[EM] Re: Proposal

[Jobst Heitzig]

Dear Forest!

I fear your hope concerning the Condorcet Criterion is unjustified:

you wrote:
> If there is a CW, the method seems to always converge to it fairly
> quickly, but suppose that the set is
> 
> 48 A(rank=1)  B(rank=3)  C(rank=4)
> 2  B(rank=1)  A(rank=2)  C(rank=4)
> 3  B(rank=1)  C(rank=2)  A(rank=4)
> 47 C(rank=1)  B(rank=50) A(rank=51) .
> 
> It will take about fifty iterations for the approval cutoff to work its
> way down under rank 50 in the C faction ballots.  From that point on B is
> the winner.  So the marble method gives A and B about equal chances of
> winning, while the deterministic method makes the CW the sure winner.

But see the following example (which is the reverse of an example I gave
on June 13): 9 voters, 4 options A,B,C,D. Sincere preferences:
1 B<C<D<A
1 C<D<B<A
1 D<B<C<A
2 B<A<C<D
2 C<A<D<B
2 D<A<B<C

A is the CW but will only receive approval from the first 3 voters in
each iteration, while B,C,D will always receive approval from 5 voters
(1 of the first three and 2 of the last six), hence B,C,D end up having
probability 1/3 each while A has nothing... Am I right?

Actually, your proposal reminds me of something I tried in the context
of that June 13 post, to make sure the final distribution is such that
for no single alternative there would be a majority having this majority
above the *median* rank. I tried several iterative methods which
increase the weights of such "attractive" options and/or decrease the
weights of options below such attractive options and so on, but I ended
up finding that all methods fulfilling the task would give a Condorcet
winner a positive weight in that example...

Jobst