[EM] Truncation

[matt at tidalwave.net]

On 18 Sep 2002 at 14:25, Bart Ingles wrote:

> Adam Tarr wrote:
....
> > 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.
> 
> Never is a strong word.  How about the following:
> 
> 45%   A  B  C
>  5%   B  A  C
>  5%   B  C  A
> 45%   C  B  A
> 
.... 
> On the other hand, if only one side truncates, there is the potential
> for a cycle, in which case if winning votes can guarantee a win for B
> then the method at least avoids a prisoner's dilemma (is this the
> case?).  Example:  Suppose one side truncates and the final result turns
> out to be:
> 
> 44%   A  B  C
>  5%   B  A  C
>  5%   B  C  A
> 45%   C
> 
> If I'm not mistaken, WV would elect B in this case, while margins would
> pick A.  Margins seems to actually punish truncation in this case.  This
> punishment then sets up the prisoner's dilemma, in which it doesn't pay
> for either side to truncate unless both do.

You are clearly right,  so Adam Tarr and others are mistaken.  Truncation by voters 
for C elected A instead of B, thus hurting the C voters who preferred B to A.  
However, you are wrong about wv.  Wv also elects A because
55 B>C
50 A>C
45 A>B
leaves A undefeated (as does margins with 55 B>C 45 A>C and 35 A>B).
So wv has no advantage over margins as far as I can see.

> But then I don't see truncation as necessarily a bad thing.  If
> truncation can defeat a "hated middle" candidate, it addresses my main
> misgiving about the Condorcet methods.

This is the lesser of of two misgivings I have (my bigger misgiving is the potential 
impact of strategic voting).  I don't see either encouraging or discouraging 
truncation as a satisfactory remedy because some people will truncate and others 
won't no matter what the proper authorities tell them.  Ultimately, the problem is 
unresolvable when dealing with any rank based ballot system because one person's 
grade A is another person's grade B is another person's grade C.  For preference 
ballots, requesting that the voter identify the approval cutoff and then inserting the 
unranked ballots at the cutoff still seems to me to be the fairest method.  As 
suggested by Forest Simmons, maybe this can be combined with disqualifying 
candidates who do not receive a minimum approval percent.  However, I don't know 
how to pre-determine a sensible minimum approval percent.  Should the minimum 
required approval percent depend on the number of winners and number of 
candidates or maybe based on the statistical properties of the actual post-vote 
approval percentages?  Any meaningful pre-vote determined minimum may have to 
be lowered (or scrapped) if not enough winners meet that percent, but that doesn't 
subtract any from the idea's merit.  Does anyone have ideas?

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