[EM] Re: Markus, criteria

[Kevin Venzke]

Hi,

I assume the definitions at http://www.barnsdle.demon.co.uk/vote/stfree.html are
correct.

It seems to me that Mike's criteria aren't ambiguous, but it can be hard to decide
for certain whether methods satisfy them.

WDSC:
>If a majority of all the voters prefer A to B, then they should have a way of 
>voting that will ensure that B won't win, without any member of that majority 
>voting a less-liked candidate over a more-liked one.

So, a method would satisfy WDSC if the C>A>D>E>B>F>G voters, comprising a
majority, could deny B the win by voting C=A>D=E>B=F>G. It isn't necessary
that there be any other way for them to deny B the win. I think that's kind
of a silly way to satisfy WDSC, not to mention the fact that it could be
very hard to spot the specific possibility that voting that way could keep
B from winning.

So I think a criterion like WDSC could afford to be more precise. As a first
guess, I suggest: "If a majority of all the voters vote A in first or equal
first, and B in last or equal last, then B mustn't win." If that doesn't
resemble Mike's intention, I'm not sure what his intention is by WDSC.

This way one is spared from having to contemplate all the "ways of voting."

SDSC:
>(Same as WDSC, except that "over a more-liked candidate" is replaced by "...equal 
>to or over a more-liked candidate") If a majority of all the voters prefer A to 
>B, then they should have a way of voting that will ensure that B won't win, 
>without any member of that majority voting a less-liked equal to or over a more-
>liked candidate.

Actually, I think this is either mistaken or unclear. Is it permissible for
the majority to have to truncate B and all candidates ranked below B, or would
that be considered ranking those candidates equal?

Steve Eppley's counterparts to these criteria differ in that it's only A, not
all candidates, that the majority mustn't have to rank equal to or over anyone 
preferred. (One can see those at http://alumnus.caltech.edu/~seppley/ . If one
clicks the "minimal defense" link, one can see Steve Eppley's votes-only versions
of Minimal Defense and Non-Drastic Defense, counterparts to SDSC and WDSC
respectively, although his Non-Drastic Defense votes-only version seems wrong.)

FBC:
>By voting a less-liked candidate over his/her favorite, a voter should never gain 
>an outcome that he/she likes better than every outcome that he/she could get 
>without voting a less-liked candidate over his/her favorite.

I think this is clear, but hard to use. Suppose if I vote B>A>C>D>E, when A is my
sincere favorite (that is, I like candidates who come earlier alphabetically), then 
B is elected. Suppose we try 20 other ways of voting, all with A at the top or
equal top, and these all elect E. I want to conclude that this is an FBC failure.
I can't, though, because it might be the case that e.g. A=E>B=D>C will elect A.

Also, in general I have to check what results one could get from B>C>D>E>A, D>C>E>B>A, 
C>B>E>D>A, etc., no matter how unlikely it is to occur to someone to vote in such
insincere ways.

So I would say, not only is FBC hard to check, but it doesn't seem to be sensitive
enough to "bad behavior" of the method. Both of these could be addressed by
making FBC apply to more specific scenarios.

Those are just my thoughts.

Kevin Venzke



	

	
		
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