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<p>A question I forgot to answer:<br>
<blockquote type="cite">It makes sense to start with
Approval-ordering & then adjust to fix the most important
pairwise contradictions by switching. But aren’t the *
biggest* margins more important than the smallest ones? Then
why fix the smallest-margin mis-orderings first?</blockquote>
<br>
Our aim it produce a "beat chain" (if that's the right term)
where every candidate beats the next-lowest in the order down to
the bottom, which is most in harmony with the approval order. No
out-of-order pair of adjacent candidates is going to be left out
of order.<br>
<br>
As we switch the smaller-margin out-of-order adjacent pairs the
larger-margin ones will strongly tend to go away, with the
result that the final order will be more in harmony with the
approval order.<br>
</p>
<br>
My earlier incomplete answer to Michael O.'s questions:<br>
<p>
<blockquote type="cite">
<br>
Margins Sorted Approval (explicit) doesn't use any information
other than the approval scores and the plain win-loss-draw
results of (usually only some of) the pairwise contests based
on the rankings.<br>
<br>
So the "margins" referred to are about the approval scores of
adjacent pairs of candidates in the approval order. There are
no "winning votes" or "losing votes".<br>
<br>
Most of the time we can operate Margins Sorted Approval
without even finding out if there is a cycle or not. If the
Condorcet winner is the least approved candidate then it will
work its way up to the top of the final order and we'll know
that it pairwise beat all the other candidates. Otherwise
there is no need for us to know the pairwise result between
the candidate at the top of the final order and the candidate
at the bottom (and maybe other pairwise results if there are
more than three candidates.)<br>
<br>
This makes it quite a bit easier to operate than
Smith//Approval and some other methods.<br>
<br>
I admit that it might be a bit of a challenge to explain and
sell to an at all sceptical non-expert audience.
Smith//Approval is much easier in that way.<br>
<br>
Chris</blockquote>
<br>
<br>
</p>
<div class="moz-cite-prefix">On 21/04/2024 4:37 am, Michael
Ossipoff wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAOKDY5CSJYmPBKsy_CfOE3DX2QJAVjqge6GYh5=cpJgHGkxsBg@mail.gmail.com">
<div dir="auto">If a single example can’t be found in which wv
Condorcet does better than Approval-Sorted Margins, then of
course I’ll admit that Approval-Sorted Margins is better.</div>
<div dir="auto"><br>
</div>
<div dir="auto">I have a few questions about
Margins-Sorted-Approval:</div>
<div dir="auto"><br>
</div>
<div dir="auto">If I want to propose it to (say) a city-council
or an initiative-committee or focus-group, someone will ask
what it’s advantage is…in what way it’s better. What valuable
property does it offer that other methods don’t?</div>
<div dir="auto"><br>
</div>
<div dir="auto">What’s the answer to that inevitable question?</div>
<div dir="auto"><br>
</div>
<div dir="auto">…& there’s the matter of motivation. What is
it about double sorting that motivates it?</div>
<div dir="auto"><br>
</div>
<div dir="auto">It makes sense to start with Approval-ordering
& then adjust to fix the most important pairwise
contradictions by switching. But aren’t the * biggest* margins
more important than the smallest ones? Then why fix the
smallest-margin mis-orderings first? & what’s special
about adjacency in the Approval-ordering? Isn’t the biggest
pairwise contradiction most important even between candidates
not adjacent in the Approval-ordering?</div>
<div dir="auto"><br>
</div>
<div dir="auto">…& why margins instead of wv, losing-votes,
or any of the various measures of a pairwise-defeat? In my
experience, wv has been the important defeat-measure for
strategic protection.<br>
<div class="gmail_quote" dir="auto">
<div dir="ltr" class="gmail_attr"><br>
</div>
<div dir="ltr" class="gmail_attr"><br>
</div>
<div dir="ltr" class="gmail_attr">On Sat, Apr 20, 2024 at
11:03 Chris Benham <<a
href="mailto:cbenhamau@yahoo.com.au"
class="moz-txt-link-freetext">cbenhamau@yahoo.com.au</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div>
<p>Mike O.,<br>
<br>
<a
href="https://electowiki.org/wiki/Minimal_Defense_criterion"
target="_blank" class="moz-txt-link-freetext">https://electowiki.org/wiki/Minimal_Defense_criterion</a><br>
</p>
<blockquote type="cite">
<p
style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;background-color:rgb(255,255,255);color:rgb(32,33,34)"><a
href="https://electowiki.org/wiki/Stephen_Eppley"
title="Stephen Eppley"
style="text-decoration:none;background-image:none;font-family:sans-serif;color:rgb(51,102,204)"
target="_blank">Stephen Eppley</a><span
style="font-family:sans-serif"> </span>gives this
official definition:</p>
<blockquote
style="border-left-width:4px;border-left-style:solid;padding:8px 32px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;background-color:rgb(249,249,249);border-left-color:rgb(234,236,240);color:rgb(32,33,34)">
<p style="margin:0px;font-family:sans-serif">If more
than half of the voters prefer alternative y over
alternative x, then that majority must have some
way of voting that ensures x will not be elected
and does not require any of them to rank y equal
to or over any alternatives preferred over y.</p>
</blockquote>
<p
style="margin:0.5em 0px;font-family:sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;background-color:rgb(255,255,255);color:rgb(32,33,34)">This
definition is most similar to that of<span
style="font-family:sans-serif"> </span><a
href="https://electowiki.org/wiki/SDSC"
title="SDSC"
style="text-decoration:none;background-image:none;font-family:sans-serif;color:rgb(51,102,204)"
target="_blank">SDSC</a>. <a
href="https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion"
target="_blank" style="font-family:sans-serif"
class="moz-txt-link-freetext">https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion</a><br>
</p>
</blockquote>
<br>
The answer to your first question (based on the
definition I copied above) is yes. That is obviously
implied by its compliance with Double Defeat. All that
"majority" has to do is approve Y and not X. Double
Defeat says that a candidate that is pairwise beaten by
a more approved candidate can't win.<br>
<br>
The answer to your second question is yes if the other
faction doesn't approve the CW and no if it does. Like
in this old example:<br>
<br>
49 A (sincere is A>B)<br>
24 B (the "sincere CW" but the faction may be defecting
against C)<br>
27 C>B<br>
<br>
If the C>B voters approve B then the approval order
is B>A>C and since B pairwise beats A and A
pairwise beats C that order is final and B wins.<br>
But if they don't then the approval order is A>C>B
and that order is final and A wins.<br>
<br>
<blockquote type="cite">
<div dir="auto"><br>
</div>
<div dir="auto">The faction-sizes are kept as close
together as possible, because equal sizes is the
middle about which the variation happens, & is
probably the most likely single configuration.</div>
</blockquote>
<br>
I don't that is always a good idea. If the faction sizes
are close together then surely the risk for the Buriers
of their strategy back-firing would be a lot greater
than if the "bus" faction is quite a bit smaller than
theirs. Also of course two large parties and one small
one more closely resembles the current political
landscape.<br>
<br>
<blockquote type="cite">
<div dir="auto">An example can be found where one
particular method does better than another.</div>
<div dir="auto"><br>
</div>
</blockquote>
Good. I look forward to seeing your example where
Winning Votes does better than Approval Sorted Margins.<br>
<br>
I don't know the answer to your last question.<br>
<br>
Chris B.<br>
<br>
</div>
<div>
<div>On 19/04/2024 6:56 am, Michael Ossipoff wrote:<br>
</div>
<blockquote type="cite">
<div dir="auto">1) Does Margins-Sorted Approval meet
Minimal-Defense?</div>
<div dir="auto"><br>
</div>
<div dir="auto">2) Can offense-truncation by one
faction take the win from a CW ranked in 2nd place
by the other faction?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Answers for wv: 1) Yes. 2) No.</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu, Apr 18,
2024 at 14:17 Michael Ossipoff <<a
href="mailto:email9648742@gmail.com"
target="_blank" class="moz-txt-link-freetext">email9648742@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div dir="auto">An example can be found where
one particular method does better than
another.</div>
<div dir="auto"><br>
</div>
<div dir="auto">3 candidates;</div>
<div dir="auto"><br>
</div>
<div dir="auto">CW, BF, & Bus</div>
<div dir="auto"><br>
</div>
<div dir="auto">(BF is buriers’ favorite. Bus 🚌
is the candidate under whom they bury CW.)</div>
<div dir="auto"><br>
</div>
<div dir="auto">To test wv Condorcet for burial
deterrence, I checked 24 cases:<br>
</div>
<div dir="auto"><br>
</div>
<div dir="auto">All 6 faction-size orderings for
the 3 candidates.</div>
<div dir="auto"><br>
</div>
<div dir="auto">and</div>
<div dir="auto"><br>
</div>
<div dir="auto">4 ways for the middle CW’s
voters to rank the other 2, with regard to
which they rank in 2nd place:</div>
<div dir="auto"><br>
</div>
<div dir="auto">Neither </div>
<div dir="auto">BF</div>
<div dir="auto">Bus</div>
<div dir="auto">Half one & half the other </div>
<div dir="auto"><br>
</div>
<div dir="auto">The faction-sizes are kept as
close together as possible, because equal
sizes is the middle about which the variation
happens, & is probably the most likely
single configuration.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Divide the number of burial’s
backfires by the number of its successes, for
the backfire/success ratio…abbreviated </div>
<div dir="auto">b/s.</div>
<div dir="auto"><br>
</div>
<div dir="auto">For wv Condorcet, b/s = 10.</div>
<div dir="auto"><br>
</div>
<div dir="auto">What is it for Margins-Sorted
Approval?</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu,
Apr 18, 2024 at 10:14 Chris Benham <<a
href="mailto:cbenhamau@yahoo.com.au"
target="_blank"
class="moz-txt-link-freetext">cbenhamau@yahoo.com.au</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div>
<p><br>
One of my nominations and my top
choice in the current poll:<br>
<br>
Margins Sorted Approval (specified
cutoff):<br>
<br>
*Voters rank from the top however many
candidates they wish and can also
specify an approval<br>
cutoff/threshold. Default approval is
only for candidates ranked below no
others (i.e. ranked top<br>
or equal-top).<br>
<br>
A Forrest Simmons invention.
Candidates are listed in approval
score order and if any adjacent pairs<br>
are pairwise out of order then this is
corrected by flipping the out-of-order
pair with the smallest<br>
margin. If there is a tie for this we
flip the less approved pair. Repeat
until there are no adjacent pairs<br>
of candidates that are pairwise out of
order, then elect the highest-ordered
candidate.*<br>
<br>
I'm going to compare it with another
of my nominations, another Condorcet
method that collects the<br>
same information from the voters:<br>
<br>
Smith//Approval (specified cutoff):<br>
<br>
*Voters rank from the top however many
candidates they wish and can also
specify an approval<br>
cutoff/threshold. Default approval is
only for candidates ranked below no
others (i.e. ranked top<br>
or equal-top).<br>
The most approved member of the Smith
set wins.*<br>
<br>
Although it asks voters for a bit more
information than other Condorcet
methods like Ranked Pairs, <br>
Schulze, MinMax etcetera, I think it
is a lot easier than them to explain
and sell than them.<br>
<br>
Condorcet//Approval (explicit) was
discussed here in April 2002 by Adam
Tarr. I find voluntarily (in a<br>
Condorcet method) electing a candidate
outside the Smith set to be weird and
unacceptable, but all the <br>
examples he gave that I saw apply just
as well to Smith//Approval(explicit).<br>
<br>
Now why do I prefer Margins Sorted
Approval? <br>
<br>
The main reason is that it is quite a
lot less vulnerable to Burial
strategy. Say there are three
candidates<br>
and most of the voters normally
truncate. Say A is the predicted FPP
and Condorcet winner, B is the <br>
predicted FPP runner-up and C is
coming last by quite a big margin.<br>
<br>
In that case the voters most likely to
be tempted to try a Burial strategy
will be the B supporters against<br>
A, using no-threat C as the "bus".<br>
<br>
43 A|<br>
03 A>B| ("strategically naive"
voters)<br>
44 B|>C (sincere is B or B>A)<br>
10 C|<br>
<br>
The B>C Buriers have given A a
pairwise defeat, so now there is an
A>B>C>A cycle.<br>
<br>
The approval scores: B 47, A 46, C
10.<br>
<br>
Now if this was Smith//Approval the 3
A>B| voters would have blown the
election for A by approving B.<br>
<br>
But ASM notices that both
approval-score adjacent pairs (B-A and
A-C) are pairwise out of order and by
far<br>
the smallest of the two approval-score
margins is that between B and A and
so flips that order to give<br>
A>B>C. Now neither pair is
pairwise "out of order" so that order
is final and A comfortably wins.<br>
<br>
Now to borrow an old example with none
of the voters truncating:<br>
<br>
49 A|> C (sincere is A or A>B)<br>
06 B>A|<br>
06 B|>A<br>
06 B|>C<br>
06 B>C|<br>
27 C>B|<br>
<br>
Now there is a cycle A>C>B>A
and the approval scores are A 55, B
51, C 33.<br>
<br>
Again Smith//Approval has a problem,
the Burying strategists have
succeeded.<br>
<br>
But again Approval Sorted Margins
fixes it. Both adjacent approval-score
adjacent pairs (A-B and B-C)<br>
are out pairwise order and the A-B
margin (4) is smaller than the B-C
margin (18) so we flip the A-B pair<br>
to give the order B>A>C. Now
neither adjacent pair is pairwise out
of order so that order is final and<br>
B (the sincere Condorcet winner) wins.<br>
<br>
The other reason I prefer Margins
Sorted Approval to Smith//Approval
(explicit) is mostly aesthetic.<br>
<br>
I find it much more elegant (even
beautiful). It would meet as many
monotonicity criteria as it is
possible<br>
for a Condorcet method to meet.
Without even trying, it meets Reverse
Symmetry.<br>
<br>
By comparison I find
Smith//Approval(explicit) a bit
clunky. <br>
<br>
Unfortunately Benham and Woodall and
Gross Loser Elimination and "almost
Condorcet" RCIPE and<br>
Hare (aka IRV) all fail Mono-raise
(aka Monotonicity).<br>
<br>
In both my examples above, the three
Winning Votes methods in the poll
(Ranked Pairs and Schulze and<br>
MinMax and maybe "Max Strength
Transitive Beatpath") all elect the
Burier's favourite.<br>
<br>
In the second example that is also
true of Benham and Woodall and Gross
Loser Elimination.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<a
href="http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html"
target="_blank"
class="moz-txt-link-freetext">http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html</a><br>
<br>
</p>
<blockquote type="cite">
<pre style="font-family:monospace">I think that if you give people a ballot that looks like grades, they will
tend to assign candidates grades that reflect their cardinal rankings for
those candidates, provided they don't have strategic incentive to do
otherwise. If lack of slots becomes a problem, we could switch to 1-10
rankings. If a tendency to spread the candidates out tends to skew the
results, we could go with the "none of the below" candidate in ranked
ballots. But for the time being, I think the 6-slot ballot would do fine,
and if I were to advocate this method I'd go with the 6-slot ballot.
At any rate, I was just looking at how well this technique responds to
certain strategic voting scenarios. In an earlier message (March 20) I
suggested that Approval Completed Condorcet ("ACC" from here on out) passes
SFC and SDSC from Mike's criterion. It doesn't pass the "Generalized"
versions unless one slips in a Smith set requirement explicitly, which I
argued against in that message.
I'm now going to compare ACC to margins and winning votes Condorcet
methods, using the example that has become my signature example on this
list. The following are the sincere preferences of my example electorate:
49: Bush>Gore>Nader
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
If everyone votes sincerely, then Gore is the Condorcet winner. The
problem arises when the Bush voters swap Nader and Gore on their ballots
(in margins they can achieve the same effect by truncating, but I'll ignore
that for this analysis). So the new "preferences" are
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader>Gore>Bush
In margins-based methods, the only way for Gore to still win the election
is for the Nader voters to bury Nader behind Gore. The stable equilibrium
ballots become:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
39: Gore>Nader>Bush
And this allows Gore to still carry the election. This sort of equilibrium
is what Mike is talking about when he says that margins methods are
"falsifying".
In winning votes methods, the Nader camp can vote equal first-place
rankings rather than swap Gore and Nader entirely. The stable result is
therefore:
49: Bush>Nader>Gore
12: Gore>Bush>Nader
12: Gore>Nader>Bush
27: Nader=Gore>Bush
In ACC... we first have to define where the approval cutoffs on the ballots
are. Since the approval tally is only used to break cyclic ties, clearly
the Bush camp has no incentive to Approve of anyone except Bush. I'm going
to make the assumption that since Gore and Bush are the apparent front
runners in this race (the only two with a decent shot at election), every
voter will approve one and not the other. This is the logical approval
cutoff to use, based on the approval strategy threads that have been
circulating on the list of late. So the ballots could look something like
this: (>> denotes approval cutoff)
49: Bush>>Nader>Gore
12: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
In this case, Gore wins the approval runoff 51-49-33. So not only did ACC
avoid the need for defensive order-reversal like margins methods, but it
avoided the need for defensive equal-ranking like winning votes
methods. This is a super result: totally strategy-free voting for the
majority side.
There is a dark side to this result, though. Say that some of the
Gore>Bush>Nader voters were extremely non-strategic and decided to approve
both Bush and Gore. So the votes now look like:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
6: Gore>Nader>>Bush
27: Nader>Gore>>Bush
Now, Bush wins the approval runoff 55-51-33. This is where ACC's favorite
betrayal scenario comes in. Since Bush wins the approval vote, the only
way the majority can guarantee a Gore win is to make Gore the initial
Condorcet winner, which requires that the Nader camp vote Gore in first place:
49: Bush>>Nader>Gore
6: Gore>Bush>>Nader
6: Gore>>Bush>Nader
6: Gore>>Nader>Bush
33: Gore>Nader>>Bush
So this is more or less the same as the margins method equilibrium.
In summary, if the voters are fairly logical in the placement of their
approval cutoff, then ACC seems almost uniquely free of strategy
considerations. If the underlying approval votes do not back up the
sincere Condorcet winner, however, then ACC becomes just as vulnerable to
strategic manipulation as the margins methods are, if not more so.
Comments?
-Adam</pre>
</blockquote>
<br>
</div>
</blockquote>
</div>
</div>
</blockquote>
</div>
</div>
</blockquote>
</div>
</blockquote>
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