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<p>Forest (and interested others),<br>
<br>
I (or maybe we) discovered/decided some years ago that Approval
Sorted Margins is definitely better than DMC.<br>
<br>
Regarding alternatives to IRV that lay claim to be at least as
good, two of my strong standards are that the method must meet <br>
one of Condorcet and FBC and that it must meet one of (at least
in the case of methods that don't allow an explicit approval<br>
cut-off in the rankings) Minimal Defense (and maybe some
yet-to-coined irrelevant-ballot independent version of it) and
Chicken<br>
Dilemma. (I say "one of" in both cases because we know that two
of isn't possible).<br>
<br>
The main other ways I categorise methods is according to types of
ballots used and relatively simple (to explain and sell and use)<br>
versus less so.<br>
<br>
I am negative on both "Asset" voting and weakening the Plurality
criterion. <br>
<br>
Chris Benham<br>
<br>
<br>
</p>
<div class="moz-cite-prefix">On 2/06/2019 8:01 am, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAP29ondM2wWJ8dHuMusF_f4N+pA2US7P1g-Tn1e8umKTdoSeMg@mail.gmail.com">
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<div dir="ltr">just one other tweak to MDDA: Kevin's official
version of MDDA says that in the case of two of more candidates
surviving the disqualification test, in that case the most
approved candidate should be elected. My tweak is to elect from
among the undisqualified candidates the one furthest from being
disqualified; no need to switch horses in this case.<br>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat, Jun 1, 2019 at 2:41 PM
Forest Simmons <<a href="mailto:fsimmons@pcc.edu"
moz-do-not-send="true">fsimmons@pcc.edu</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="ltr">
<div>Kevin, Chris, and Kristofer:<br>
</div>
<div><br>
</div>
<div>Great ideas!.</div>
<div><br>
</div>
<div>DMC (explicit approval version) also comes to mind as
fairly simple to describe:</div>
<div><br>
</div>
<div><b>Remove candidates from the bottom of the approval
list until there is a ballot pairwise beats-all
candidate among the remaining candidates (to elect). <br>
</b></div>
<div><br>
</div>
<div>And analogous to Chris's equivalence between Approval
Sorted Margins and Condorcet(approval margins), we have
the equivalence between DMC and Condorcet(winning
approval).</div>
<div><br>
</div>
<div>Of course we are talking explicit approval every time
we say approval in this context.<br>
</div>
<div><br>
</div>
<div>We know that none of these Condorcet efficient methods
satisfies the FBC, but how about MDDA with explicit
approval instead of its implicit approval default?</div>
<div><br>
</div>
<div>This has the problem that Chris has pointed out in MJ
and other Bucklin versions where addition of irrelevant
ballots can change a majority of ballots into a minority.</div>
<div><br>
</div>
<div>So here's my idea: do MDDA with explicit approval AND
symmetric completion of all of the ballots except for the
Top Rank. By excusing the top rank from symmetric
completion, we preserve the FBC, but we lose the Condorcet
Criterion.</div>
<div><br>
</div>
<div>[This shows how close we can get to both the CC and the
FBC, if we do a full symmetric completion including the
top rank, then this version of MDDA satisfies the CC but
not the FBC. We can toggle back and forth.<br>
</div>
<div>Suppose that we balance on the edge (of symmetric
completion in the top rank or not) with asset voting so
the proxies could finesse this difference. The
unsophisticated voters could just vote their favorites,
etc. Would this come even closer to satisfying both the CC
and the FBC? In other words mightn't this expedient
externalize the strategizing enough to satisfy both FBC
and CC for all practical purposes?]</div>
<div><br>
</div>
<div>I think that the FBC is more important in this context,
so suggest that we exempt at least the top rank from
symmetric completion if not all of the approved ranks.</div>
<div><br>
</div>
<div>Now what about the irrelevant ballots problem? I think
that symmetric completion, if only for the truncated
candidates, would suffice. If X and Y are both truncated
on N new ballots then N/2 of them count for X>Y and N/2
of them count for Y>X so a majority defeat between X
and Y is preserved.</div>
<div><br>
</div>
<div>Note that symmetric completion among only the truncated
candidates is the same as "half power truncation."</div>
<div><br>
</div>
<div>This brings me to another question. Suppose that
voters knew that candidate B became a plurality loser
because of insincere truncation. Would they feel so bad
it B won anyway?</div>
<div><br>
</div>
<div>This leads to a weak form of Plurality: If a candidate
fails Plurality, even after the ballots have been
symmetrically completed, then that candidate must not be
elected.</div>
<div><br>
</div>
<div>Would this weak form be adequate?</div>
<div><br>
</div>
<div>Thanks for your great ideas and interest in these
questions!</div>
<div><br>
</div>
<div>Forest<br>
</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat, Jun 1, 2019 at
12:49 PM Kevin Venzke <<a
href="mailto:stepjak@yahoo.fr" target="_blank"
moz-do-not-send="true">stepjak@yahoo.fr</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">Hi Forest,<br>
<br>
I had two ideas.<br>
<br>
Idea 1:<br>
1. If there is a CW using all rankings, elect the CW.<br>
2. Otherwise flatten/discard all disapproved rankings.<br>
3. Use any method that would elect C in scenario 2.
(Approval, Bucklin, MinMax(WV).)<br>
<br>
So scenario 1 has no CW. The disapproved C>A rankings
are dropped. A wins any method.<br>
In scenario 2 there is no CW but nothing is dropped, so
use a method that picks C.<br>
In both versions of scenario 3 there is a CW, B.<br>
<br>
If step 3 is Approval then of course step 2 is
unnecessary.<br>
<br>
In place of step 1 you could find and apply the
majority-strength solid coalitions (using all rankings)<br>
to disqualify A, instead of acting based on B being a CW.
I'm not sure if there's another elegant way<br>
to identify the majority coalition.<br>
<br>
Idea 2:<br>
1. Using all rankings, find the strength of everyone's
worst WV defeat. (A CW scores 0.)<br>
2. Say that candidate X has a "double beatpath" to Y if X
has a standard beatpath to Y regardless<br>
of whether the disapproved rankings are counted. (I don't
know if it needs to be the *same* beatpath,<br>
but it shouldn't come into play with these scenarios.)<br>
3. Disqualify from winning any candidate who is not in the
Schwartz set calculated using double<br>
beatpaths. In other words, for every candidate Y where
there exists a candidate X such that X has a<br>
double beatpath to Y and Y does not have a double beatpath
to X, then Y is disqualified.<br>
4. Elect the remaining candidate with the mildest WV
defeat calculated earlier.<br>
<br>
So in scenario 1, A always has a beatpath to the other
candidates, no matter whether disapproved<br>
rankings are counted. The other candidates only have a
beatpath to A when the C>A win exists. So<br>
A has a double beatpath to B and C, and they have no path
back. This leaves A as the only candidate<br>
not disqualified.<br>
<br>
In scenario 2, the defeat scores from weakest to strongest
are B>C, A>B, C>A. Every candidate has<br>
a beatpath to every other candidate no matter whether the
(nonexistent) disapproved rankings are<br>
counted. So no candidate is disqualified. C has the best
defeat score and wins.<br>
<br>
In scenario 3, the first version: B has no losses. C's
loss to B is weaker than both of A's losses. B<br>
beats C pairwise no matter what, so B has a double
beatpath to C. However C has no such beatpath<br>
to A, nor has A one to B, nor has B one to A. The
resulting Schwartz set disqualifies only C. (C needs<br>
to return B's double beatpath but can't, and neither A nor
B has a double beatpath to the other.)<br>
Between A and B, B's score (as CW) is 0, so he wins. <br>
<br>
Scenario 3, second version: B again has no losses, and
also has double beatpaths to both of A and<br>
C, neither of whom have double beatpaths back. So A and C
are disqualified and B wins.<br>
<br>
I must note that this is actually a Condorcet method,
since a CW could never get disqualified and<br>
would always have the best worst defeat. That observation
would simplify the explanation of<br>
scenario 3.<br>
<br>
I needed the defeat strength rule because I had no way to
give the win to B over A in scenario 3<br>
version 1. But I guess if it's a Condorcet rule in any
case, we can just add that as a rule, and greatly<br>
simplify it to the point where it's going to look very
much like idea 1. I guess all my ideas lead me to<br>
the same place with this question.<br>
<br>
Oh well, I think the ideas are interesting enough to post.<br>
<br>
Kevin<br>
<br>
<br>
<br>
>Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons
<<a href="mailto:fsimmons@pcc.edu" target="_blank"
moz-do-not-send="true">fsimmons@pcc.edu</a>> a écrit
: <br>
><br>
>In the example profiles below 100 = P+Q+R, and
50>P>Q>R>0. One consequence of these
constraints is that in all three profiles below the cycle
>A>B>C>A will obtain.<br>
><br>
>I am interested in simple methods that always ...<br>
><br>
>(1) elect candidate A given the following profile:<br>
><br>
>P: A<br>
>Q: B>>C<br>
>R: C,<br>
>and <br>
>(2) elect candidate C given<br>
>P: A<br>
>Q: B>C>><br>
>R: C,<br>
>and <br>
>(3) elect candidate B given<br>
<br>
><br>
>P: A<br>
>Q: B>>C (or B>C)<br>
>R: C>>B. (or C>B)<br>
><br>
>I have two such methods in mind, and I'll tell you one
of them below, but I don't want to prejudice your creative
efforts with too many ideas.<br>
><br>
>Here's the rationale for the requirements:<br>
><br>
>Condition (1) is needed so that when the sincere
preferences are<br>
<br>
><br>
>P: A<br>
>Q: B>C<br>
>R: C>B,<br>
>the B faction (by merely disapproving C without
truncation) can defend itself against a "chicken" attack
(truncation of B) from the C faction.<br>
><br>
>Condition (3) is needed so that when the C faction
realizes that the game of Chicken is not going to work for
them, the sincere CW is elected.<br>
><br>
>Condition (2) is needed so that when sincere
preferences are<br>
<br>
><br>
>P: A>C<br>
>Q: B>C<br>
>R: C>A,<br>
>then the C faction (by proactively truncating A) can
defend the CW against the A faction's potential truncation
attack.<br>
><br>
>Like I said, I have a couple of fairly simple methods
in mind. The most obvious one is Smith\\Approval where the
voters have <br>
>control over their own approval cutoffs (as opposed to
implicit approval) with default approval as top rank only.
The other <br>
>method I have in mind is not quite as <br>
>simple, but it has the added advantage of satisfying
the FBC, while almost always electing from Smith.<br>
<br>
<br>
----<br>
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