<HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Alex Small wrote in part:<BR>
<BR>
"1) Elect the Condorcet winner, or the winner of the Condorcet completion<BR>
method (from now on I'll use "CW" to denote either the Condorcet winner or<BR>
the winner of the Condorcet completion method, just to be succinct).<BR>
<BR>
2) As in STV or PAV (Proportional Approval Voting) after electing<BR>
somebody we need to reduce the weight of some of the ballots. In STV we<BR>
would reduce the weight of all ballots that ranked the candidate first<BR>
(first among those remaining, that is). In Proportional Condorcet (PC) we<BR>
would reduce the weight of any ballots that prefer the most recently<BR>
elected candidate to the runner-up.<BR>
<BR>
Who is the runner-up? Whoever the CW would have been had the most<BR>
recently elected candidate (i.e. the most recent CW) not been on the<BR>
ballot. This is NOT the Condorcet Loser, at least not as I understand the<BR>
term. I always think of the Condorcet Loser as whoever loses ALL pairwise<BR>
contests (if such a candidate exists). I guess you could say that any<BR>
candidate not elected is a Condorcet Loser, but then the Condorcet Loser<BR>
is just a loser, and there's no need for a special term."<BR>
<BR>
<BR>
Alex, using a Droop quota to elect 3 from the 4 candidates given below who would be elected under your method?<BR>
<BR>
Votes <BR>
<BR>
27 A1>A2>B <BR>
26 A2>A1>B<BR>
7 B>A1>A2<BR>
6 B>C<BR>
34 C>B<BR>
<BR>
First Count<BR>
<BR>
A1 27<BR>
A2 26<BR>
B 13<BR>
C 34<BR>
<BR>
Any good ( in my opinion) method should elect A1, A2 and C who all have a Droop quota of first preference votes.<BR>
<BR>
On the first count A1 is the Condorcet winner and is elected. A1's 27 votes are now reduced to a value of 0.074 and transferred giving for the second count <BR>
<BR>
A2 27.998<BR>
B 13<BR>
C 34<BR>
<BR>
B is now the Condorcet winner (B v A2, 47 v 27.998; B v C 40.998 v 34) and elected. C is the Condorcet runner up. Presumably since the A2 votes prefer B to C some of these votes are transferred at a reduced value to elect B. <BR>
<BR>
C wins the final seat against A2.<BR>
<BR>
Am I misunderstanding your method or does it allow the defeat of candidates who have obtained a quota of first preference votes?<BR>
<BR>
David Gamble<BR>
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