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Stéphane Rouillon wrote:<br>
<blockquote type="cite">
<pre wrap="">I am fed up a bit with that discussion about non-monotonicity because it
depends how
monotonicity is defined. IRV is monotonic when you consider adding or
retrieving
ballots with you preffered candidate as first choice. IRV is non-monotonic
when
you consider highering or lowering the positions of your preferred candidate
on several ballots...
Maybe some concision and precision in the definitions would help.
Could we use 2 different names for monotonicities please?
Or maybe they exist and I don't know these definitions...
S. Rouillon</pre>
</blockquote>
<br>
In this 1996 paper Douglas Woodall defines and discusses some
different versions of "monotonicity":<br>
<br>
<a class="moz-txt-link-freetext" href="http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf">http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf</a><br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Monotonicity_criterion">http://wiki.electorama.com/wiki/Monotonicity_criterion</a><br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Mono-add-top_criterion">http://wiki.electorama.com/wiki/Mono-add-top_criterion</a><br>
<br>
Two that Woodall only mentions in that paper, "Mono-append" and
"Mono-add-plump" are very very<br>
weak (meaning very easy to meet) and not doing so is (in my book) very
very silly.<br>
<br>
"Mono-add-plump" says that adding ballots that plump for X (i.e.
"bullet-votes" for X) should never reduce<br>
X's chance of winning.<br>
<br>
"Mono-append" says that if some ballots that didn't rank X (above
equal-bottom) are changed so that now <br>
X is ranked immediately below the candidates that previously were the
only ones ranked (above equal-bottom),<br>
then X's chance of winning must not be reduced.<br>
<br>
(These definitions are my paraphrasing)<br>
<br>
Chris Benham<br>
<br>
<br>
<blockquote cite="midBAY104-F224748165E03CEACDED3668F470@phx.gbl"
type="cite">
<pre wrap="">
</pre>
<blockquote type="cite">
<pre wrap="">From: Jonathan Lundell <a class="moz-txt-link-rfc2396E" href="mailto:jlundell@pobox.com"><jlundell@pobox.com></a>
To: Steve Eppley <a class="moz-txt-link-rfc2396E" href="mailto:SEppley@alumni.caltech.edu"><SEppley@alumni.caltech.edu></a>
CC: <a class="moz-txt-link-abbreviated" href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>
Subject: Re: [Election-Methods] Why monotonicity?
Date: Tue, 15 Jan 2008 08:38:36 -0800
On Jan 15, 2008, at 8:22 AM, Steve Eppley wrote:
</pre>
<blockquote type="cite">
<pre wrap="">The strategy of raising a candidate in order to defeat it may
legitimately be counted as one more strategy in the voter's toolbox of
strategies, but I think the (narrow) question here is whether the
number
of manipulable scenarios is greater given non-monotonic methods, given
the same set of candidates and same voters' preferences. To my
knowledge, this has not been demonstrated.
Furthermore, since the assumptions of the same set of candidates and
same voters' preferences are dubious--candidates may adopt different
positions on the issues, and make different decisions about whether to
run, given a different voting method--monotonicity may be unimportant
even if it does reduce the number of manipulable scenarios.
I think all we can say for sure about the desirability of monotonicity
is that, all else being equal, it's better to be monotonic.
</pre>
</blockquote>
<pre wrap="">I'm reminded of Douglas Woodall's argument that STV's monotonicity
failures occur in scenarios where it's not obvious to begin with which
candidate(s) "ought" to be elected.
<a class="moz-txt-link-freetext" href="http://www.votingmatters.org.uk/ISSUE4/P5.HTM">http://www.votingmatters.org.uk/ISSUE4/P5.HTM</a>
</pre>
<blockquote type="cite">
<pre wrap="">There are certain regions in which it is quite clear who ought to be
elected, and in these regions STV elects the candidate that one
would expect. But in the middle there is a grey area, where it is
not at all clear who ought to be elected, and it is in this grey
area that STV behaves in a somewhat haphazard manner; it is really
doing no more than making a pseudo-random selection from the
appropriate candidates, and it is here that small changes in the
profile of ballots can cause perverse changes in the result.
The effect of this is to blur the result of an STV election. Nobody
is being wrongly elected, because the problem only arises in the
region where one cannot say for certain who ought to be elected
anyway. And there is no systematic bias that would, for example,
favour one political party rather than another. But the accuracy
with which the person or persons elected in an STV election can be
said to represent the views of the voters is less precise than it
would be if this sort of anomaly did not arise.
The obvious question at this point is whether one can find a system
that retains the essential features of STV while avoiding this sort
of anomaly. The answer depends on what one regards as the essential
features of STV. As we shall see in a later article, it is not
possible to avoid this anomaly without sacrificing at least one
property that many supporters of STV regard as essential.
</pre>
</blockquote>
<pre wrap="">...by which he means later-no-harm.
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