At 08:32 PM 4/10/2010, Kevin Venzke wrote:
In a given election yes, it is easy to miss the mark. But in general,
aiming for the median voter is the most reliable. (That is assuming you
don't know utilities, which I'm really not sure you showed how to find.)
To see this, you assume utility is based on issue space distance, and
that the voters aren't distributed unevenly.
I didn't show how to find utilities, I only showed various
possibilities consistent with the votes.
To study voting system performance, I'm saying, one must *start* from
utilities, not from preference order without preference strength
information. Voter behavior is not predictable without preference
strength information. Strategy, in general, doesn't make sense
without an understanding of preference strength.
Thus when you have a situation where every voter chimed in on some
question, and they didn't do that for any other question, you should
expect (on average) a utility problem when the outcome goes against the
majority opinion.
I'll agree that this is the "norm." However, it can go drastically wrong.
How can we detect the exceptions?
Sure, the majority criterion and the condorcet criterion are usually
a sign of good performance, but it is obvious that exceptions exist,
and we should not denigrate a voting system if it, under an exception
condition, it violates the criteria!
I was just pointing out that the outcome you claimed was obviously
bad wasn't. It might be that, on average, this outcome would be
poorer than the other, but it was not a truly bad outcome, under
reasonable assumptions of likely utility, the first utility scenario
I gave, which used Range 2 utilities, i.e., normalized and rounded
off so as to make all the votes sincere and sensible. The bullet
voters then had equal bottom utilities for the other candidates, and
those who ranked had stepped utilities. Simple. And showing that A
was, indeed (with these assumptions, which seem middle-of-the-road to
me), the utility maximizer, by a fairly good margin!
You can make a contrary assumption, that the A voters were
"strategic." That they "really" would be happy with B. I'm assuming,
instead, that their votes would be sincere. And likewise the votes of
the other voters.
Look, A *almost* has a majority in first preference. I'm very
suspicious of claims that an election outcome is "terrible" if it
depends on some close-shave majority that failed. Certainly the 2000
U.S Presidential election outcome was awful, from my partisan point
of view, but I have to understand that about half the people wanted
Bush. The real problem is electing officers by public elections, with
long fixed terms!
(It's a continuation of the concept of a King, only restricted to
four-year terms. No corporation would hire a President like that.)
Rather, have chosen representation (per Asset Voting, but a good
proportional representation system wouldn't be terrible), and elect
officers deliberatively, majority required (in the Assembly) to serve
at the will of the people, as expressed through their
representatives. Parliamentary system.
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