Condorcet(x( ))

[Steve Eppley]

Mike O wrote:
>I chose, for my Condorcet proposal, to not count any preferences
>not expressed by the voter, for 2 reasons:
>1. Why count, on the voter's behalf, what he didn't say?

Counting ties as "zero votes against" is "counting", in a way.  The
word count has more than one meaning, so we need to be careful about
what is meant by claims that counting as zero is different from
counting as some other value.  Counting as zero is interpreting the
vote in that pairing as being "not against" both candidates, since
nonzero means "against".

The voter isn't able to say one way or the other what his/her equal
rankings mean.  I think that if asked, the typical voter would give
the same Yes answer to the following two questions: (1) Do you want
vote full strength against your least preferred candidate?  (2) Do
you want to vote full strength against your two equally-least
preferred candidates?  Doesn't a Yes answer to the second question 
mean this voter would want x as large as possible in that pairing?

Here's an illustrative example, a 3-way race between Good, Evil1, and 
Evil2.  One voter's ballot: {Good > Evil1 = Evil2}
I chose the candidate's names from this one voter's perspective.  
Other voters might see things differently, producing a close election 
and maybe a circular tie.  Not counting ballots like this against both 
Evil1 and Evil2 in their pairing might throw the election from Good 
to one of the evils.  

Maybe the voting system *should* infer the voter wants his/her
ballot to count full strength against the last ranked (or unranked, 
when the ballot is truncated).

>2. Condorcet would lose its lesser-of-2-evils properties if
>voters were counted as giving preference votes that they
>never indicated.

Would you elaborate?  How is this true of Condorcet(.5) and 
Condorcet(x2()), where x2() is one of the formulas I suggested a 
couple days ago?

If this is true, I'll lose interest in x<>0.

--Steve