On Mar 9, 2007, at 7:00 , Scott Ritchie wrote:
On Thu, 2007-03-08 at 10:56 -0500, Abd ul-Rahman Lomax wrote:
Under what conditions could random ballot be the
ideal method? What goal of an election would be best served by random
ballot, and not by another method designed specifically for that
goal?
I didn't mean ideal method, I meant sometimes it gets better results.
The reason is that random _candidate_ will sometimes pick the
"best" (however defined) choice. Since no deterministic election
method
will consistantly pick the "best" choice in all circumstances, that
means sometimes you might get lucky by ignoring the ballots altogether
and picking a random winner.
My basic approach is that there are different utility functions that
can be used / approximated in different voting methods that are
intended for different needs. Some of the methods my however be quite
general purpose methods that can be used in many typical elections.
I'll give some examples to demonstrate the differences.
US presidential elections have the property that the man/woman that
will be elected has lots of power and can do many things without the
control of others. The president gets e.g. the keys to the nuclear
bombs. If there are no strong limitations on who can be a candidate
in the presidential elections, then I think random ballot would be a
poor method. Let's say there are 10 candidates. One of them wants to
start a war with Canada. Even if the support of that candidate would
be less than 1% taking the risk of electing him/her with a random
ballot doesn't sound like a good idea. In this case the intended
utility function must thus be such that it seeks for a compromise
candidate, or maybe for a candidate that is not strongly opposed.
Random ballot would be more fair in the sense that all citizens would
get their voice heard and their candidate elected one day. But we do
not want that to happen.
On the other hand random ballot would probably be an excellent method
for deciding who will get today the only olive in the pizza that we
decided to buy today. Giving that olive every day to the
representative of the majority or always to the same compromise
candidate wouldn't make sense. Better to give it proportionally with
best probability to one of the nicest persons of the day. A method
that would be good for the US presidential elections would not work
here. We want all the candidates to have a chance. (This example not
really from real life and it is bad also in the sense that a pure
lottery could be the best method, but I hope you got the point.)
When discussing on what the ideal method is I'd thus like to hear
also what the targets of the election are and maybe also what the
target utility function (to be approximated) is.
Some common targets are e.g. to maximize the mean utility, to
maximize the worst utility, to be proportional, to guarantee wide
support, to guarantee big first place support (this last target is
usually not very popular on this list :-).
Juho
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