> >> the voters (without much details),
> > I do use the minimal defense criterion, which represents the notion that
> a full
> > majority of voters can always get their way if they want to, so it will
> reduce
> > compromise strategy for the majority if you just give them their way
> when you
> > know what it is.
> >
> > To me, WV resolution is an approximation of an ideal. I made a webpage
> that
> > attempts to show what options are available for electing from a provided
> cycle,
> > with the aim of avoiding compromise incentive when you can:
> >
> > https://votingmethods.net/check
> >
> > This doesn't always favor WV, and sometimes there are no actual
> solutions.
> >
> >> but do you have any idea how to justify WV
> >> more "intuitively" or "philosophically", assuming sincere votes?
> Margins are
> >> very easy to justify. I came up with two possible justifications for WV
> here
> >> (described below), but I'm not sure how convincing they could be for the
> >> general audience.
> > Here I'm not sure. I guess by "sincere votes" you mean that absence of a
> > pairwise preference indicates an expression that two candidates are
> equal. Or
> > maybe that truncation is not different from explicit equal ranking.
> >
> >> 3. Don't you think it is "ugly" that the WV measure applied e.g., to
> Schulze
> >> or RP/MAM requires us to artificially exclude "50% vs. 50%" ties between
> >> candidates from consideration (or equivalently, to mark them as the
> weakest)
> > That's never occurred to me actually. All non-wins are excluded from
> > consideration.
> >
> >> --- and that a victory "50%+1 vs. 50%-1" is rapidly considered to be
> quite
> >> strong, stronger than e.g., a "45% vs. 1%" victory (with 54% voters who
> rank
> >> both candidates equally)? Under margins, ties or close ties are
> naturally
> >> considered the weakest. How would you refute this argument?
> > Ideally by some kind of rephrasing. I don't know if this is possible,
> but it
> > would be nice if the matter could be presented without making it feel
> like the
> > defeats themselves have an interest in being respected.
> >
> > Alternatively, you want to find a explanation where losing votes are just
> > meaningless, because for the practical purposes (the strategic incentive
> ones),
> > they are. You don't obtain a valid complaint against the method by
> losing a
> > close race, you can only get one by winning races and losing anyway
> because you
> > didn't lie.
> >
> > (In a 51:49 matchup, those on the losing side have no power to lie and
> change
> > the outcome (we hope), while there is considerable possibility that
> those on the
> > 51 side *could* lie and win (i.e. if they had not), because they
> comprise more
> > than half the voters. With 45:1, there are decent odds that those on the
> 45%
> > side could win by lying; your method could determine this to be sure, if
> you
> > wanted, before ruling for instance that 45:1 prevails over a win of
> 40:39. WV is
> > just making a mathematically easy "best guess.")
> >
> >> Regarding pt. 2, here are my ideas for a high-level intuitive principle
> behind
> >> WV:
> >> (1) "It is much harder (infinitely harder?) to convince a voter to
> change his
> >> mind from B<A to A>B, than it is to change his mind from A=B to A>B".
> Then, in
> >> particular, it is more probable that a "45% vs. 1%" victory would
> become a
> >> "45% vs. 55%" defeat, than that a "51% vs. 49%" victory would become a
> defeat.
> > That has some familiarity to me. If the winning side has a full majority
> then we
> > "know" it is right. In fact if you entertain the concept of an overall
> "median
> > voter" it suggests to us something about what that voter thinks.
> >
> > Though I understand that you want to suppose that the equalities are in
> fact
> > sincere.
> >
> > In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation would be
> that the
> > median position is that A and B are equal. The 54% aren't just
> abstaining, are
> > they? I don't think that's what the assumption of sincerity implies.
> >
> > Your second idea is kind of suggestive of this actually... You're just
> focusing
> > more on voters' desire for how the matchup is handled.
> >
> >> (2) "If a voter votes for A=B, then he is not neutral, but he is
> actively
> >> voting against treating the resolution of the matchup between A and B as
> >> important". Then, in particular, in the case of a "45% vs. 1%" victory,
> we in
> >> fact have 45% of voters who consider it important to resolve the
> matchup in a
> >> particular direction, and 55% of voters who think otherwise. This is a
> smaller
> >> number than for a "51% vs. 49%" victory.
> > I view this possibility of voters having such a sentiment, and acting on
> it in
> > this way, more as something useful that WV enables. I don't think we can
> say
> > it's intuitively the case that voters are meaning to do this.
> >
> > Kevin
> > votingmethods.net
> >
> > ----
> > Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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