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<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>
<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>
</p>
<div class="moz-cite-prefix">On 27/06/2025 8:10 pm, Grzegorz
Pierczyński wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAAik+bUfAQ=DavinaTNthb9tV9++CCwPys9q07rNBw7ak5BoGQ@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<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 gmail_quote_container">
<div dir="ltr" class="gmail_attr">czw., 26 cze 2025 o
23:31 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(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"
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" 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" target="_blank"
moz-do-not-send="true">votingmethods.net</a><br>
><br>
> ----<br>
> Election-Methods mailing list - see <a
href="https://electorama.com/em" rel="noreferrer"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://electorama.com/em</a>
for list info<br>
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