Margins Example Continued

[David Marsay]

I've come back to an interesting thread:

> From:          Mike Ositoff <ntk at netcom.com>
> Subject:       Margins Example Continued

The debate is between 'margins' and 'votes-against' in variations of 
Condorcet, who does not explicitly deal with tied rankings. The 
differences cited so far concern tactical voting.

I suggest that we consider tactical voting in the particular case 
where one has spatial voting. This is often used in voting theory. In 
the simplest case one has a left/right scale. Voters have views along 
this scale, and candidates take positions along the scale. Voters, we 
suppose, never rank a candidate below candidates who are 'more 
extreme'.

It is well known that one cannot avoid tactical voting in the general 
case. I consider 'tactical spatial voting', where the voter's 
true preferences are spatial, but their declared preferences may not 
be. I claim that Condorcet with the 'margins' interpretation 
(e.g., see:
>From:             Norman Petry <npetry at sk.sympatico.ca>
>Subject:          Re: Schulze Method - Simpler Definition
)
is immune to tactical spatial voting. My tentative proof relies on the 
following observation:

If x <a y and y <b z (where x,y,z are candidates and  a,b are the 
'margins') then x < c z, where c >= min{a,b}.

The proof is done by cases, over the possible spatial relationships 
between x, y and z. Incidentally, this shows that the only Condorcet 
cycles one can have are indifferences.

Being able to say that 'Condorcet/margins' copes well with spatial 
voting seems to me to a big plus for 'margins'. Is the same true for 
'votes-against'? 


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Sorry folks, but apparently I have to do this. :-(
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