<div dir="ltr"><div dir="ltr"><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Apr 20, 2024 at 12:07 PM Michael Ossipoff <<a href="mailto:email9648742@gmail.com">email9648742@gmail.com</a>> wrote:<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 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></blockquote><div><br></div><div>It is more resistant to burial and defection.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><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></blockquote><div><br></div><div>First of all, I think the name is something of a misnomer.<br><br>If all ranked candidates are approved in some way, the initial ordering is not based on approval but rather on <i>strong preference</i>.</div><div><br></div><div>So you start with a ranking of candidates based on which candidates are most strongly preferred. But we want to end up with list of candidates such that each pair of candidates is in order based on their <i>pairwise</i> preferences. Therefore we will have to rearrange the initial <i>strong preference</i> ordering in some way, based on adjacent pairwise orderings. See below.</div><div><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 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></blockquote><div><br></div><div>Remember that here margins are <i style="font-weight:bold">not</i> based on votes in pairwise contests but rather in comparing the strong preferences for two consecutive candidates in the ordered ranking. </div><div><br></div><div>Sorting the candidate list, based on pairwise contests, can be done by several means. Upward bubble sort gives you DMC. Downward bubble sort gives you something different. But either of those could move candidates far from their original strong preference ranking.<br><br>Margin sort (that is, the margin of adjacent strong preference metrics for pairwise-out-of-order consecutive candidates) is a variation on bubble sort that locally minimizes the change from the original strong preference rating.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="auto"><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" target="_blank">cbenhamau@yahoo.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><u></u>
<div>
<p>Mike O.,<br>
<br>
<a href="https://electowiki.org/wiki/Minimal_Defense_criterion" target="_blank">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:4px solid rgb(234,236,240);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);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" style="font-family:sans-serif" target="_blank">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>
<p></p></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">email9648742@gmail.com</a>>
wrote:<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 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">cbenhamau@yahoo.com.au</a>>
wrote:<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>
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 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></div></div>
----<br>
Election-Methods mailing list - see <a href="https://electorama.com/em" rel="noreferrer" target="_blank">https://electorama.com/em</a> for list info<br>
</blockquote></div></div>