[EM] Condorcet Loser Elimination PR

[James Green-Armytage]

Chris Benham wrote:
>Until this method can be shown to be non-monotonic or to have serious
>strategy problems,I think it remains an interesting contender.

David Gamble wrote:
>Basically so far Condorcet elimination PR has not been proved worse than
>Sequential STV. 
>Could anybody provide a full preference set example in which Condorcet
>elimination PR and sequential STV provide a different result?


Dear Chris, David, and other voting fans, 

	Yesterday I sat down and tried to work through this puzzle. It took a few
hours, but I think that I have some examples that will satisfy you.
	First, let me show an example where CLE-STV (Condorcet loser elimination)
differs from SSTV (sequential STV), and where I believe that the SSTV
outcome is clearly more fair.
	(By the way, yes, I do think that SSTV is the next best thing to CPO-STV,
and agrees with CPO-STV very often. I am talking about SSTV in this
posting, but I am pretty confident that CPO-STV gives the same results as
SSTV in the examples I'm presenting. Of course, if anyone can show me
otherwise, that would be important for me to know.)

300 votes
2 seats
Droop quota = 100
I am assuming Newland-Britain for all of these examples, although I doubt
that it matters.

35: ABCD
17: ABDC
66: BACD
33: BADC
50: CDBA
99: DCBA

	I'm sure that you will correct me if I have made any more mistakes, but I
think that the CLE outcome is BC, while the SSTV outcome is BD. I hope
that you will agree that the BD outcome is clearly more fair. 
	You will see that using CLE, the A and B voters are given more power than
they deserve in terms of deciding the winner between C and D. They should
only have 51 votes worth of power, because that is how many votes they
have left after their quota is achieved, but in CLE they wield their full
151 votes worth of power over the C vs. D decision, simply because they
happen not to have achieved a quota in the first round. If B had gotten
two more votes in relation to A from the beginning, then A and B voters
would only be wielding 51 votes worth of power over the B vs. C decision.
	Using SSTV, on the other hand, A and B voters can never wield the 151
voting power in the C vs D decision; The A and B votes must satisfy the
quota and undergo fractional transfer first, which is much more fair.
	By the way, the numbers are not very tight on this example, that is, it
is not hard to create more examples like it. The key is that at least some
portion of the AB voters must prefer D over C. 


	I believe that a minor modification to this example can show how CLE
fails monotonicity. I am not necessarily claiming that CPO-STV passes
monotonicity, and of course plain STV does not either, but it is good to
know that monotonicity is not an advantage that CLE has over these methods.
	First, let me restate the monotonicity criterion for convenience. 
	"With the relative order or rating of the other candidates unchanged,
voting a candidate higher should never cause the candidate to lose, nor
should voting a candidate lower ever cause the candidate to win." (This is
the definition from Mike Ossipoff's web site, electionmethods.org.)

300 votes
2 seats
Droop quota = 100

ranking #1
35: ABCD
17: ABDC
66: BACD
33: BADC
50: CDBA
97: DCBA
2: DBCA

CLE outcome: BC

ranking #2
35: ABCD
17: ABDC
66: BACD
33: BADC
50: CDBA
97: DCBA
2: BDCA

CLE outcome: BD

	Please verify that I have gotten the results correct here.
	The only difference between the two outcomes is that 2 voters switch from
DBCA to BDCA. That is, 2 voters rank D one place lower, without changing
the order of the other candidates. The result is that BD wins instead of
BC.
	The reason it works this way is that in ranking #2, B has a quota in the
first round, and therefore the later preferences of the A and B voters
have less weight in favor of C, which means in turn that D beats out C for
the second seat.
	As in the previous example, BD wins both cases using SSTV.


	In conclusion, I think that Condorcet Loser Elimination PR has some very
serious disadvantages to SSTV and CPO-STV. I doubt that it has any
advantages which are nearly as significant. Therefore, I don't see why it
should ever be used instead of SSTV or CPO-STV.


best wishes,
James