[EM] Truncation

[Blake Cretney]

On Wed, 2002-09-18 at 11:23, Adam Tarr wrote: 
> Joe Weinstein wrote:
> 
> >There is no point in invalidating or penalizing ballots of voters who have 
> >reason to lack perfect information (especially when there is a gaggle of 
> >mostly unknown candidates), or who do have (for their purposes) perfect 
> >information but are simply trying to minimize time and effort and 
> >confusion in marking their ballots.   Rather, when a given candidate has 
> >not been explicitly marked, he can still be given a default evaluation.
> 
> I think virtually everyone agrees with this.  The debate is not really 
> whether we ALLOW truncation in ballots.  The debate, rather, is what 
> strategic impact truncation has in various voting systems, and what sort of 
> incentives that gives to the voter.

And there is some debate over what constitutes penalizing. 


> Recently, there has been a revival of the debate about margins-based 
> Condorcet completion methods versus winning votes-based Condorcet 
> completion methods, with an eye towards the effects of truncation on 
> each.  Specifically, there is the remarkable fact that a voter in a winning 
> votes-based Condorcet voting system can NEVER be hurt by fully expressing 
> their preferences.  There are cases where fully voting your preferences can 
> fail to help you, but it can never actually hurt you.

It is remarkable, but also false. 


12:A>B>C 
12:A>C>B 
16:A # truncated 
21:B>C>A 
4:B>A>C 
10:B 
15:C>A>B 
10:C 

VOTES   100 
Non-wins Zero'd out 
           A     B     C 
A          X    55     0 
B          0     X    47 
C         46     0     X 

Minmax 
Cand  Max Loss 
A           46 
B           55 
C           47 

A > C > B 

vs. 

12:A>B>C 
12:A>C>B 
16:A>C>B # filled in
21:B>C>A 
4:B>A>C 
10:B 
15:C>A>B 
10:C 


VOTES   100 
Non-wins Zero'd out 
           A     B     C 
A          X    55     0 
B          0     X     0 
C         46    53     X 

Minmax 
Cand  Max Loss 
A           46 
B           55 
C            0 

C > A > B 


> This is not a distinction without a difference.  In every other ranked 
> balloting method I am familiar with, the voter could potentially look at 
> the results of an election and say, "If only I (and others like me) had 
> just left some information off the bottom of our ballot, without changing 
> the order of any candidates above that point, then I could have gotten a 
> better result."  This is not the case in winning votes-based Condorcet 
> methods, and that's an incredibly powerful statement.
> 
> One of Donald Davidson's favorite criticisms of non-IRV alternative voting 
> methods is that, "your vote for your second choice can help defeat your 
> first choice." (paraphrasing).  This is simply not true in winning 
> votes-based Condorcet methods.  It is true, however, in margins-based 
> Condorcet voting, or in Borda count, or in cardinal rankings, or in 
> approval voting.  IRV itself is immune to this criticism, but in IRV your 
> first place vote can help defeat your second place vote (and give the 
> election to someone else altogether), which is not really any better.

Of course, the above argument is unsound. 

I think it is possible to penalize partial rankings more severely than
winning-votes does in order to meet the criterion you want.  For
example, consider the following method,

For each candidate, find the pairwise comparison that has the most votes
against this candidate.  For example, A:B of 51:49 is 51 votes against B
and 49 against A.  The candidate for whom this greatest number of votes
against is smallest, is the winner.

It is possible for a candidate to lose despite having a pairwise victory
over every other candidate.  If that's considered a problem, you could
automatically elect such a candidate.  I'd have to think about how that
would affect your criterion, though.

---
Blake Cretney 
http://condorcet.org


----
For more information about this list (subscribe, unsubscribe, FAQ, etc), 
please see http://www.eskimo.com/~robla/em