[EM] D2MAC can be much more efficient than Range Voting (corrected)

[Juho]

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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