<html>
<head>
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<p>Juho,<br>
<br>
<blockquote type="cite"> If vote A>B=C is not the same as vote
A in a three candidate election, then there is an implicit
cutoff at the truncation point. (Or maybe someone wants to put
the special "given any preference" point after A in the first
vote.)</blockquote>
To be clear, I interpret "vote" as meaning vote above at least one
other candidate and not just any mark or number next to a
candidate's name on the ballot paper.<br>
<blockquote type="cite">Ranked methods work well only if voters
give us their preferences (of all the relevant candidates)</blockquote>
As long as the truncation incentive isn't stronger than the voters
like and generally the incentives for voters to misrepresent their
true <br>
preferences are as low as possible then if voters choose not
reveal their weaker preferences that should be no problem.<br>
<br>
<blockquote type="cite">But when reading the definition, a natural
thought is that if you do not rank some of the candidates that
you don't like at all, that might improve the chances of your
favourite candidates to win.</blockquote>
Yes, it might or it might not. No-one suggests that the Plurality
criterion should be posted in the polling booth. <br>
</p>
<p>
<blockquote type="cite">One quite possible (real life?) risk is
that competing factions start truncating the candidates of the
other factions. That might lead to bad results.</blockquote>
Yes, I suppose it could lead to slightly "bad" results. But I
think it is more likely to lead to relatively good results.
Generally speaking I would guess that<br>
pairwise preferences among candidates the voter "doesn't like at
all" would be weaker, probably less well-informed, if the method
meets Later-no-Harm<br>
the preferences could be light-minded (almost arbitrary). That
could result in a winner with relatively low Social Utility and
less legitimate-looking.<br>
<br>
And of course since all Condorcet methods have some Burial
incentive, preferences among candidates the voter doesn't like are
less likely to be <br>
sincere in any case. So arguably we should err on the side of
trying to avoid a "garbage in, garbage out" scenario rather than
fret about electing<br>
the candidate who would be the CW if only the voters could be
induced to reveal their sincere full rankings.<br>
<br>
<blockquote type="cite">
<div class="">
<blockquote type="cite" class="">
<div bgcolor="#FFFFFF" class="">
<p class="">46: A<br class="">
44: B>C<br class="">
10: C<br class="">
</p>
</div>
</blockquote>
</div>
<div class="">To people who are used to methods where the first
positions are the key thing, and that's everything that is
important in the election, these votes seem to say that A is
the strongest of the candidates.</div>
</blockquote>
Here you are somewhat missing the point again. It's not just
"first" positions, it's <b>any</b> (above bottom) positions. And
it's not that A is "the strongest <br>
of the candidates". It is that A is so much stronger than B that
electing B can't be justified. The Plurality criterion says
nothing about C.<br>
<br>
<blockquote type="cite"> Since information given in the votes
above is very limited, we can imagine various reasons why all A
and C supporters truncated their vote.</blockquote>
It would be much more to the point if you instead try to "imagine
various reasons" why all the B supporters didn't.<br>
<blockquote type="cite">One way to see those votes is to ask what
would happen if A, B or C wins. There would be an interest to
change B to A, but just a small interest.</blockquote>
That is "one way" which I regard as very stupid and completely
reject. Instead of scratching your head wondering why the A and C
supporters<br>
deprived us of so much "information", why don't you seriously
consider the possibility that the B supporters' ranking of C is
completely insincere?!<br>
<br>
With no explicit approval (or any other sort of ratings)
information the best winner is arguably C. Then the 46 A voters
have no strong complaint: C<br>
pairwise beats A, C is voted above bottom on more ballots than is
A. The 44 B>C voters have no complaint: if they hadn't ranked
C then A would have<br>
won, if they really prefer A to C then it serves them right for
telling lies.<br>
<br>
But electing B and then telling the A supporters "If only two of
you later change your A>B preference to B>A then everything
will be ok, and maybe<br>
the B supporters were all sincere in ranking C and it was just
their good luck that doing so caused their favourite to be elected
instead of yours" to<br>
me just doesn't wash.<br>
<br>
<blockquote type="cite">I'd like my favourite method to meet all
the sensible sounding criteria. Unfortunately that is not
possible. My philosophy is that the best method might violate
all of the mutually incompatible useful criteria a bit, but only
so little that those violations do not cause any problems in
practice.</blockquote>
<br>
So have I been wrong in assuming that you insist on compliance
with the Condorcet criterion?<br>
<br>
Chris Benham<br>
<br>
</p>
<div class="moz-cite-prefix">On 1/07/2019 5:38 pm, Juho Laatu wrote:<br>
</div>
<blockquote type="cite"
cite="mid:5955EFE7-0598-4966-89DB-C097D01C7BD5@gmail.com">
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
<div class="">I guess the key point that I was referring to is
that if you read the definition verbally, it has words "votes in
total". Or the wikipedia version of the definition (<a
href="https://en.wikipedia.org/wiki/Plurality_criterion"
class="" moz-do-not-send="true">https://en.wikipedia.org/wiki/Plurality_criterion</a>)
has words "given any preference". Usually people talk about
"truncation" of the vote. That seems to indicate that the point
of truncation has some special meaning (in addition to just
indicating that the unlisted candidates should be seen to be in
the "shared last" position in the pure rankings).</div>
<div class="">
<blockquote type="cite" class="">
<div text="#000000" bgcolor="#FFFFFF" class="">
<p class="">So what is the point of the Plurality
criterion? To my mind it is simply about not offending
obvious fairness and common-sense.</p>
</div>
</blockquote>
</div>
<div class="">I believe that is the case. I just don't like the
idea of giving the truncation point any special meaning. If vote
A>B=C is not the same as vote A in a three candidate
election, then there is an implicit cutoff at the truncation
point. (Or maybe someone wants to put the special "given any
preference" point after A in the first vote.) Different methods
may meet this criterion in different ways (some trivially). But
when reading the definition, a natural thought is that if you do
not rank some of the candidates that you don't like at all, that
might improve the chances of your favourite candidates to win.
(Also if there is a fourth totally hopeless candidate D, those
two votes should be in practice similar, in all typical methods
in which the existence of D has no effect on the outcome, or
otherwise they seem to have a meaningful implicit cutoff.)</div>
<div class=""><br class="">
</div>
<div class="">My philosophy is thus that pure ranked votes are
pure ranked votes (usually completed so that unlisted candidates
are seen as "shared last"). If methods derive some (cutoff like)
additional information from the ballots, then I typically prefer
methods where that cutoff is explicit (not implicit at the
truncation point). And the reason is that I want to see complete
rankings (of all the relevant candidates) instead of truncated
(= lost) preferences. Ranked methods work well only if voters
give us their preferences (of all the relevant candidates). One
quite possible (real life?) risk is that competing factions
start truncating the candidates of the other factions. That
might lead to bad results. For these reasons the idea of
rewarding truncation in some cases is not a very good idea.
Sometimes it may be acceptable though, just like violations of
most criteria sometimes are, if there are no better ways
available around the problem in question.</div>
<div class="">
<blockquote type="cite" class="">
<div text="#000000" bgcolor="#FFFFFF" class="">
<p class="">46: A<br class="">
44: B>C<br class="">
10: C<br class="">
</p>
</div>
</blockquote>
</div>
<div class="">To people who are used to methods where the first
positions are the key thing, and that's everything that is
important in the election, these votes seem to say that A is the
strongest of the candidates. Condorcet methods (that I guess we
are mainly discussing here) however can be said to aim at
electing the best compromise candidate. That candidate might not
have any first preference supporters, and still be a Condorcet
winner. Since information given in the votes above is very
limited, we can imagine various reasons why all A and C
supporters truncated their vote. One way to see those votes is
to ask what would happen if A, B or C wins. There would be an
interest to change B to A, but just a small interest. One may
consider the interest to change the others to some other
candidate to be stronger.</div>
<div class=""><br class="">
</div>
<div class="">If there is a Condorcet winner, as in votes 49:
A>>>B>C, 03: B>A>>>C, 48:
C>>>B>A, one could ask the voters, would they prefer
to change the winner to B, if A or C would win. B may not be
very popular, but maybe still a better choice than electing one
of the more "extreme" alternatives. If people want the first
preferences to have a strong influence, they might prefer
methods like IRV (where candidates with small amount of first
preferences support may often be eliminated quickly.). Having
that kind of a "cutoff" would be another interesting discussion.</div>
<div class=""><br class="">
</div>
<div class="">
<blockquote type="cite" class="">
<div text="#000000" bgcolor="#FFFFFF" class="">If voters
decline to (or don't bother to) express some or all of their
very weak (possibly light-minded) pairwise preferences by
truncating, then I don't classify that as "insincere" voting</div>
</blockquote>
<br class="">
</div>
<div class="">I would not call those votes "insincere" either. But
they would be "incomplete", and possibly "lazy" in some cases.
It is not important to give opinions on the "irrelevant"
candidates, but it is important to give opinions on the
"relevant" candidates (unless one really thinks they are tied).</div>
<div class=""><br class="">
</div>
<div class="">
<blockquote type="cite" class="">
<div text="#000000" bgcolor="#FFFFFF" class="">Since therefore
there could be several (or even many) alternative "sincere
voting" profiles it follows that there could be more than
one "sincere CW".</div>
</blockquote>
</div>
<div class=""><br class="">
</div>
<div class="">I wouldn't say so. There would be only (max) one
sincere CW, based on what we know about the opinions of the
voters. Information that is not there is not information to the
method. Next day voters might vote differently, but that would
be another day, and possibly another CW.</div>
<div class="">
<blockquote type="cite" class="">
<div text="#000000" bgcolor="#FFFFFF" class="">
<p class="">Later-no-Help criterion ...</p>
</div>
</blockquote>
</div>
<div class="">I'd like my favourite method to meet all the
sensible sounding criteria. Unfortunately that is not possible.
My philosophy is that the best method might violate all of the
mutually incompatible useful criteria a bit, but only so little
that those violations do not cause any problems in practice. It
is however possible that a method like that would be quite
complex. I put some considerable weight also on simplicity and
understandability, so I might prefer some simpler method instead
of the "theoretically optimal" one. I also often tend to
emphasise performance with sincere votes in cases, since in many
elections strategic voting may not emerge even if there are some
small theoretical possibilities of some strategy possibly being
successful sometimes. It is important to elect the best winner
(= performance with sincere votes), and not tweak the method to
do something else because of some far fetched strategy concerns.
Often the situation is thus such that there is no need to defend
against strategies that are not likely to emerge and succeed
anyway. Different elections have different needs. A repeated
competitive poll among few EM strategy experts is different from
a public election with millions of voters, clear frontrunners,
and a wide mixture of continuously changing opinions.</div>
<div class=""><br class="">
</div>
<div class="">Juho</div>
<div class=""><br class="">
</div>
<br class="">
<div>
<blockquote type="cite" class="">
<div class="">On 30 Jun 2019, at 19:00, C.Benham <<a
href="mailto:cbenham@adam.com.au" class=""
moz-do-not-send="true">cbenham@adam.com.au</a>> wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<meta http-equiv="content-type" content="text/html;
charset=windows-1252" class="">
<div text="#000000" bgcolor="#FFFFFF" class="">
<p class="">Juho (and interested others),<br class="">
<br class="">
The Plurality criterion was coined in 1994 by Douglas
Woodall. Quoting him exactly from then:<br class="">
</p>
<blockquote type="cite" class="">The following rather weak
property was formulated with single-seat elections in
mind, but it makes sense also for multi-seat elections
and, again, it clearly holds for STV .<br class="">
<br class="">
Plurality. If some candidate <i class="">a</i> has
strictly fewer votes in total than some other candidate
<i class="">b</i> has first-preference votes, then <i
class="">a</i> should not have greater probability
than <i class="">b</i> of being elected.<br class="">
<b class=""><br class="">
</b></blockquote>
No mention of any "implicit approval cutoff". I know that
at the time Woodall was only thinking about strict
rankings from the top with truncation allowed. <br
class="">
If equal-first ranking is allowed, then for the purpose of
this criterion we should be using the fractional (summing
to 1) interpretation of the number of <br class="">
"first-preference votes".<br class="">
<div class=""><br class="webkit-block-placeholder">
</div>
<p class="">Juho seems to think that the Plurality
criterion is a "feature" or strategy device that
somehow encourages truncation. It isn't and doesn't. <br
class="">
<br class="">
If the method uses one of the traditional Condorcet
algorithms that are almost the same as each other
(Smith//MinMax, Schulze, River, Ranked Pairs)<br
class="">
and uses Winning Votes as the measure of pairwise defeat
strength, then the method meets Plurality and also has,
at least in the zero-info case, a weak<br class="">
<b class="">random-fill incentive.<br class="">
</b></p>
<p class="">IRV, and IRV modified to meet Smith by before
each elimination checking to see if there is
pairwise-beats-all candidate among those remaining, both
meet<br class="">
the Plurality criterion. In those methods do the voters
have any have any incentive "not to rank the candidates
of the competing groupings" ? No they <br class="">
don't.<br class="">
<br class="">
So what is the point of the Plurality criterion? To my
mind it is simply about not offending obvious fairness
and common-sense.<br class="">
<br class="">
Juho, try to imagine that you have no interest in or
knowledge about voting algorithms, you've never thought
about the split-vote problem. You are accustomed<br
class="">
to voting in plurality elections (or even perhaps
Approval elections) and you've never been interested in
doing anything other than voting for your sincere<br
class="">
favourite, who regularly wins. You are content with the
current voting method and can't see any point in
changing it.<br class="">
<br class="">
Now imagine some voting-reform movement succeeds and the
new method is, say, MinMax(Margins). You hear that
voters can now rank more<br class="">
than one candidate and you simply seek assurance that
you will be allowed to go on voting as before and you
assume that the government must<br class="">
more-or-less know what it's doing and assume the method
won't in any way be less fair than before.<br class="">
</p>
<p class="">In this election your favourite is A.<br
class="">
46: A<br class="">
44: B>C<br class="">
10: C<br class="">
<br class="">
It is announced that the winner is B. At first you
think "A got more first-preference votes than B, it must
have something to do with some voters'<br class="">
second preference votes", but then you notice that B got
the same number of second-preference votes as A (zero),
and then you ask "How on earth<br class="">
did this crazy new method elect B over my favourite A,
who very clearly got more "votes" (marks next to his
name on the paper ballots) all of which<br class="">
were first-preference votes!"<br class="">
<br class="">
On hearing the reply "Oh, that's because B was the
fewest votes shy of being the Condorcet winner" do you
(a) say "Oh how silly of me, obviously<br class="">
that's fair!" or (b) say .. something much less
understanding and accepting ?<br class="">
</p>
<p class="">This scenario also works if the old method was
IRV. You might also notice that this first MMM election
scenario is also a massive egregious failure<br class="">
of the Later-no-Help criterion (because if the B voters
had truncated then B wouldn't have won). Do you like
that criterion?<br class="">
<br class="">
If the old method had been Approval, you would then
presumably be understanding and resigned if it is
announced that C won. <br class="">
In fact electing A is a failure of the Minimal Defense
criterion. Do you like that one? So methods that meet
both MD and Plurality (such as Winning<br class="">
Votes and Smith//implicitA) must elect C.<br class="">
<br class="">
</p>
<blockquote type="cite" class=""> ... methods might not
elect the best winner (sincere Condorcet winner). </blockquote>
If voters decline to (or don't bother to) express some or
all of their very weak (possibly light-minded) pairwise
preferences by truncating, then I don't<br class="">
classify that as "insincere" voting. Since therefore
there could be several (or even many) alternative "sincere
voting" profiles it follows that there<br class="">
could be more than one "sincere CW". It seems obvious to
me that the one of of those that is based on only the
relatively strong pairwise preferences<br class="">
will have a higher "social utility" than one based on all
pairwise preferences which include a lot of very weak
ones.<br class="">
<br class="">
49: A>>>B>C<br class="">
03: B>A>>>C<br class="">
48: C>>>B>A<br class="">
<br class="">
Say these are the sincere preferences. If the voters care
to express all their pairwise preferences then the
"sincere CW" is B, but if they choose<br class="">
what I consider to be an alternative way of sincere voting
and truncate where that will only "conceal" some weak
pairwise preferences then<br class="">
an alternative "sincere CW" is (the apparently higher
Social Utility candidate) A.<br class="">
<div class=""><br class="webkit-block-placeholder">
</div>
<p class="">In fact if the method used was the tweaked
IRV method with an explicit approval cutoff that I
recently suggested and the cast votes were<br class="">
49: A>>B<br class="">
03: B>A>><br class="">
48: C>>B<br class="">
<br class="">
then only C would be disqualified (because A both
pairwise beats C and is more approved than C) and then B
is eliminated and A wins.<br class="">
I doubt that there would much blood flowing in the
streets caused by the failure to elect the voted CW (B).<br
class="">
</p>
<p class="">As consolation for not meeting the Condorcet
criterion we would have a method much more resistant to
Burial strategy than any Condorcet<br class="">
method (and maybe more appealing to people who like
IRV).<br class="">
<br class="">
<b class=""><br class="">
Juho Laatu</b> <a 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=%3C06DA7FE6-AAF5-4684-B448-7FD93DCA0E35%40gmail.com%3E"
class="" moz-do-not-send="true">juho.laatu at
gmail.com </a><br class="">
<i class="">Sat Jun 29 07:43:29 PDT 2019</i> <br
class="">
</p>
<blockquote type="cite" class="">P.S. I don't like the
plurality criterion. It actually sets an implicit
approval cutoff at the end of the listed candidates. The
worst part of that idea is that it encourages voters not
to rank the candidates of the competing groupings. That
(potentially huge amount of missing information) is not
good for ranked methods. If voters learn to use that
feature, methods might not elect the best winner
(sincere Condorcet winner). </blockquote>
<br class="">
<br class="">
<br class="">
The following rather weak property was formulated with
single-seat elections in mind, but it makes sense also for
multi-seat elections and, again, it clearly holds for STV
.<br class="">
Plurality. If some candidate a has strictly fewer votes in
total than some other candidate b has first-preference
votes, then a should not have greater probability than b
of being elected.<br class="">
<div class=""><br class="webkit-block-placeholder">
</div>
<div id="DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2" class=""><br
class="">
<table style="border-top: 1px solid #D3D4DE;" class="">
<tbody class="">
<tr class="">
<td style="width: 55px; padding-top: 13px;"
class=""><a
href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient&utm_term=oa-4885-b"
target="_blank" class=""
moz-do-not-send="true"><img
src="https://static2.avg.com/2000491/web/i/ipm/icon-envelope-tick-green-avg-v1.png"
alt="" style="width: 46px; height: 29px;"
class="" moz-do-not-send="true" width="46"
height="29"></a></td>
<td style="width: 470px; padding-top: 12px; color:
#41424e; font-size: 13px; font-family: Arial,
Helvetica, sans-serif; line-height: 18px;"
class="">Virus-free. <a
href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient&utm_term=oa-4885-b"
target="_blank" style="color: #4453ea;"
class="" moz-do-not-send="true">www.avg.com</a>
</td>
</tr>
</tbody>
</table>
<a
href="x-msg://13/#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"
width="1" height="1" class="" moz-do-not-send="true">
</a></div>
</div>
</div>
</blockquote>
</div>
<br class="">
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<pre class="moz-quote-pre" wrap="">----
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="https://electorama.com/em">https://electorama.com/em</a> for list info
</pre>
</blockquote>
</body>
</html>