<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">cbenhamau@yahoo.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><u></u>
<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">http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html</a><br>
<br>
</p><blockquote type="cite">
<pre>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>
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