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<p><br>
<blockquote type="cite">
<div dir="auto"><br>
</div>
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.</blockquote>
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.<br>
<br>
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.<br>
<br>
<blockquote type="cite">"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".</blockquote>
And they are right. <br>
<br>
<blockquote type="cite">..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"</blockquote>
<br>
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?" <br>
<br>
That to me very easily trumps "Oh but according to the Margins
algorithm B was the closest to being the Condorcet winner."<br>
<br>
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".<br>
<br>
<blockquote type="cite">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.</blockquote>
<br>
If this discussion was private I might have come to the same
conclusion sooner. You have ignored several of my direct
questions. <br>
<br>
Chris <br>
<br>
</p>
<div class="moz-cite-prefix">On 30/06/2025 3:12 am, Grzegorz
Pierczyński via Election-Methods wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAAik+bWU5-kqk8Mb=wCTJL6sj3HVUMw_xs8WcQTuO3_Pe=5n0A@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="auto">Chris,
<div dir="auto"><br>
</div>
<div dir="auto">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.</div>
<div dir="auto"><br>
</div>
<div dir="auto">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".</div>
<div dir="auto"><br>
</div>
<div dir="auto">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.</div>
<br>
<div dir="auto">Grzegorz</div>
</div>
<br>
<div class="gmail_quote gmail_quote_container">
<div dir="ltr" class="gmail_attr">niedz., 29 cze 2025, 02:46
użytkownik Chris Benham <<a
href="mailto:cbenhamau@yahoo.com.au" moz-do-not-send="true"
class="moz-txt-link-freetext">cbenhamau@yahoo.com.au</a>>
napisał:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<p>Grzegorz,<br>
</p>
<p> </p>
<blockquote type="cite"> 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.
<div><br>
</div>
</blockquote>
<br>
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.<br>
<br>
46 A<br>
44 B<br>
10 C<br>
<p>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."<br>
<br>
So in the actual election we get:<br>
<br>
46 A<br>
44 B>C <br>
10 C<br>
<br>
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.)<br>
<br>
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"?<br>
<br>
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??<br>
<br>
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.<br>
<br>
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.<br>
So WV elects C.<br>
<br>
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.<br>
<br>
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. <br>
<br>
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.<br>
<br>
</p>
<blockquote type="cite">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.</blockquote>
<br>
Possibly, but why do you assume that this approach is
correct? <br>
<br>
Chris Benham<br>
<br>
<div>On 27/06/2025 8:10 pm, Grzegorz Pierczyński wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">Hi Chris,
<div><br>
</div>
<div>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".</div>
<div><br>
</div>
<div>"Any close election (Condorcet or not) can be
"unstable" in this way."</div>
<div><br>
</div>
<div>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). </div>
<div><br>
</div>
<div>"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."</div>
<div><br>
</div>
<div> 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.
<div><br>
<br>
</div>
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.</div>
<div><br>
</div>
<div>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: </div>
<div>(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). </div>
<div>(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. </div>
<div><br>
</div>
<div>"I look forward to reading someone's argument that
electing A in my other example is justified."</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>Best,</div>
<div>Grzegorz</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">czw., 26 cze 2025 o
23:31 Chris Benham <<a
href="mailto:cbenhamau@yahoo.com.au" target="_blank"
rel="noreferrer" moz-do-not-send="true"
class="moz-txt-link-freetext">cbenhamau@yahoo.com.au</a>>
napisał(a):<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<p><br>
</p>
<blockquote type="cite">
<div>46: A</div>
<div>44: B>C</div>
<div>10: C</div>
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. </blockquote>
<br>
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.<br>
<br>
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?<br>
<br>
46 A<br>
44 B<br>
10 C<br>
<br>
Let me guess that you agree with me that the answer
is A. Now let's change that a little bit to this:<br>
<br>
46 A<br>
44 B>C <br>
10 C<br>
<br>
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).<br>
<br>
<blockquote type="cite">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.</blockquote>
<br>
I find this to be a very weak and bizarre argument.
Any close election (Condorcet or not) can be
"unstable" in this way. <br>
<br>
<blockquote type="cite">Moreover, B has much broader
support than C (assuming that A's supporters are
truly indifferent between both).</blockquote>
<br>
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.<br>
<br>
In this example the most approved candidate can only
be A or C.<br>
<br>
My favourite Condorcet method is Margins Sorted
Approval (explicit):<br>
<br>
*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.* <br>
<p>(The "implicit" version is the same except that
ranking is interpreted as approval.)<br>
<br>
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.<br>
<br>
"Benham" is the simplest and best of the
Hare-Condorcet hybrids. <br>
<br>
*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.*<br>
<br>
(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.)<br>
<br>
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.<br>
<br>
46 A>C <br>
17 B<br>
17 B>C<br>
20 B=C <br>
<br>
Chris Benham<br>
<br>
<br>
</p>
<div>On 26/06/2025 9:12 pm, Grzegorz Pierczyński
wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">Hi all,
<div><br>
</div>
<div>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".</div>
<div><br>
</div>
<div>For example, the second example of Chris
rather convinces me to support margins and
oppose WV, than the other way around. Let's
see:</div>
<div>46: A</div>
<div>44: B>C</div>
<div>10: C</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>Best,</div>
<div>Grzegorz</div>
<div><br>
</div>
<div><br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">czw., 26 cze
2025 o 05:57 Chris Benham <<a
href="mailto:cbenhamau@yahoo.com.au"
target="_blank" rel="noreferrer"
moz-do-not-send="true"
class="moz-txt-link-freetext">cbenhamau@yahoo.com.au</a>>
napisał(a):<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><br>
There is also the Non-Drastic Defense
criterion, which says that if more <br>
than half the voters vote X above Y and X no
lower than equal-top then <br>
Y can't win.<br>
<br>
46 A>C (maybe sincere is A or A>B)<br>
17 B<br>
17 B>C<br>
20 C=B (maybe sincere is C>B)<br>
<br>
B>A 54-46, A>C 63-37, C>B
46-34.<br>
<br>
Here B is above A and no lower than equal-top
on more than half the <br>
ballots, but Margins elects A. Winning Votes
elects B.<br>
<br>
Also Margins can fail Later-no-Help especially
egregiously and elect the <br>
weakest candidate:<br>
<br>
46 A<br>
44 B>C (sincere might be B or B>A)<br>
10 C<br>
<br>
Margins elects B (failing the Plurality
criterion). How does the B <br>
voters ranking C remotely justify switching
the win from A to B?? A <br>
pairwise beats and positionally dominates B,
and C is ranked above <br>
bottom on the most number of ballots. I can't
accept any method that <br>
elects B here. (Or A in the previous
example.)<br>
<br>
I have long since decided that resolving
Condorcet top cycles by <br>
deciding (on some basis or another) that some
pairwise defeats are <br>
"weaker" than others is a dead end. I vastly
prefer 3 other Condorcet <br>
methods: Margins Sorted Approval(explicit),
Margins Sorted Approval <br>
(implicit), and "Benham".<br>
<br>
They all resist Burial better than Margins or
Winning Votes, and Margins <br>
Sorted Approval is very elegant.<br>
<br>
Chris Benham<br>
<br>
On 26/06/2025 1:50 am, Kevin Venzke via
Election-Methods wrote:<br>
> Hi Grzegorz,<br>
><br>
>> 1. What exactly are the axioms that
Condorcet rules with WV satisfy, but with<br>
>> margins do not? (I'm only aware of
the Plurality criterion)<br>
> Very few have been articulated, but:<br>
><br>
>> 2. I have sometimes read that WV are
better to prevent strategic behavior of<br>
>> the voters (without much details),<br>
> I do use the minimal defense criterion,
which represents the notion that a full<br>
> majority of voters can always get their
way if they want to, so it will reduce<br>
> compromise strategy for the majority if
you just give them their way when you<br>
> know what it is.<br>
><br>
> To me, WV resolution is an approximation
of an ideal. I made a webpage that<br>
> attempts to show what options are
available for electing from a provided cycle,<br>
> with the aim of avoiding compromise
incentive when you can:<br>
><br>
> <a
href="https://votingmethods.net/check"
rel="noreferrer noreferrer" target="_blank"
moz-do-not-send="true"
class="moz-txt-link-freetext">https://votingmethods.net/check</a><br>
><br>
> This doesn't always favor WV, and
sometimes there are no actual solutions.<br>
><br>
>> but do you have any idea how to
justify WV<br>
>> more "intuitively" or
"philosophically", assuming sincere votes?
Margins are<br>
>> very easy to justify. I came up with
two possible justifications for WV here<br>
>> (described below), but I'm not sure
how convincing they could be for the<br>
>> general audience.<br>
> Here I'm not sure. I guess by "sincere
votes" you mean that absence of a<br>
> pairwise preference indicates an
expression that two candidates are equal. Or<br>
> maybe that truncation is not different
from explicit equal ranking.<br>
><br>
>> 3. Don't you think it is "ugly" that
the WV measure applied e.g., to Schulze<br>
>> or RP/MAM requires us to artificially
exclude "50% vs. 50%" ties between<br>
>> candidates from consideration (or
equivalently, to mark them as the weakest)<br>
> That's never occurred to me actually. All
non-wins are excluded from<br>
> consideration.<br>
><br>
>> --- and that a victory "50%+1 vs.
50%-1" is rapidly considered to be quite<br>
>> strong, stronger than e.g., a "45%
vs. 1%" victory (with 54% voters who rank<br>
>> both candidates equally)? Under
margins, ties or close ties are naturally<br>
>> considered the weakest. How would you
refute this argument?<br>
> Ideally by some kind of rephrasing. I
don't know if this is possible, but it<br>
> would be nice if the matter could be
presented without making it feel like the<br>
> defeats themselves have an interest in
being respected.<br>
><br>
> Alternatively, you want to find a
explanation where losing votes are just<br>
> meaningless, because for the practical
purposes (the strategic incentive ones),<br>
> they are. You don't obtain a valid
complaint against the method by losing a<br>
> close race, you can only get one by
winning races and losing anyway because you<br>
> didn't lie.<br>
><br>
> (In a 51:49 matchup, those on the losing
side have no power to lie and change<br>
> the outcome (we hope), while there is
considerable possibility that those on the<br>
> 51 side *could* lie and win (i.e. if they
had not), because they comprise more<br>
> than half the voters. With 45:1, there
are decent odds that those on the 45%<br>
> side could win by lying; your method
could determine this to be sure, if you<br>
> wanted, before ruling for instance that
45:1 prevails over a win of 40:39. WV is<br>
> just making a mathematically easy "best
guess.")<br>
><br>
>> Regarding pt. 2, here are my ideas
for a high-level intuitive principle behind<br>
>> WV:<br>
>> (1) "It is much harder (infinitely
harder?) to convince a voter to change his<br>
>> mind from B<A to A>B, than it
is to change his mind from A=B to A>B".
Then, in<br>
>> particular, it is more probable that
a "45% vs. 1%" victory would become a<br>
>> "45% vs. 55%" defeat, than that a
"51% vs. 49%" victory would become a defeat.<br>
> That has some familiarity to me. If the
winning side has a full majority then we<br>
> "know" it is right. In fact if you
entertain the concept of an overall "median<br>
> voter" it suggests to us something about
what that voter thinks.<br>
><br>
> Though I understand that you want to
suppose that the equalities are in fact<br>
> sincere.<br>
><br>
> In that case, if it's 45% A>B, 54%
A=B, 1% B>A, my observation would be that
the<br>
> median position is that A and B are
equal. The 54% aren't just abstaining, are<br>
> they? I don't think that's what the
assumption of sincerity implies.<br>
><br>
> Your second idea is kind of suggestive of
this actually... You're just focusing<br>
> more on voters' desire for how the
matchup is handled.<br>
><br>
>> (2) "If a voter votes for A=B, then
he is not neutral, but he is actively<br>
>> voting against treating the
resolution of the matchup between A and B as<br>
>> important". Then, in particular, in
the case of a "45% vs. 1%" victory, we in<br>
>> fact have 45% of voters who consider
it important to resolve the matchup in a<br>
>> particular direction, and 55% of
voters who think otherwise. This is a smaller<br>
>> number than for a "51% vs. 49%"
victory.<br>
> I view this possibility of voters having
such a sentiment, and acting on it in<br>
> this way, more as something useful that
WV enables. I don't think we can say<br>
> it's intuitively the case that voters are
meaning to do this.<br>
><br>
> Kevin<br>
> <a href="http://votingmethods.net"
rel="noreferrer noreferrer" target="_blank"
moz-do-not-send="true">votingmethods.net</a><br>
><br>
> ----<br>
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