[EM] Condorcet loser elimination PR

[James Green-Armytage]

Chris Benham wrote:
>So this is the corrected version: Ranked ballots, equal preferences ok,
>truncation ok,truncation treated just like equal prefernces. Elect those
>candidates with a Droop quota (1/number of seats to be filled + 1) of
>first preferences (equal first preferences count as fractions).
>Distribute the surplus preferences ("the overflow") of those candidates
>all-at-once  as fractions, elect any who now have a quota and in the same
>way distribute the new surpluses and so on. If at the end of this process
>there are still seats unfilled, NOT counting those votes and fractions of
>votes that make up the quotas of  those already elected candidates,
>determine among the remaining candidates the Condorcet Loser and
>eliminate that candidate. Distribute that candidate's preferences, elect
>any who have a Droop quota, distribute any surplus and so on until all
>the seats/positions have been filled.


Dear Chris,

	Unfortunately, I think that the revised Condorcet loser elimination
method, while perhaps better than the first one, would not do very well as
far as producing proportional results.
	I agree with you in principle, of course, that the best proportional
system should somehow combine the principles of STV and Condorcet. As far
as I know, CPO-STV is the most satisfactory method for doing this, but who
knows for sure. Certainly it would be nice to find a method with the same
benefits as CPO-STV but without the computational cost. So, I applaud your
efforts to find one, and hope that you keep innovating.
	I am glad that you responded to my first counter-example by revising your
method. For a few days, I couldn't think of a flaw in the revised method.
But then it came to me all of a sudden, as I was walking home.
	Below is an illustrative example where, I think you will agree, your
revised method produces an unfair or counterintuitive result.

	The election is between 5 candidates, for 3 seats.
	There are 300 voters.
	I will use a Hare quota, to keep things simple. (Yes, I know your method
specifies a Droop quota, but it doesn't matter for these purposes.)
	The Hare quota is 300 / 3 = 100 votes.
	The preference rankings are as follows:

86: A, B, C, D, E
15: B, A, C, D, E
100: C
15: D, E, C, B, A
84: E, D, C, B, A

	I think that we can agree that the appropriate outcome is ACE, correct?
This is the outcome that plain STV gives, and it is the outcome that
CPO-STV gives. 
	Unfortunately, your revised method seems to produce an outcome of ABC.

86: A, B, C, D, E
15: B, A, C, D, E
100: C
15: D, E, C, B, A
84: E, D, C, B, A	

	This is the initial condition. At this point, E is a clear Condorcet
loser in terms of votes not absorbed in elected quotas, so he is
eliminated, resulting in this condition:

86: A, B, C, D
15: B, A, C, D
100: C
99: D, C, B, A

	Now, D is a clear Condorcet loser. He is eliminated, and the outcome is
ABC.


my best,
James