<HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Rob Speer wrote:<BR>
<BR>
>Didn't we hear this same debate, oh, a week ago? And the week before<BR>
>that? It seems like every thread on this list eventually turns into<BR>
>"Weak centrist!" "Condorcet winner!" "Weak centrist!" "Condorcet winner!"<BR>
<BR>
>Unless someone's providing some new information (like, say, the results<BR>
>of an experiment to _find out_ whether people prefer a weak centrist or<BR>
>a Condorcet non-winner), there is no value to repeating the argument.<BR>
<BR>
What I was trying to do in my original post was give details of a method which gives high utility centrist, low first preference vote- winner ( as in Condorcet ) and low utility centrist, low first preference vote- loser ( as in IRV ).<BR>
<BR>
Take the following examples:<BR>
<BR>
Low utility centrist:<BR>
<BR>
48 1.00A > 0.3B<BR>
5 1.00B > 0.5C<BR>
47 1.00C > 0.3B<BR>
<BR>
Pairwise comparisons using utilities <BR>
<BR>
A versus B 48 v 19.1 <B>A wins</B><BR>
A= 48 @ 1.00 =48.00 B = 5 @ 1.00 + 47 @ 0.3 = 19.1<BR>
<BR>
A versus C 48 v 49.5 <B>C wins<BR>
</B>A= 48 @ 1.00 = 48.00 C = 5 @ 0.5 + 47 @ 1.00 = 49.5<BR>
<BR>
B versus C 19.4 v 47 <B>C wins<BR>
</B>B= 5 @ 1.00 + 48 @ 0.3 = 19.4 C = 47 @ 1.00 = 47.00<BR>
<BR>
B is the Condorcet loser and is eliminated.<BR>
<BR>
B votes transfer to C at a utility of 1.00 giving:<BR>
<BR>
1st 2nd<BR>
A 48 48<BR>
B 5 ---<BR>
C 47 52<BR>
<BR>
<B>C is the winner ( as in IRV).<BR>
<BR>
</B><BR>
<BR>
High utility centrist:<BR>
<BR>
48 1.00A > 0.95B<BR>
5 1.00B > 0.5C<BR>
47 1.00C > 0.95B<BR>
<BR>
A versus B 48 v 49.65 <B>B wins<BR>
</B>A = 48 @ 1.00 = 48.00 B = 5 @ 1.00 + 47 @ 0.95 = 49.65<BR>
<BR>
A versus C 48 v 49.5 <B>C wins<BR>
</B>A = 48 @ 1.00 = 48.00 C = 5 @ 0.50 + 47 @ 1.00 = 49.5<BR>
<BR>
B versus C 50.6 v 47 <B>B wins<BR>
</B>B = 48 @ 0.95 + 5 @ 1.00 C = 47 @ 1.00<BR>
<BR>
A is the Condorcet loser and is therefore eliminated.<BR>
<BR>
A votes transfer to B at a utility of 1.00 giving:<BR>
<BR>
1st 2nd<BR>
A 48 -----<BR>
B 5 53<BR>
C 47 47<BR>
<BR>
<B>B is the winner ( as in Condorcet ).</B><BR>
<BR>
David Gamble<BR>
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