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</head><body text="#000000" bgcolor="#FFFFFF">Thanks for all the useful
feedback from everyone on this topic.<br>
<br>
I decided to implement Minimax with the following ordering: defeats are
ordered by margins (W-L), and by ratios (W/L) when margins are tied.
Further, two candidates are compared first by their weakest defeats;
then, if tied on those, by their 2nd weakest defeats, and so on. This
comparison method was suggested by Richard Darlington. It seems to work
well in practice -- the results seem intuitive and reasonable, and the
algorithm is also efficient.<br>
<br>
-- Andrew<br>
<br>
<span>Juho Laatu wrote:</span><br>
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<div class="">That was a good summary of the weaknesses of the
Plurality criterion. I wonder if the Plurality criterion could be
reformulated so that it would not refer to the first preferences at all,
and it would make its message on the implicit approvals clearer.</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 28 Apr 2017, at
15:45, Toby Pereira <<a moz-do-not-send="true"
href="mailto:tdp201b@yahoo.co.uk" class="">tdp201b@yahoo.co.uk</a>>
wrote:</div><br class="Apple-interchange-newline"><div class=""><div
class=""><div style="background-color: rgb(255, 255, 255); font-family:
'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif;
font-size: 13px;" class=""><div
id="yui_3_16_0_ym19_1_1493383131536_3677" dir="ltr" class=""><span
id="yui_3_16_0_ym19_1_1493383131536_3685" class="">I think I basically
agree with Juho on this. The plurality criterion sounds like a
reasonable criterion on the surface, but think about it more and it's
arguably less so. To summarise, in a pairwise method, first place on a
ballot doesn't hold any special status, nor does indeed last place (or
joint last place or "unranked"). And a criterion shouldn't be used to
impose an approval cut-off on a method that doesn't have one in its
definition.</span></div><div id="yui_3_16_0_ym19_1_1493383131536_3757"
dir="ltr" class=""><span class=""><br class=""></span></div><div
id="yui_3_16_0_ym19_1_1493383131536_3750" dir="ltr" class=""><span
id="yui_3_16_0_ym19_1_1493383131536_3749" class="">So while it sounds
like a good criterion, removing the special status of these positions
means that we are left with just saying that a candidate who pairwise
beats another candidate should finish ahead in the overall ranking.
Which is what all Condorcet methods do - except when there's a cycle.</span></div><div
id="yui_3_16_0_ym19_1_1493383131536_3756" dir="ltr" class=""><span
class=""><br class=""></span></div><div
id="yui_3_16_0_ym19_1_1493383131536_3751" dir="ltr" class=""><span
id="yui_3_16_0_ym19_1_1493383131536_3768" class="">Toby</span></div><div
class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1493383131536_3644"><br
class=""><br class=""></div><div class="yahoo_quoted"
id="yui_3_16_0_ym19_1_1493383131536_3689" style="display: block;"> <div
id="yui_3_16_0_ym19_1_1493383131536_3688" style="font-family: Helvetica
Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;"
class=""> <div id="yui_3_16_0_ym19_1_1493383131536_3687"
style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial,
Lucida Grande, Sans-Serif; font-size: 16px;" class=""> <div
id="yui_3_16_0_ym19_1_1493383131536_3686" dir="ltr" class=""> <font
id="yui_3_16_0_ym19_1_1493383131536_3693" class="" size="2" face="Arial">
<hr id="yui_3_16_0_ym19_1_1493383131536_3692" class="" size="1"> <b
class=""><span style="font-weight: bold;" class="">From:</span></b> Juho
Laatu <<a moz-do-not-send="true" href="mailto:juho.laatu@gmail.com"
class="">juho.laatu@gmail.com</a>><br class=""> <b class=""><span
style="font-weight: bold;" class="">To:</span></b> Election Methods <<a
moz-do-not-send="true"
href="mailto:election-methods@lists.electorama.com" class="">election-methods@lists.electorama.com</a>>
<br class=""> <b class=""><span style="font-weight: bold;" class="">Sent:</span></b>
Thursday, 27 April 2017, 22:57<br class=""> <b class=""><span
style="font-weight: bold;" class="">Subject:</span></b> Re: [EM] Fwd:
Ordering defeats in Minimax<br class=""> </font> </div> <div
class="y_msg_container" id="yui_3_16_0_ym19_1_1493383131536_3691"><br
class=""><div id="yui_3_16_0_ym19_1_1493383131536_3690" dir="ltr"
class="">> On 27 Apr 2017, at 10:25, Kristofer Munsterhjelm <<a
moz-do-not-send="true" id="yui_3_16_0_ym19_1_1493383131536_3696"
href="mailto:km_elmet@t-online.de" shape="rect"
ymailto="mailto:km_elmet@t-online.de" class="">km_elmet@t-online.de</a>>
wrote:<br class="" clear="none"><br class="" clear="none">> Do you
consider Plurality a strategic criterion? It seems to me to be<br
class="" clear="none">> more of a "natural behavior" criterion: if A
gets more first preferences<br class="" clear="none">> than B gets
any preferences, then B shouldn't win. This seems reasonable<br class=""
clear="none">> from a natural behavior perspective because A
dominates B in some<br class="" clear="none">> Approval-ish sense.<br
class="" clear="none">> <br class="" clear="none">> If that's a
"natural behavior" criterion, then you could say that<br class=""
clear="none">> margins is more natural from a descriptive point of
view (no<br class="" clear="none">> discontinuities) while wv is more
natural from a criterion point of<br class="" clear="none">> view.
Though, if we're to go by the apparent popularity of IRV, it seems<br
class="" clear="none">> that descriptive clarity weighs heavier than
criterion clarity.<br class="" clear="none"><br class="" clear="none">First
of all, my thinking when it comes to practical election methods is not
very criterion oriented. I tend to see criteria and criterion
compatibility as important theoretical results that are mostly too far
from practical election method considerations to be applied directly on
them as viability criteria. The relevance of different criteria to
practical election methods is almost as low as the relevance of latest
mathematical inventions to practical everyday economic calculations
(well, not quite, but something in that direction). I'm about at the
level of accepting Condorcet criterion if we seriously want to have a
neutral majority based method for consensus oriented single winner
elections. One has to take also into account the fact that all election
methods are bound to break some potentially useful criteria. All this
means that I classify Plurality and most other criteria as an
interesting discussion points but not something to be followed
categorically. There are many<br class="" clear="none"> criteria that
are useful in the sense that most elections should have strong
orientation in the described direction, but no need, or possibly with
strong reasons to deviate from some criteria in some special (usually
marginal) situations.<br class="" clear="none"><br class="" clear="none">I
think Plurality is a bit strange. Actually it is not even a criterion
of of ranked methods. It is a criterion for ranked methods with implicit
approval cutoff. It makes the assumption that a voter that casts a
short vote has somehow approved those candidates that he marked, and not
approved the others. In different elections the behaviour of voters
with respect to which candidates will be marked on the ballot may vary a
lot, and that may have nothing to do with how much the voters support
or approve those candidates. In order to make any sense of the Plurality
criterion we are thus tied to having an assumption of implicit approval
in the ballots, where marking a candidate means approving that
candidate at some level.<br class="" clear="none"><br class=""
clear="none">One reason why I don't like implicit approval in general
(as a fact that is known by the voters) is that it encourages voters not
to rank candidates that they don't like. Ranked methods work well only
if most voters do rank explicitly at least all the potential winners (or
all of them except one). If there is an approval cutoff, it would be
better if it was an explicit one (this comment is not Plurality
criterion specific but a general one).<br class="" clear="none"><br
class="" clear="none">Plurality criterion is a "heuristic" criterion in
the sense that its message somehow sounds good (e.g. to people that do
not regularly deal with election methods and their peculiarities).
People would like also criterion "if voters would prefer A to B, then B
should not win". But EM experts know that this criterion would not be a
very good one, although it states something that we all would like to be
true in all elections. What I'm trying to say here is only that we
should be careful with cyclic group opinions. They will contain some
nasty features. Instead of trying to pick a set of criteria that should
be met 100%, my preferred approach is to see what kind of problems each
method would be likely to face in real elections (typically but not
necessarily large public elections with many different kind of voters
that the strategists can not control), and evaluate them based on their
performance in such real life situations.<br class="" clear="none"><br
class="" clear="none">I'm not well prepared to comment how margins can
handle Plurality criterion but I'll address one basic (but theoretical
and extreme, i.e. unlikely to happen in typical elections) example.
35:A, 34:B>C, 31:C. A has more first preferences than B has ballots
where B is marked. B's worst defeat margin is however smallest (1), so
it will win in typical margins based methods. Plurality criterion says
that B should not win. B is however two votes short of being a Condorcet
winner, so it can't be the worst of the worst. What if A would win?
Plurality criterion pays special attention to A's high number of first
preferences. But on the other hand voters would like to elect C instead
of A with large majority (C>A voters would not be happy with the
result). How about C then? Plurality criterion accepts C too, but using
the high number of first preference votes of A as an argument that
supports C does not make much sense. My conclusion is that this is a
typical mess that we can get with c<br class="" clear="none"> ircular
preferences. Our voters were quite stupid when they didn't sufficiently
rank the potential winners. There are many different possible scenarios
on what the truncated opinions might have been, and different results
emerging from that. In this example my recommendation would be to tell
to the voters that they should rank all potential winners (except maybe
the worst one). I don't see any need to start blaming (or praising)
margins on what happened. Maybe you have some realistic examples in your
mind, that would give better justification to the Plurality criterion.<div
class="yqt3747196044" id="yqtfd47276"><br class="" clear="none"><br
class="" clear="none">Juho<br class="" clear="none"><br class=""
clear="none"><br class="" clear="none">----<br class="" clear="none">Election-Methods
mailing list - see <a moz-do-not-send="true"
href="http://electorama.com/em" target="_blank" shape="rect" class="">http://electorama.com/em
</a>for list info<br class="" clear="none"></div></div><br class=""><br
class=""></div> </div> </div> </div></div></div></div></blockquote></div>
<br class="">
</blockquote>
<br>
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