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

[Closed Limelike Curves]

*Once again -- your argumentation is based on the assumption that
preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences
are 46: A, 44: B, 10: C. I see no reason for a voting rule to presume that,
having only the actual results in hand. *

If we’re assuming complete honesty from the voters, score voting becomes
optimal almost by definition (or by Harsanyi’s utilitarian theorem). The
advantage of median and Condorcet rules is supposed to be better
performance if only some voters strategically exaggerate.

The major issue for margins is that, with strategic voters, the election
results become effectively random just like for Borda, and even a
universally-ranked-last candidate can win. The mailing list calls this DH3
and talks about “burial resistance criteria”, but I find this focus on
criteria instead of specific models of election outcomes kind of silly, so
I’ll say it’s better explained in Burt Monroe’s turkey-raising paper, where
he games out Myerson-Satterthwaite-style equilibria.

On Mon, Jun 30, 2025 at 1:36 AM Juho Laatu via Election-Methods <
election-methods at lists.electorama.com> wrote:

> Hi,
>
> I think it is quite natural that the circular Condorcet examples can be
> seen from multiple viewpoints (even too many to cover them all), based on
> what one is studying, what one is seeking to prove, what the details of the
> given example happen to be, and where one's random thoughts might lead him
> to. E.g. are the described votes sincere or strategic, and what the
> original sincere preferences could be, what alternative strategic votes
> there could be, or who would be the best winner (in the absence of a
> Condorcet winner). Discussions on the EM list have been active for many
> years, and still are. It is far from easy to pack the final conclusions
> from the numerous, typically cyclic voting scenarios in few sentences that
> everyone would agree.
>
> One problem is that we often tend to focus and limit ourselves to
> "laboratory examples" where all the preferences of the voters are 100%
> known, they are 100% stable, and we can 100% decide what kind of (sincere
> of strategic) votes the voters will cast, usually as few uniform blocks of
> voters. With that we can typically prove that something like that would be
> theoretically possible also in real life elections. But in order to draw
> more stable conclusions on how different methods tend to behave in real
> life elections, we would have to include in the picture also changes in
> time and inaccuracy of  the (multiple) polls, later changes in the opinions
> of the voters, possible multiple rational and irrational strategic plans,
> strategies of individual voters, strategies recommended by experts (from
> the party office), ability of those experts to influence on how people
> vote, willingness and ability of the voters to follow the proposed
> strategies, reactions of voters to the plans to "fool the system", high
> number of different preferences among the voters (not just three of four)
> etc. That is a softer and more difficult target to reach.
>
> I think we are still missing a "generic short handbook for voters on how
> to vote in real life elections". How close do we get by saying "just vote
> sincerely", or by saying "just let the party office tell you how to vote in
> these elections"? (maybe a separate handbook needed for those party
> strategists?)
>
> One question that was also present in this discussion is how much emphasis
> we should put on defending against some strategic voting threats vs how
> much we should concentrate on providing best results with sincere votes. We
> need to convince the voters (and the politicians) that the proposed method
> behaves well, any make sure that the method is understandable, and its
> philosophy makes sense to them. Different audiences may have different
> needs, voting traditions, fears, and old habits that they need to learn
> away from.
>
> Most people on this list (including me) agree that Condorcet methods might
> have something to offer to the world. Condorcet methods are quite good in
> general, of course depending on if the compromise seeking philosophy of
> Condorcet methods is what the society needs and wants (instead of e.g.
> allowing the first preference plurality winner always win).
>
> Juho
>
>
> On 30. Jun 2025, at 7.59, Chris Benham <cbenhamau at yahoo.com.au> wrote:
>
>
>
> Once again -- your argumentation is based on the assumption that
> preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences
> are 46: A, 44: B, 10: C.
>
> Not entirely.  I am arguing that electing B is a complete nonsense result
> regardless of whether the votes are sincere or not due to the egregious
> failure of the Plurality criterion.  I am not arguing that WV is a great
> method or even that is in every way superior to Margins.
>
> The A supporter's complaint against the Margins result is not that C
> didn't win, it is that their candidate was defeated by B. Suppose this is
> the first post FPP election, the A supporters were quite happy with FPP and
> are not interested in either the preferential voting algorithm at least
> partly because they dislike both the other candidates equally.   Their
> complaint is that their candidate clearly has more support on the ballots
> than B, and whatever convoluted algorithm/argument that says that B should
> win must be BS.
>
> "No rule could respect all pairwise defeats between A, B and C, and the
> one between A and B was the least decisive. If you only cared about having
> A elected, then sorry, but 54 voters preferred C. And according to your
> preferences B is as good choice as C, so if you preferred C to be elected,
> you should have voted A>C, not A".
>
> And they are right.
>
> ..to me it would be more egregious to say to B's supporters "the rule
> elected C instead of B, because it presumed that your preference C>A was
> dishonest"
>
>
> I don't see why, but my answer to the B supporters' complaint would be
> "You cannot imagine that your candidate should be elected because A has
> more first-place votes than your candidate has any sort of votes. C has
> more (some sort of ) votes than B. No-one told you that this method meets
> Later-no-Harm so why did you rank C if you are not content for C to win?"
>
> That to me very easily trumps "Oh but according to the Margins algorithm B
> was the closest to being the Condorcet winner."
>
> Answering the A supporters' possible complaint against C winning is not
> too difficult: "C pairwise beats A and is ranked above bottom on more
> ballots than A.  Electing A could cause the B>C voters to regret not voting
> B=C or C>B or C".
>
> I don't believe our discussion is decidable so maybe we have reached the
> point where we should just "agree to disagree" on that matter.
>
>
> If this discussion was private I might have come to the same conclusion
> sooner.  You have ignored several of my direct questions.
>
> Chris
>
>
> On 30/06/2025 3:12 am, Grzegorz Pierczyński via Election-Methods wrote:
>
> Chris,
>
> Once again -- your argumentation is based on the assumption that
> preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences
> are 46: A, 44: B, 10: C. I see no reason for a voting rule to presume that,
> having only the actual results in hand. But even if we accept this
> assumption, it only demonstrates that Margins can violate IIA/Later-no-help
> (bad, but unavoidable for Condorcet) if you alter preferences in 44 votes
> out of 100 (quite a lot). In the same way you could e.g., presume that the
> real preferences are 46: A, 44: B>C, 2: C>B, 8: C and then WV would violate
> Later-no-harm with only altering 2 votes out of 100, while Margins would be
> resistant to that. In fact, the "stability" of Margins provides us (as a
> side effect) that, since it is harder than under WV to alter the result by
> changing preferences of a tiny fraction of the voters, it is also harder to
> successfully strategize by a tiny fraction of the voters.
>
> In general, I haven't seen a convincing argument that C is a good winner
> under honest votes in this election and to me it would be more egregious to
> say to B's supporters "the rule elected C instead of B, because it presumed
> that your preference C>A was dishonest" than to say to A's supporters: "No
> rule could respect all pairwise defeats between A, B and C, and the one
> between A and B was the least decisive. If you only cared about having A
> elected, then sorry, but 54 voters preferred C. And according to your
> preferences B is as good choice as C, so if you preferred C to be elected,
> you should have voted A>C, not A".
>
> I don't believe our discussion is decidable so maybe we have reached the
> point where we should just "agree to disagree" on that matter.
>
> Grzegorz
>
> niedz., 29 cze 2025, 02:46 użytkownik Chris Benham <cbenhamau at yahoo.com.au>
> napisał:
>
>> Grzegorz,
>>
>> Since you had to alter a lot of votes to get this effect (and in fact
>> obtain a completely new election), I wouldn't say it is a particularly
>> outrageous failure of these axioms.
>>
>>
>> No, not a "completely new election".  Say the first one is the result of
>> a completely accurate poll. Say all the voters really want their favourites
>> to win and their preferences among their non-favourites are very weak or
>> non-existent.
>>
>> 46  A
>> 44  B
>> 10  C
>>
>> Come the actual election the A supporters think "We are the largest
>> faction and we know this method fails Later-no-Harm, so we shall (quite
>> sincerely) truncate."  The B supporters think "If we (sincerely) truncate
>> then we will almost certainly lose to A. We know this method fails
>> Later-no-Help, so why don't we rank C in second place and see what
>> happens?  This can't do any harm because C is on 10% and so presumably
>> can't win, and/or if our favourite B can't win then we don't care who
>> wins."  The C voters think "We don't like or care about A or B. We are just
>> here to fly the flag for our candidate with a view to maybe being
>> competitive in a future election."
>>
>> So in the actual election we get:
>>
>> 46  A
>> 44  B>C
>> 10  C
>>
>> And Margins elects B. Yes all Condorcet methods fail Later-no-Help, but
>> this is an especially egregious and simple example. And it is combined with
>> a failure of the Plurality criterion, which says that if A has more
>> first-place votes than B has any (above-bottom) votes then B can't win.  I
>> like something similar, that says if A both positionally dominates B and
>> pairwise beats B, then B can't win. By "positionally dominate" I mean that
>> A has more first place votes, more first and second place votes, and so on
>> down to more above-bottom votes.)
>>
>> So forget about C for the time being and just focus on the A>B pairwise
>> comparison. To any person who doesn't fetishise the Margins algorithm and
>> has some common sense, there is no case for A losing to B.  When the A
>> supporters ask you "How did our candidate lose to B?? We understand this is
>> some sort of preferential system, but B got no second-place votes and A got
>> more first-place votes" you tell them what?   Do you really think that they
>> will and should be satisfied with some mumbo-jumbo about B being "closer to
>> being the CW"?
>>
>> You and Juho like to talk about "stability".  Do you really think that
>> (if the stakes are high)  that this (social stability) is enhanced by you
>> openly shafting the largest faction??
>>
>> Hopefully I have now got it through your  skull that B is an unacceptable
>> winner due to A.    So what about the C>A comparison?  The WV philosophy is
>> that if there is no voted CW and enough truncation then it is possible that
>> there is a sincere CW due to some sincere preferences that the truncation
>> is concealing and so it is important that we elect one of the candidates
>> who could be that sincere CW.
>>
>> C has a  pairwise win over A that can't be undone by filling in some
>> truncated  ballots in a way that favours A, so A can't be this
>> (hypothetical, imaginary) "sincere CW".  But C's pairwise loss to B could
>> go away if the A truncating ballots were filled in (changed) to A>C.
>> So WV elects C.
>>
>> But I am not  on board with this philosophy. If voters choose not to
>> express some of their pairwise preferences I don't see how doing anything
>> other than simply assuming they don't exist is justified.
>>
>> It could be that the only insincerity is the C faction truncating against
>> B, so B is the sincere CW and electing C is letting that faction get away
>> with defecting from the presumed BC coalition.
>>
>> That is one of the main reasons I like Margins Sorted Approval
>> (explicit). If the B<C voters have beating A no-matter-what as a high
>> priority then they can approve C.  If on the other hand they were expecting
>> the C supporters to return the favour and vote C>B and they want to ensure
>> that they can't steal the election from B by defecting then they can
>> approve B only.
>>
>> Well, the intuition that "if there is no CW, then the candidate who was
>> (in some sense) the closest to be the CW should win" is a high-level
>> rationale behind a lot of rules (Minimax, Kemeny-Young, Dodgdon, Ranked
>> Pairs, Schulze, etc.) introduced by different people over time.
>>
>>
>> Possibly, but why do you assume that this approach  is correct?
>>
>> Chris Benham
>>
>> On 27/06/2025 8:10 pm, Grzegorz Pierczyński wrote:
>>
>> Hi Chris,
>>
>> Well, the intuition that "if there is no CW, then the candidate who was
>> (in some sense) the closest to be the CW should win" is a high-level
>> rationale behind a lot of rules (Minimax, Kemeny-Young, Dodgdon, Ranked
>> Pairs, Schulze, etc.) introduced by different people over time. I
>> understand that you don't share this intuition and prefer different
>> methods, but it's quite radical to call it "very weak" and "bizzarre".
>>
>> "Any close election (Condorcet or not) can be "unstable" in this way."
>>
>> Yes, but for me there is a difference whether the result of the closest
>> (least stable) comparison between A and B decides between the election of A
>> or B (which is natural) or between the election of B or C (which is weird).
>>
>> "By what bizarre stretch of the imagination has extra (second place)
>> votes for C strengthened any candidate other than C? The winner should
>> either still be A or change to C."
>>
>> Since you had to alter a lot of votes to get this effect (and in fact
>> obtain a completely new election), I wouldn't say it is a particularly
>> outrageous failure of these axioms.
>>
>>
>>  In both cases this is unavoidable under any Condorcet rule, so I'm a bit
>> surprised by this argument. Since you had to alter a lot of votes to get
>> this effect (and in fact obtain a completely new election), I wouldn't say
>> it is a particularly outrageous failure of these axioms.
>>
>> In general, the discussion about "which method is least vulnerable to
>> strategy" is quite arbitrary and hand-wavy for me in the situation where
>> all the methods are vulnerable and there is no single objective measure of
>> this vulnerability. And the arguments based on that don't justify
>> sacrificing the quality of the winner under sincere votes. For your example
>> with 46: A, 44: B>C, 10: C, I really can't convince myself that electing C
>> is justified. The argument that "B's supporters could have a preference of
>> B or B>A instead of B>C, and then B would have lost" is not convincing to
>> me if we only have the actual results of the election and don't know if
>> such an alternative scenario was even seriously considered by B's
>> supporters. Your argument with "Possible Approval Winner" is more
>> convincing, but I have two problems with it:
>> (1) A practical one: if you want to use AV as a justification, you
>> additionally need to explain AV to people, convince them that AV is a good
>> method (so that the possibility of being the AV winner is a good
>> justification) and at the same time, convince them that it is a bad method
>> (so that you do not advocate for it but for Condorcet).
>> (2) A theoretical one: using AV as a quality measure, requires us to
>> assume that people have objective "approval sets" in mind. I don't
>> believe so, but even if we take this for granted, then it is arbitrary to
>> assume that they are non-empty. It is perfectly possible that some of A's
>> supporters have a weak preference of A>B=C but in fact do not like anyone,
>> and the most approved candidate is B.
>>
>> "I look forward to reading someone's argument that electing A in my other
>> example is justified."
>>
>> My honest and totally subjective opinion about this example is that the
>> preferences there are quite weird and (if they are sincere) I have little
>> intuition for or against any of these candidates. It's clear to me that B
>> is a better candidate than A, but it's also at least equally clear that C
>> is better than B and A is better than C. And WV would elect B in this
>> example even if you change 17: B>C to 17: B=C, where I would strongly lean
>> towards either A or C.
>>
>> Best,
>> Grzegorz
>>
>> czw., 26 cze 2025 o 23:31 Chris Benham <cbenhamau at yahoo.com.au>
>> napisał(a):
>>
>>>
>>> 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.
>>>
>>>
>>> I don't see "closest to the Condorcet winner" as being necessarily
>>> especially positive, let alone the compelling consideration. The actual
>>> voted CW has a strong case to be elected and of course must be in a
>>> Condorcet method. But "close to" doesn't mean anything.
>>>
>>> Imagine you are an A supporter, or simply a sane sensible person
>>> (preferably one who has never heard of Condorcet or Margins).  Who do you
>>> think should win this election?
>>>
>>> 46  A
>>> 44  B
>>> 10  C
>>>
>>> Let me guess that you agree with me that the answer is A.  Now let's
>>> change that a little bit to this:
>>>
>>> 46  A
>>> 44  B>C
>>> 10  C
>>>
>>> By what bizarre stretch of the imagination has extra (second place)
>>> votes for C strengthened any candidate other than C ?   The winner should
>>> either still be A  (the Hare and Benham winner) or change to C (the WV and
>>> Margins Sorted Approval(implicit) and Smith//Approval(implicit) 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.
>>>
>>>
>>>  I find this to be a very weak and bizarre argument. Any close election
>>> (Condorcet or not) can be "unstable" in this way.
>>>
>>> Moreover, B has much broader support than C (assuming that A's
>>> supporters are truly indifferent between both).
>>>
>>>
>>> Only C is voted above bottom on more than half the ballots. There was a
>>> criterion suggested called something like "Possible Approval Winner" that
>>> said that if the voters all inserted an approval cutoff in their rankings
>>> either only approving those candidates they vote below no others or all
>>> except those they vote below no others or anywhere in between, then a
>>> candidate who can't possibly be the most approved candidate can't win.
>>>
>>> In this example the most approved candidate can only be A or C.
>>>
>>> My favourite Condorcet method is  Margins Sorted Approval (explicit):
>>>
>>> *Voters rank however many candidates they wish and also indicate an
>>> approval threshold. Initially order the candidates according to their
>>> approval scores. Check the pairwise result of the adjacent pair of
>>> candidates with smallest difference in their approval scores.(If there is a
>>> tie for this then the lowest-ordered pair among the tied pairs.) If the
>>> lower-ordered of the two  pairwise beats the higher-ordered candidate, then
>>> those two candidates change places in the order. Repeat this procedure to
>>> the end. The candidate at the top of the final order is the winner.*
>>>
>>> (The "implicit" version is the same except that ranking is interpreted
>>> as approval.)
>>>
>>> In this example, depending on whether or not the B>C voters approve C,
>>> the  initial order (based on approval scores) is either  A>B>C or  C>A>B.
>>> In neither case is any pair of adjacent candidates out of order pairwise,
>>> i.e. in the first case  A pairwise beats B and B pairwise beats C and in
>>> the second case C pairwise beats A and A pairwise beats B.   So either way
>>> the initial order is the final order and so the winner is either A or C.
>>>
>>> "Benham" is the simplest and best of the Hare-Condorcet hybrids.
>>>
>>> *Voters strictly rank from the top however many candidates they wish.
>>> Before any and each elimination we check for a pairwise-beats-all candidate
>>> among the remaining candidates and elect the first one we find. Until then
>>> we one-at-a-time eliminate the candidate that is the highest voted
>>> remaining candidate on the smallest number of ballots.*
>>>
>>> (Allowing above-bottom equal ranking makes Push-over strategy easier. I
>>> suggest interpreting ballots that have more than one candidate at the same
>>> rank as having truncated just above that rank. I have the same opinion
>>> about Hare.)
>>>
>>> These methods I  prefer to Winning Votes.  Margins is beyond the pale. I
>>> look forward to reading someone's argument that electing A in my other
>>> example is justified.
>>>
>>> 46  A>C
>>> 17  B
>>> 17  B>C
>>> 20  B=C
>>>
>>> Chris Benham
>>>
>>>
>>> On 26/06/2025 9:12 pm, Grzegorz Pierczyński wrote:
>>>
>>> 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
>>>> >
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>>>> list info
>>>>
>>>
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