[EM] More about some 3P methods

[MIKE OSSIPOFF]

(Sorry--I've just posted this without a subject-line. Now I'm reposting it with a subject-line)

For my definition of 3PD, I should define "discriminate":



A voter discriminates among a set of candidates iff s/he votes some of 
them over others in any order she wants to.



I referred to a method that I call "DP". That stands for 
Defection-Proof. It was proposed by Chris Benham. It doesn't meet CD,

and I guess that only pairwise-count methods can, but it doesn't fail in
 the Approval bad-example, something that can be said for

only very few methods.



Definition of DP:



Voting is 3-slot: Preferred, Middle, and Bottom.



Bottom is the default for a candidate not ranked on a ballot.



To rank a candidate other than at bottom is to "approve" that candidate.



If the number of voters approving X but not Y is greater than the number
 of voters approving Y, then disqualify Y.



Among the undisqualified candidates, elect the one preferred on the most
 ballots.



[end of DP definition]



DP meets FBC and 3P, and doesn't fail in the Approval bad-example.



CD is probably too demanding, referring, as it does, to a Condorcet 
candidate.



Maybe a criterion an be written that better reflects the Approval bad 
example (the ABE).



Maybe something like:



If a majority prefer A and B to all the other candidates, and if, A 
would win if the 1st choice supporters of both candidates 

voted both over all the others, then A should win even if A's 1st choice
 voters vote B over the others, but the B

voters don't vote A over the others.



[end of tentative CD definition]



When I have a good definition to reflect the ABE, I'll call it CD. 



As for the criterion that I've previously called CD, I'll call it CCD 
(Condorcet Co-operation/Defection Criterion).



Maybe someone has already posted about this, but Bucklin gives the voter
 a lot more than 3 protection-levels, as I've

defined that term. It gives the voter as many protection levels as there
 are rank positions in the voter's ballot.



So I'll modify the 3P criterion to say "..at least three...", instead of
 "...three..."



And, if a method, like Bucklin, gives an unlimited number of protection 
levels, then it meets the

Unlimited-Protection-Levels Criterion, which I abbreviate "UP".



MDDA meets 3P and 3PD, but fails UP. Bucklin meets 3P, 3PD and UP.



But, regrettably, Bucklin fails in the ABE.



Can a method meet UP and not fail in the ABE? 



Yes. IRV (= whole) meets FBC and UP, and doesn't fail in the ABE.



I now consider IRV (= whole) to be the best method. Certainly the best 
for public political elections.



Between MDDA and DP, I prefer DP, because I consider the ABE to be more 
important than

discrimination among candidates protected at a protection-level.



(Below "ABE" means "doesn't fail in the ABE")





A criterion compliance chart:



-----------------FBC--------3P-----3PD--------UP----ABE



Bucklin---------Yes--------Yes-----Yes--------Yes----No

MDDA----------Yes---------Yes----Yes---------No----No

DP--------------Yes---------Yes-----No---------No----Yes

MCA------------Yes---------Yes-----No---------No----No

MAMPO---------Yes---------No-----No----------No---No

IRV(= whole)---Yes-------Yes-----Yes--------Yes---Yes



Mike Ossipoff 		 	   		  
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