[EM] Range Voting fails IIA

[David Cary]

--- MIKE OSSIPOFF <nkklrp at hotmail.com> wrote:

> 
> IIAC:
> 
> Deleting a nonwinning candidate from the ballots, and then
> recounting those 
> ballots should never change who wins.
> 
> (end of IIAC definition|
> 
> RV and Approval pass IIAC.
> 
> The above IIAC definition is the only complete and precise one that
> I've 
> seen. Yes, lots of people invoke an IIAC that is about preferences,
> but no 
> one defines it. Sorry, but an undefined criterion isn't useful.
> 

It seems that standard plurality voting would satisfy this version of
IIAC, unless the deletion of a nonwinning candidate is allowed to
turn invalid votes (for example due to overvoting) into valid votes. 
But however that ambiguity in the criterion gets resolved, the
application to plurality voting illustrates how an IIAC that just
recounts ballots is insensitive to important phenomenon compared to
an IIAC that is more preference based.  

The preference-based varieties detect a susceptibility to
manipulation of the result through the nomination process, something
that typically is completed before voters cast their ballots, not
afterwards.  Also, the preference-based varieties are not dependent
on which set of candidates might be considered first, so they apply
equally well to adding a candidate as well as removing a candidate.

The two varieties tend to coincide when applied to sincerely voted,
ordinally ranked voting methods, but otherwise the ballot-recounting
variety of IIAC has at best a more limited role to play.

One fairly rigorous definition of a preference-based IIAC can be
found in the book by  Thomas Schwartz:  The Logic of Collective
Choice.  That definition is not general enough to apply to Range
Voting, but extending it to handle Range Voting doesn't seem to be a
big hurdle.  If there is any interest in seeing such an extension, I
might try to document one, though probably not before Mike returns to
the countryside.  The Schwartz definition does have the advantage
that it is general enough to not explicitly require voting as the
mechanism for reaching a collective choice.

-- David Cary


 
____________________________________________________________________________________
Do you Yahoo!?
Everyone is raving about the all-new Yahoo! Mail beta.
http://new.mail.yahoo.com