[EM] About random election methods

[Eric Gorr]

Andrew Myers wrote:

> A lot of Condorcet election methods use randomness to elect
> a winner, but in a way that I think voters will find unsatisfactory.
> They simply produce a winner as part of a complex algorithm that
> uses randomness at various points. MAM is an example of such
> an algorithm.

Actually, MAM does not use randomness at various points.

It only uses randomness at the beginning when it determines the Random 
Voter Hierarchy (RVH). Once the RVH has been computed, it is remains the 
same and only used to break ties when required.

If one uses the same RVH for each subsequent calculation using MAM, one 
will always get the same winner back - and MAM is always guaranteed to 
return a single winner.


> A voter might reasonably wonder whether the
> random number generator has been "fixed" to generate the desired
> result.
> 
> It seems to me that it would be more easy to justify the election method if
> it consisted of two phases:
> 
> 1. Deterministically generate a separate probability in [0,1]
>    for a win by each alternative (i.e., no randomness is used).
> 
> 2. Randomly choose among the alternatives according to their
>    respective probabilities. This can be done outside the
>    electronic system to make it completely clear that the
>    procedure is fair.
> 
> You can imagine "lifting" existing algorithms to satisfy this description. For
> example, with MAM you could consider all possible permutations of the ballots.
> Of course, the problem is that this is very expensive.
> 
> Thoughts?

Unless I am mistaken, the use of randomness is required to pass several 
desirable criteria of an election method. Passage of these criteria 
helps minimize the potential for strategic manipulation of the election.

This is one of the reasons why MAM is currently my favorite Condorcet 
variant.

Of course, Steve could provide further details...I am merely repeating 
my understanding of his method based on past conversations with him.



-- 
== Eric Gorr =============================== http://www.ericgorr.net ===
"The more you study, the more you know. The more you know, the more you
forget. The more you forget, the less you know. So, why study?" - ???
== Insults, like violence, are the last refuge of the incompetent... ===