On Mar 3, 2007, at 9:06 , Abd ul-Rahman Lomax wrote:
However, if we assume sincere voters, what is the ideal election
method, or the best among the options we know?
I very much support evaluating also the performance with sincere
votes / the utility function that a methods tries to implement (in
addition to evaluating its strategy resistance).
However, is Range ideal with sincere voters? If not, why not?
It is at least good.
And, please, explain to me why a method that will work well for
selecting pizzas, with sincere votes, will not work well selecting
political officers, similarly with sincere votes. If you think that.
If we cannot agree on the best method with sincere votes, we are
highly unlikely to agree on the best method in the presence of
strategic voting, though I suppose it is possible....
Range is good with sincere votes. Its utility function (sum of
individual utilities) is good. I think there are however also other
good utility functions that can be used depending on the election and
its targets. Therefore it is maybe not necessary to "agree on the
best method with sincere votes".
Let's say we are selecting pizzas (A,B). There are three voters whose
preferences are (9,6), (9,5) and (0,6). Pizza A is the best selection
according to Range. I can however imagine that when selecting a pizza
the intention could be to have nice time out with friends. The third
voter obviously hates the A pizza. Maybe we should use some other
utility function, maybe one that maximizes the worst utility to any
individual voter. This kind of a method would select pizza B.
It is also questionable if it always makes sense to select the
favourite alternatives of those votes that have strong feelings and
not to respect the opinions of voters with milder feelings that much.
In some election it may make sense to give each voter same weight.
One could either normalize the votes or accept the one man one vote
principle (= weight of each opinion is 1.0). (Note that e.g. in the
Condorcet methods weight of each expressed preference ("X is better
than Y") is exactly 1. That does not take into account different
preference strengths of different voters but gives all opinions the
same weight.)
You also questioned the vulnerability of Range to strategic voting.
Approval style voting may be either sincere or strategic. Let's say
that X and Y go out for pizza. All the pizzas are quite ok to both
but X is a bit selfish and wants to make the decision on which pizza
to order. Voting strategically in bullet style makes perfect sense to
him. The worst outcome is to toss a coin on which one's favourite
pizza to take. If Y votes sincerely, X will decide.
Using Condorcet or other more majority oriented methods instead of
Range may either be a result of favouring more strategy resistant
methods (and corresponding utility functions) or sometimes also a
direct result of electing the most applicable utility function.
In addition to the viewpoints tat I discussed above there are at
least the proportionality cosiderations, both with multiple winners
and single winners distributed over time, but I understood that these
already fall out of the scope of your mail.
Juho
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