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<div>Hi Chris,</div><div><br></div><div><div><div><blockquote type="cite" style="margin: 0px; padding: 8px; color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">>>I don't think it's ideal if burying X under Y (both disapproved) can only backfire when Y is made the CW.<div>>></div></blockquote><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">>Why is that? </span></div><div><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></div><div><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">Because I think if voters decide to attempt to prevent another candidate from being CW, via insincerity, there should be risks to doing that. Of course there is already some risk. But if you "knew" that a given candidate had no chance of being CW then there would be nothing to lose in using that candidate in a burial strategy.</span></div><div><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></div><div><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">>The post-election complaint (by any of the voters) would be .. what?</span></div><div><br></div><div>For either a successful burial strategy, or one that backfires and elects an arbitrary candidate, I think the possible complaints are clear. Maybe someone would argue that a backfiring strategy proves the method's incentives are just fine. But that wouldn't be how I see it. I think if, in actual practice, it ever happens that voters calculate that a strategy is worthwhile, and it completely backfires to the point that everyone would like the results discarded, then that method will probably get repealed.</div><div><br></div><div>><br clear="none" style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">>If you don't allow voters to rank among their unapproved candidates then arguably you are not even trying to elect the sincere CW.</span><br clear="none" style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">>Instead you are just modifying Approval to make it a lot more Condorcet-ish. </span></div><div><br></div><div>Not an unfair statement. If you require voters to have that much expressiveness then you can't use implicit.</div><div><br></div><div>To me, the motivation for three-slot C//A(implicit) is partly about burial, partly about method simplicity, partly about ballot simplicity. C//A(explicit) retains 1 of 3. (Arguably slightly less for the Smith version.) Possibly it has its own merits, but they will largely be different ones.</div><div><br clear="none" style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">><br clear="none" style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">>A lot of voters like relatively expressive ballots. I think that is one of the reasons why Approval seems to be a lot less popular than IRV.</span><br clear="none" style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"></div></div><div><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></div><div><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">I have no *inherent* complaints about the ballot format of explicit approval plus full ranking.</span></div><div><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></div><div><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">Kevin</span></div><br></div><div><br></div><div><br></div><div><br></div>
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Le jeudi 6 juin 2019 à 21:03:19 UTC−5, C.Benham <cbenham@adam.com.au> a écrit :
</div>
<div><br></div>
<div><br></div>
<div><div id="ydpb6a32dd9yiv8583323751"><div>
<p>Kevin,<br clear="none">
</p><blockquote type="cite">Specifically should "positional dominance"
have the same meaning whether or not the method has approval in
it?</blockquote>
<br clear="none">
If the voters all choose to approve all the candidates they rank,
then yes. (For a while I was wrongly assuming that Forest's
suggested<br clear="none">
default approval was for all ranked-above-bottom candidates, but
then I noticed that he specified that it was only for top voted
candidates).<br clear="none">
<br clear="none">
One of my tired examples:<br clear="none">
<br clear="none">
25: A>B<br clear="none">
26: B>C<br clear="none">
23: C>A<br clear="none">
26: C<br clear="none">
<br clear="none">
Assuming all the ranked candidates are approved, C is by far the
most approved and the most top-voted candidate. <br clear="none">
Normal Winning Votes (and your idea 2 in this example) elect B.<br clear="none">
<br clear="none">
<blockquote type="cite">I will go easy on these methods over
failing MD, because it happens when some of the majority don't
approve their common candidate.</blockquote>
<br clear="none">
For me this this type of ballot avoids the Minimal Defense versus
Chicken Dilemma dilemma, rendering those criteria inapplicable.<br clear="none">
<p>48: A<br clear="none">
27: B>C<br clear="none">
25: C<br clear="none">
<br clear="none">
The problem has been that we don't know whether the B>C voters
are thinking "I am ranking C because above all I don't want that
evil A<br clear="none">
to win" or "My C>A preference isn't all that strong, and I
think that my favourite could well be the sincere CW, and if C's
supporters rank<br clear="none">
B above A then B has a good chance to win. But if they if they
create a cycle by truncating I'm not having them steal it".<br clear="none">
<br clear="none">
With the voters able to express explicit approval we no longer
have to guess which it is.<br clear="none">
<br clear="none">
</p><blockquote type="cite"> I don't think it's ideal if burying X
under Y (both disapproved) can only backfire when Y is made the
CW.
<div><br clear="none">
</div>
</blockquote>
Why is that? The post-election complaint (by any of the voters)
would be .. what?<br clear="none">
<br clear="none">
If you don't allow voters to rank among their unapproved
candidates then arguably you are not even trying to elect the
sincere CW.<br clear="none">
Instead you are just modifying Approval to make it a lot more
Condorcet-ish. <br clear="none">
<br clear="none">
A lot of voters like relatively expressive ballots. I think that
is one of the reasons why Approval seems to be a lot less popular
than IRV.<br clear="none">
<br clear="none">
Chris Benham<br clear="none">
<br clear="none">
<div class="ydpb6a32dd9yiv8583323751yqt8593146214" id="ydpb6a32dd9yiv8583323751yqt96283"><div class="ydpb6a32dd9yiv8583323751moz-cite-prefix">On 6/06/2019 5:34 pm, Kevin Venzke
wrote:<br clear="none">
</div>
<blockquote type="cite">
</blockquote></div></div><div class="ydpb6a32dd9yiv8583323751yqt8593146214" id="ydpb6a32dd9yiv8583323751yqt32286"><div><div class="ydpb6a32dd9yiv8583323751ydpe4c7db39yahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:16px;">
<div>Hi Chris,</div>
<div><br clear="none">
</div>
<div>I've been short on time so I don't actually have much
thought on any of the methods, even my own.</div>
<div><br clear="none">
</div>
<div>I suppose Idea 2 is the same as Schwartz-limited MinMax(WV)
if nobody submits disapproved rankings. I'm not sure if it
makes sense to reject the method over that. Specifically
should "positional dominance" have the same meaning whether or
not the method has approval in it? As a comparison, I will go
easy on these methods over failing MD, because it happens when
some of the majority don't approve their common candidate.</div>
<div><br clear="none">
</div>
<div>I would have liked to simplify Idea 2, but actually
Forest's eventual proposal wasn't all that simple either. As I
wrote, if you add "elect a CW if there is one" it can become
much simpler, so that it isn't really distinct from Idea 1. I
actually tried pretty hard to present three "Ideas" in that
post, but kept having that problem.</div>
<div><br clear="none">
</div>
<div>I posted those ideas because I thought Forest posed an
interesting challenge, and I thought I perceived that he was
trying to fix a problem with CD. That said, I am not a fan of
Smith//Approval(explicit). If all these methods are basically
the same then I probably won't end up liking any of them. I
don't think it's ideal if burying X under Y (both disapproved)
can only backfire when Y is made the CW.</div>
<div><br clear="none">
</div>
<div>Kevin</div>
<div><br clear="none">
</div>
<div><br clear="none">
</div>
</div>
<div class="ydpb6a32dd9yiv8583323751ydp50d5cd69yahoo_quoted" id="ydpb6a32dd9yiv8583323751ydp50d5cd69yahoo_quoted_0454840046">
<div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;">
<div> Le mercredi 5 juin 2019 à 21:26:23 UTC−5, C.Benham
<a shape="rect" class="ydpb6a32dd9yiv8583323751moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au" rel="nofollow" target="_blank"><cbenham@adam.com.au></a> a écrit : </div>
<div><br clear="none">
</div>
<div>Kevin,<br clear="none">
</div>
<div>
<div id="ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920">
<div>
<p>I didn't comment earlier on your "idea 2". <br clear="none">
<br clear="none">
If there no "disapproved rankings" (i.e. if the voters
all approve the candidates they rank above bottom),<br clear="none">
then your suggested method is simply normal Winning
Votes, which I don't like because the winner can<br clear="none">
be uncovered and positionally dominant or
pairwise-beaten and positionally dominated by a single
other<br clear="none">
candidate.<br clear="none">
<br clear="none">
On top of that I don't think it really fills the bill
as "simple". Approval Margins (using Sort or
Smith//MinMax<br clear="none">
or equivalent or almost equivalent algorithm) would be
no more complex and in my opinion would be better.<br clear="none">
<br clear="none">
I would also prefer the still more simple
Smith//Approval.<br clear="none">
<br clear="none">
What did you think of my suggestion for a way to
implement your idea 1? </p>
<div class="ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqt3873327189" id="ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqtfd25173"><br clear="none">
Chris <br clear="none">
</div>
<div class="ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqt3873327189" id="ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqtfd71007">
<div class="ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920moz-forward-container"><br clear="none">
<br clear="none">
<br clear="none">
<blockquote type="cite">
<p><b>Kevin Venzke</b> <a shape="rect" title="[EM] What are some simple methods that accomplish the following conditions?" href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3C1931864740.14928463.1559418507456%40mail.yahoo.com%3E" rel="nofollow" target="_blank">stepjak at yahoo.fr </a><br clear="none">
Sat Jun 1 12:48:27 PDT 2019 </p>
<p><br clear="none">
Hi Forest,<br clear="none">
<br clear="none">
I had two ideas.<br clear="none">
<br clear="none">
Idea 1:<br clear="none">
1. If there is a CW using all rankings, elect
the CW.<br clear="none">
2. Otherwise flatten/discard all disapproved
rankings.<br clear="none">
3. Use any method that would elect C in scenario
2. (Approval, Bucklin, MinMax(WV).)<br clear="none">
<br clear="none">
So scenario 1 has no CW. The disapproved C>A
rankings are dropped. A wins any method.<br clear="none">
In scenario 2 there is no CW but nothing is
dropped, so use a method that picks C.<br clear="none">
In both versions of scenario 3 there is a CW, B.<br clear="none">
<br clear="none">
If step 3 is Approval then of course step 2 is
unnecessary.<br clear="none">
<br clear="none">
In place of step 1 you could find and apply the
majority-strength solid coalitions (using all
rankings)<br clear="none">
to disqualify A, instead of acting based on B
being a CW. I'm not sure if there's another
elegant way<br clear="none">
to identify the majority coalition.<br clear="none">
<br clear="none">
Idea 2:<br clear="none">
1. Using all rankings, find the strength of
everyone's worst WV defeat. (A CW scores 0.)<br clear="none">
2. Say that candidate X has a "double beatpath"
to Y if X has a standard beatpath to Y
regardless<br clear="none">
of whether the disapproved rankings are counted.
(I don't know if it needs to be the *same*
beatpath,<br clear="none">
but it shouldn't come into play with these
scenarios.)<br clear="none">
3. Disqualify from winning any candidate who is
not in the Schwartz set calculated using double<br clear="none">
beatpaths. In other words, for every candidate Y
where there exists a candidate X such that X has
a<br clear="none">
double beatpath to Y and Y does not have a
double beatpath to X, then Y is disqualified.<br clear="none">
4. Elect the remaining candidate with the
mildest WV defeat calculated earlier.<br clear="none">
<br clear="none">
So in scenario 1, A always has a beatpath to the
other candidates, no matter whether disapproved<br clear="none">
rankings are counted. The other candidates only
have a beatpath to A when the C>A win exists.
So<br clear="none">
A has a double beatpath to B and C, and they
have no path butt. This leaves A as the only
candidate<br clear="none">
not disqualified.<br clear="none">
<br clear="none">
In scenario 2, the defeat scores from weakest to
strongest are B>C, A>B, C>A. Every
candidate has<br clear="none">
a beatpath to every other candidate no matter
whether the (nonexistent) disapproved rankings
are<br clear="none">
counted. So no candidate is disqualified. C has
the best defeat score and wins.<br clear="none">
<br clear="none">
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 clear="none">
beats C pairwise no matter what, so B has a
double beatpath to C. However C has no such
beatpath<br clear="none">
to A, nor has A one to B, nor has B one to A.
The resulting Schwartz set disqualifies only C.
(C needs<br clear="none">
to return B's double beatpath but can't, and
neither A nor B has a double beatpath to the
other.)<br clear="none">
Between A and B, B's score (as CW) is 0, so he
wins. <br clear="none">
<br clear="none">
Scenario 3, second version: B again has no
losses, and also has double beatpaths to both of
A and<br clear="none">
C, neither of whom have double beatpaths butt.
So A and C are disqualified and B wins.<br clear="none">
<br clear="none">
I must note that this is actually a Condorcet
method, since a CW could never get disqualified
and<br clear="none">
would always have the best worst defeat. That
observation would simplify the explanation of<br clear="none">
scenario 3.<br clear="none">
<br clear="none">
I needed the defeat strength rule because I had
no way to give the win to B over A in scenario 3<br clear="none">
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 clear="none">
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 clear="none">
the same place with this question.<br clear="none">
<br clear="none">
Oh well, I think the ideas are interesting
enough to post.<br clear="none">
<br clear="none">
Kevin<br clear="none">
<br clear="none">
>Le jeudi 30 mai 2019 à 17:32:42 UTC−5,
Forest Simmons <fsimmons at pcc.edu> a
écrit : <br clear="none">
><br clear="none">
>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 clear="none">
><br clear="none">
>I am interested in simple methods that
always ...<br clear="none">
><br clear="none">
>(1) elect candidate A given the following
profile:<br clear="none">
><br clear="none">
>P: A<br clear="none">
>Q: B>>C<br clear="none">
>R: C,<br clear="none">
>and <br clear="none">
>(2) elect candidate C given<br clear="none">
>P: A<br clear="none">
>Q: B>C>><br clear="none">
>R: C,<br clear="none">
>and <br clear="none">
>(3) elect candidate B given<br clear="none">
<br clear="none">
><br clear="none">
>P: A<br clear="none">
>Q: B>>C (or B>C)<br clear="none">
>R: C>>B. (or C>B)<br clear="none">
><br clear="none">
>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 clear="none">
><br clear="none">
>Here's the rationale for the requirements:<br clear="none">
><br clear="none">
>Condition (1) is needed so that when the
sincere preferences are<br clear="none">
<br clear="none">
><br clear="none">
>P: A<br clear="none">
>Q: B>C<br clear="none">
>R: C>B,<br clear="none">
>the B faction (by merely disapproving C
without truncation) can defend itself against a
"chicken" attack (truncation of B) from the C
faction.<br clear="none">
><br clear="none">
>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 clear="none">
><br clear="none">
>Condition (2) is needed so that when
sincere preferences are<br clear="none">
<br clear="none">
><br clear="none">
>P: A>C<br clear="none">
>Q: B>C<br clear="none">
>R: C>A,<br clear="none">
>then the C faction (by proactively
truncating A) can defend the CW against the A
faction's potential truncation attack.<br clear="none">
><br clear="none">
>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 clear="none">
>control over their own approval cutoffs (as
opposed to implicit approval) with default
approval as top rank only. The other <br clear="none">
>method I have in mind is not quite as <br clear="none">
>simple, but it has the added advantage of
satisfying the FBC, while almost always electing
from Smith.<br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
</p>
</blockquote>
<i><br clear="none">
</i> </div>
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