Abd ul-Rahman Lomax wrote:
At 03:57 PM 1/18/2009, Kristofer Munsterhjelm wrote:
Wouldn't it be stricter than this? Consider Range, for instance. One
would guess that the best zero info strategy is to vote Approval style
with the cutoff at some point (mean? not sure).
Actually, that's a lousy strategy. The reason it's lousy is that the
voter is a sample of the electorate. Depending on the voter's own
understanding of the electorate, and the voter's own relationship with
the electorate, the best strategy might be a bullet vote. Saari showed
why "mean cutoff" is terrible Approval strategy. What if every voter
agrees with you but one? The one good thing Saari shows is that this
yields a mediocre outcome when 9999/10000 voters prefer a candidate, but
also approve another "above the mean."
Essentially, the voter doesn't need to know anything specific about the
electorate in a particular election, but only about how isolated the
voter's position *generally* is.
For most voters, zero-knowledge indicates a bullet vote unless there are
additional candidates with only weak preference under the most-preferred
one, such that the voter truly doesn't mind voting for one or more of
them in addition.
Perhaps. My point is not this. I explicitly said that I didn't know the
zero info strategy ("not sure"). But also note that what I'm talking
about is /zero info strategy/, i.e. how you'd vote if you were stuck on
Mars with the candidates (who had broadcast systems with which to run
their campaigns), and then you all traveled back to Earth just before
the vote. The zero-info strategy may be something else than mean cutoff
(again, *I don't know!*), but it may also just be lousy because the
method has a bad zero-info strategy and voters have to know how others
are likely to vote.
However, it would also be reasonable that a sincere ratings ballot
would have the property that if the sincere ranked ballot of the
person in question is A > B, then the score of B is lower than that of
A; that is, unless the rounding effect makes it impossible to give B a
lower score than A, or makes it impossible to give B a sufficiently
slightly lower score than A as the voter considers sincere (by
whatever metric).
Yes. Indeed, I've suggested that doing pairwise analysis on Range
ballots, with a runoff when the Range winner is beaten by a candidate
pairwise, would encourage maintenance of this preference order.
Think of Range as a Borda ballot with equal ranking allowed and
therefore with empty ranks. (Not the ridiculous suggestions that
truncated ballots should be given less weight). If a voter really has
weak preference between two candidates, the obvious and simple vote is
to equal rank them. But then where does one put the empty rank?
There are two approaches, and both of them are "sincere," though one
approach more accurately reflects relative preference strength. There
are ways to encourage that expression.
But here is the real problem: trying to think that a zero-knowledge
ballot is somehow ideal is discounting the function of compromise in
elections. That is, what we do in elections is *not only* to find some
sort of supposed "best" candidate, but also to find compromises. That's
what we do in deliberative process where repeated Yes/No voting is used
to identify compromises, until a quorum is reached (usually a majority,
but it can be supermajority). Deliberative process incorporates
increasing knowledge by the electorate of itself. It extracts this with
a series of elections in which sincerity is not only expected, it's
generally good strategy. In that context, "approval" really is approval!
If a majority agrees with your approval, the process is over.
A few nits: first, equal preference allowed doesn't imply empty rank,
though I see that Borda would have to in order to be equivalent to
Range. For that matter, any weighted positional system where you can
give fractional votes and all positions have a nonzero weight can be
reduced to Range in that way.
Second, zero-information strategy may still be strategy, and this
possible presence of strategy would show that voters could expect a
personally better result from altering their ballots. For instance, if
Range has a zero-info strategy that lies in voting Approval style
according to some cutoff, and if all voters were limited to zero
knowledge and voted one way, yet this person voted according to zero
info strategy, and the latter voter got greater power because of this,
then strategy exists. This strategy presents as noise whenever the
zero-info strategy results in a different ballot than a sincere ballot does.
I consider election methods as shortcuts, attempts to discover quickly
what the electorate would likely settle on in a deliberative
environment. As such, it is actually essential that whatever knowledge
the electorate has of itself be incorporated into how the voters vote.
And that's what happens if, in a Range election, voters vote von
Nuemann-Morganstern utilities. They have one full vote to "bet." They
put their vote where they think it will do the most good. They can put
it all on one candidate, i.e., bullet vote. They can put it on a
candidate set, thus voting a full vote for every member of the set over
every nonmembe, i.e., they vote Approval style. They can split up their
vote in more complex ways. What they can't do in this setup is to bet
more than one vote. I.e., for example, one full vote for A over B, and
one full vote for B over C. If we arrange their votes in sequence, from
least preferred to most, the sum of votes in each sequential pairwise
election must total to no more than one vote.
My opinion is that this places a burden on the voters because now they
don't just have to model themselves, but they have to model the other
voters (and the other voters' models of themselves) in order to devise
the "correct" way of voting.
It's not so hard to see that this could lead to a true compromise if the
iteration happens for long enough - say that the communication is
sufficiently advanced that one can run a deliberative assembly on top.
Then everybody votes [whatever was agreed upon] > [everything else]
afterwards. For some, that's not a sincere vote (it's even an order
reversal), but it would "work".
You say that VNM utilities are instinctive. To me it seems they make
things more complex. They introduce feedback, and through it, possible
cycling. If there's a Condorcet situation and there are poll iterations,
the poll winner could change from A to B to C then to A again.. whereas
Condorcet methods handle this implicitly if they deal with sincere votes.
Beyond simple VNM utilities, there's also Range zero-info strategy (vote
Approval style - again I don't know where the cutoff is, but it doesn't
matter in this respect). However you may present it, I think that voters
will say that that looks like Plurality strategy - "so I have to vote
Approval style in order to maximize the punch of my vote, but then I
have to vote for the frontrunner unless he's not a frontrunner - do I
have to vote for the lesser evil?". In Condorcet (or Bucklin or
whatnot), you simply vote minor > lesser > greater and that's it.
Calling them VNM utilities sounds complex, but it's actually
instinctive. If we understand Range, we aren't going to waste
significant voting power expressing moot preferences. Suppose someone
asks you what you want. But you understand that you might not get what
you want. You prefer A>B>C>D, lets say with equal preference steps. You
think it likely that A or B might be acceptable to your questioner, but
not C or D. You have so much time to convince your questioner to give
you what you argue for. How much time are you going to spend trying to
convince the person to give you C instead of D?
When you vote, it's not against the clock. To some extent, ranked
ballots are contingent ones. If you vote A > B > C and A wins, that you
voted > B > C doesn't really matter (unless B was a compromise, in which
case A wouldn't have won). IRV takes this to an extreme - too far,
probably - but the point is that votes don't have to be "out of a fixed
pool". In a method that satisfies local independence of irrelevant
alternatives, if you vote A > B > C > D or A > B > E > D, which you vote
has the same effect if C and E were not in the Smith set, so you can add
as many write-ins as you desire.
You might mention it, but you wouldn't put the weight there unless you
thought that the real possibilities were C or D.
Voter knowledge of the electorate is how elections reach compromise, and
it's very important. Of course, there is also the process for getting on
the ballot, in some places, but where ballot access is easy, it's about
the only way we have in single-winner elections of finding an acceptable
compromise.
That's not to deny the value of voting systems which can extract a
probably reasonable compromise from expressed preferences, but one of my
points has been that unless preference strength *can* be expressed, we
are presenting distorted information to the voting system.
At least the voters should be able to "distort" as they choose, seeking
compromise, instead of the system inherently distorting.... we know that
some voters will simply vote as accurately as they can and, it turns
out, from at least one study (mine) this tends to improve expected
results for all the voters,
You provide the method with the option to accept more information,
though exactly what that information is is not very well defined (at
least not in the sense of the voter's own preferences). The question is
whether the push towards a more accurate result will be stronger than
the push away due to distortion (both unintentionally, e.g from having
to vote Approval style or from cycling, and intentionally, as with
parties using central resources to calculate the optimal vote).
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