Condorcet truncation example

[Saari at aol.com]

>Here is an example to show why voters would truncate, if
>a Condorcet Criterion Method is used:
>
>Case 1:
>
>47 voters vote ABC.
>10 voters vote BAC.
> 8 voters vote BCA.
>35 voters vote CBA.

Wouldn't it be nice if we could just find out which candidate was liked by
the most voters?  For example, suppose that some voters only really liked one
of the three.  Other voters liked two of the three, and some voters are
actually content to choose any of the three.

SUPPOSE I CLAIM that in the above example, there is one candidate who is
liked by EVERY SINGLE VOTER (whereas the other two candidates are thoroughly
disliked by roughly half [between one-third and two-thirds] of the voters).

>From the above data, I challenge you to identify the candidate who is
universally liked.  It is impossible - the ranked data given conveniently
hides the necessary information.

Ranked voting data make it impossible to collectively choose a candidate (if
there is one) which could satisfy every voter.  It also makes it impossible
to collectively choose the candidate who is liked by the most people - for
the same reason.

Some might say that like/dislike info is too subjective, and that only
preference data (A >B > C) has any "true meaning".  Well, "If you have only a
hammer, then everything in the world looks like a nail."  

If you start out with preference ballots e.g. A > B > C, it is easy to
believe that this is the only data which is useful or relevant.  I claim
there is a strong difference between "I like B." and "I hate B." - and
preference voting does not allow me to express these opinions.  No wonder we
have such a hard time finding the best tallying system!  Once the raw
like/dislike data is lost, there is no way to confirm whether any given
outcome makes sense or not.

Mike Saari