[EM] Winning-votes intuitive?

[Blake Cretney]

Here's how I look at it.  Let's say you don't allow partial rankings.
  Then, people will have to randomly rank candidates if they have no
preference.  They will mostly be doing this at the ends of their ballots.

Now, you notice this, so you suggest a new option that will save them
effort.  If they don't rank all the candidates, you will ensure that the
remaining candidates are randomly ranked before the ballot is counted.
  In other words, you are just doing automatically what the voters
previously had to do themselves.

The interesting question is whether this makes the method more
vulnerable to strategy.  In a sense it does, and in another sense it
doesn't.  It does in the sense that voters can now choose to leave
candidates unranked as a strategy where before they couldn't.  It
doesn't in the sense that the new method only automates a process that
the voter could go through anyway.  Margins is pretty obviously an
approximation of the "new option", with the randomness removed.  The
criteria that say margins is too affected by "truncation" would also
declare the automatic-random-completion method as too affected by
truncation, so the method is worth considering for what this reveals.

The argument is basically psychological.  If voters know that they
prefer B to C, maybe it is easier to convince them to leave the
candidates unranked (to be randomly ranked by the method), than to
randomly rank them themselves, or to rank C over B.  That's really the
winning-votes argument.

Partial rankings are penalized.  I hope that no one doubts that the word
"penalized" is justified.  I mean, if my favourite is A, then on
average, any complete ranking is better for electing A, than ranking A
alone.  I don't see how that can be characterized as other than
penalizing partial rankings.  Anyway, if partial rankings are penalized,
then strategizers have to either accept the penalty, or knowingly
reverse their rankings.

If the voter behaves rationally, this won't make any difference.
  Obviously there is no rational difference between ranking the
candidates randomly yourself and letting the method do it.  Less
obviously, you should use reversal instead of doing either.

So, this is what it comes down to.  On the margins side, we don't want
to impose any particular penalty for leaving candidates unranked, since
we want this to be a reasonable option for people.  This means we can't
set up specific penalties against insincere partial rankings (without
mind-reading).  We note that although people can gain through
truncation, they can also lose by it.  It's not like it's a good
strategy in general.  We note that if voters behave rationally the whole
issue is moot.

Winning votes advocates could argue as follows.  Since voters can be
expected to behave irrationally, we might as well take advantage of this
fact.  And the possibility of sensible partial rankings isn't completely
gone.  Voters can still leave candidates unranked, if they are confident
that they are fringe choices.

I think it is obvious that it is undesirable that people who leave
candidates unranked are tricked into lessening the power of their
ballot.  On the other hand, if we can prevent voters from defeating a
sincere CW with strategy, that's a good thing.  Although it's
unfortunate that this is done by taking advantage of their ignorance.

I don't think this argument is going away any time soon.

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