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<font face="Helvetica, Arial, sans-serif">Terry and all,<br>
<br>
I, too,am interested in Stephane's explanation. Meanwhile, I thought he
was referring to a different way of broadening the notion of
monotonicity. I understood him to be saying that, because of strategic
voting, the relationship between true preferences and outcome is
non-monotonic even when the relationship between votes cast and outcome
is monotonic. In any case, this is how I understand David Austen-Smith
and Jeffrey Banks, "Monotonicity in Electoral Systems", American
Political Science Review, Vol. 85, No. 2 (June 1991): 531-537. As I
understand it, this important paper argues that, when monotonicity is
defined relative to true preferences, and when the legislative process
is considered in combination with the voting rule, monotonicity becomes
a non-issue.<br>
<br>
--Bob Richard<br>
</font><br>
Terry Bouricius wrote:
<blockquote cite="mid:CE0DBDF976BE4F73945F0A02B4297B00@UPSTAIRS"
type="cite">
<pre wrap="">Stephane,
In what way are you calling FPTP vote-splitting non-monotonic? It is
normally considered monotonic in that a voter raising the rank of a
candidate to number 1 can never hurt that candidate. Are you using the
broader non-standard definition of monotonicity that some particular
election method advocates have started using...where raising the rank of a
candidate to number 1 may hurt that VOTER'S interests (rather than that
first ranked CANDIDATE) by causing the election of that voter's least
favorite candidate. I have feel that is an overly broad expansion of the
concept of monotonicity, that some have seized on so they could claim
there are examples of non-monotonicity where there really aren't.
While I am one of those who thinks monotonicity is of relatively small
practical importance compared to certain other criterion, I think our
terminology definitions need to be standardized to allow us to understand
each other...and I would say IRV is a non-monotonic system and FPTP is
monotonic. Can you show that this is wrong?
Terry Bouricius
----- Original Message -----
From: "Stéphane Rouillon" <a class="moz-txt-link-rfc2396E" href="mailto:stephane.rouillon@sympatico.ca"><stephane.rouillon@sympatico.ca></a>
To: "Abd ul-Rahman Lomax" <a class="moz-txt-link-rfc2396E" href="mailto:abd@lomaxdesign.com"><abd@lomaxdesign.com></a>
Cc: <a class="moz-txt-link-rfc2396E" href="mailto:election-methods@lists.electorama.com"><election-methods@lists.electorama.com></a>
Sent: Wednesday, November 04, 2009 11:20 PM
Subject: [EM] About non-monotonicity and non-responding to previous
posts...
Miss Dopp was promoting FPTP in the past, saying IRV is non-monotonic,
until I showed that FPTP vote-splitting behaviour is non-monotonic too.
</pre>
<blockquote type="cite">
<pre wrap="">- more voters prefer B to C
- a fraction of those voters will vote for A because they even prefer
A to other candidates
- thus C can get elected because of vote-splitting between A and B
Even if more voters prefer B to C, the result is that C wins over B.
This is clearly non-monotonic.
This is a typical vote-splitting case using FPTP.
</pre>
</blockquote>
<pre wrap=""><!---->
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</pre>
</blockquote>
<br>
<pre class="moz-signature" cols="72">--
Bob Richard
Executive Vice President
Californians for Electoral Reform
P.O. Box 235
Kentfield, CA 94914-0235
415-256-9393
<a class="moz-txt-link-freetext" href="http://www.cfer.org">http://www.cfer.org</a>
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