Jonathan Lundell wrote:
On Nov 27, 2008, at 11:47 AM, Kristofer Munsterhjelm wrote:
I guess what I'm trying to say is that the problem of discerning a
honest vote from a strategic (optimizing) one seems to be inherent to
all cardinal methods, because we can't read voters' minds. That is,
unless the external comparison can be made part of the ballot itself.
I suggest that the problem is worse than that: that the voters can't
even read their own minds, in this sense. Suppose that I would have
ranked Edwards > Obama > Clinton in the recent US primaries. Fine, I can
make Edwards=100, but I really don't have the foggiest idea what it
would mean to make Obama=75 as opposed to Obama=50. Do I like Edwards
"twice as much" as Obama? What can that possibly mean? It seems to me
that range voting (including approval) immediately reduces to a purely
strategic exercise. And what I'd prefer to do is to eliminate (to the
extent possible) the motivation to strategize at all.
I basically agree with you, but I'll try to think contrarily and see if
there's any way to pin down the idea of honest ratings. If I do, I may
contradict what I said earlier, but let's see..
For an FPTP ballot, the sincere ballot is that which you'd want to apply
if you were dictator. For a rank ballot without equal ranks, the sincere
ballot is: "first choice is what you'd pick if you were a dictator -
second choice is what you'd pick if you were a dictator but the first
choice wasn't available", and so on.
Perhaps we could define sincere equal rank by that a set that's equally
ranked is one, that, if you were given the ultimate decision which of
the set to pick, you'd have to flip a coin / roll dice / whatever to
find out. Your solution to collapse equal-rank onto a ballot that
doesn't support it does just that, prior to the decision itself.
That leaves ratings. Ratings could be either absolute (relative to an
external event) or relative (to the topmost or bottom-most rated). If
we're going to set a standard for sincere ratings, it would be easiest
to do so with relative ratings. Say that candidate Y is the worst on the
ballot. Then rating X as 0.3 means "I'd rather have a p = 70%+e chance
of X (30%-e of nothing) than Y", for some very low positive value e, and
that p = 0.7 (1 - 0.3) is the lowest value for which this is the case.
The top rating of 1.0 means you'd take even a tiny chance at the
top-rated candidate instead of Y.
Now, there are problems with this. First, if Y is better than the status
quo, it doesn't work (at least I think it won't). Second, the rating for
Y is undefined (should be 0). Most importantly, this is not how people
think - even if the ballot was supposed to be like this, people would
have to think very hard to fill it out.
Are there any other ways of defining a sincere and "non-strategic"
ratings ballot? Direct external reference of the sort "I'd pay amount Z
to have X elected" fails because of income differences and the
nonlinearity of money. Definitions based on expected value do not
differentiate between strategic (planned though "sincere") and
non-strategic ballots.
Or maybe we're right, and voters can't read their own minds. In any
event, we (the counters) definitely can't.
----
Election-Methods mailing list - see http://electorama.com/em for list info
