[EM] What is the ideal election method for sincere voters?

[Juho]

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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