Will truncated ballots elect Hitler?

[Hugh Tobin]

Limiting the number of rankings allowed, and requiring them to be listed
from the top only, seems to give the advantage to an extremist running
against a large field of indistinguishable moderates. As others have
referred back to prior years' discussions, allow me to refloat a modest
proposal from 1996:

"I think there is something to be said for a different option that
allows
a voter more easily to vote in certain pairwise races without voting a
ranking that includes all the candidates in those races.  For example,
suppose there are 20 candidates, and the voter knows nothing about most
of them but believes X must be worse than all others.  The voter can
vote A, B, then 17 equal rankings, then X (or leave X off).  But this
may be cumbersome enough that the voter will not bother (he will simply
vote A,B) or he may negligently fail to rank one or more of the 17. 
(Ossipoff has argued that ballots frequently will be "truncated.") 
Psychologically a voter may feel that he should evaluate the other
candidates and decide that they really are equal before ranking them
that way, even though he would be willing to vote X last with the same
effect.  Moreover, the voter might want to prefer even any unknown
write-in candidate over X.  One could give the voter the option to rank
his ballot from the bottom, leaving the middle (and even the top, if the
voter so chose) unfilled.  This would not be a substantive change in
Condorcet (except perhaps for the implied insertion of "any write-in
candidate" in the ranking of the voter who chooses to vote from the
bottom); it is merely a shorthand method of voting.  But if we let X=
Hitler with a plurality, and if we posit that the rest of the political
spectrum is fractured among a large number of candidates whose
supporters may fail to recognize the importance of casting a complete
ranking, then it could be important to allow the voter easily to vote
"anyone but X" or "A over everyone, and everyone over X"."

To elaborate slightly without a rigorous mathematical example:  In STV,
if X has 40% of the first place votes and no other rankings, and 12
other candidates fragment the remaining first place votes (average 5%
each, say the highest has 10%) and the 2nd-4th votes from non-X-voters
(again averaging 5% in each of those positions), it is easy to see how
enough voters' ballots may be discarded when their first through fourth
choices are eliminated, so that X will win even though 60% would have
preferred any of the other choices to X.  In Condorcet, on the same
facts, X would win all the pairwise races because more than 20% would
have effectively ranked X equal to each other candidate.

Thus, IMHO, enforced truncation would exacerbate a problem: the natural
tendency to truncate from the top when the field is large.  This problem
could be addressed by making it easier to vote against the extremist as
suggested.  The proposed approach is less coercive, and less likely to
disenfranchise voters, than the alternative of requiring that a ballot
have a complete ranking (even if it may include equal rankings) in order
to be counted.

-- Hugh Tobin