[EM] Re:[Condorcet elimination PR]

Chris Benham chrisbenham at bigpond.com
Wed Jul 30 11:47:33 PDT 2003

James G-A,
In response to my proposal to modify STV-PR by  instead of  IRV-style 
plurality elimination ,eliminating the Condorcet loser among the ballots 
and fractions of ballots not tied up in quotas, you wrote:

"Modified example:

300 votes
3 seats
Droop quota = 75

74: A, B, C, D, E
39: B, A, C, D, E
75: C
39: D, E, C, B, A
73: E, D, C, B, A

	Once again, I would say that the appropriate result would be ACE, but I
believe that your revised method gives an outcome of ABC. Hopefully this
makes things more clear."

My proposed method definitely doesn't elect ABC. In your example the candidates can be thought of as representing points on a political spectrum: A and E are the far wings,C is the centre,B and D are the moderate wings.The votes are all consistent with this idea.From this point of view the E and D supporters comprise a faction with more than a third of the vote,so it would be absurd and unacceptable to deny them a seat.
The election of C is automatic, and to me the example would essentially be the same if C didn't stand,those 75 voters stayed home and there were only 2 seats.(The Droop quota would be the same.)
A and E both have very strong claims, but from any Condorcet-like point of view,I don't see that E's claim is unassailable.E is short of a quota and is the Condorcet Loser.
So to work through your example:
C has a (bare)Droop quota of first preference votes and so is elected. 
There were no surplus votes, so still no other candidate has a quota. So among those votes not tied up in quotas, E is the Condorcet loser and so is eliminated. Those 73 EDCBA ballots can now merge with the 39 DECBA ballots to become 112 DBA ballots. D now has a quota and so is elected.
75 (a quota) of those 112 ballots play no further part in the election, but the 37 surplus (now BA) ballots are still active. So now the active ballots reduce to:
 76 BA 
 74 AB
 so B is elected and the final result is CDB.

Your example shows that this method is biased toward the centre in the way it tidies up.Some people would regard this as a positive. With nation-wide inexact proportionality caused by lowish 
"district magnitude", this feature might be regarded as wisely cautious.
Until this method can be shown to be non-monotonic or to have serious strategy problems,I think it remains an interesting contender.

Chris Benham 

More information about the Election-Methods mailing list