[EM] Anyone got a good analysis on limitations of approval and range voting?

[Kristofer Munsterhjelm]

Jobst Heitzig wrote:
> Dear Kristofer,
> 
> both Approval Voting and Range Voting *are* majoritarian: A majority
> can always get their will and suppress the minority by simply bullet-voting.
> 
> So, a more interesting version of your question could be: Which
>*democratic* method (that does not allow any sub-group to suppress the
>rest) has (usually or on average or in the worst case) the least
>Bayesian Regret.

Yes. A majority that acts in a certain way can get what it wants. That's 
true for Range and Approval, and it's true for Condorcet, Plurality, 
etc. However, my point was that Range goes further: a minority that acts 
in a certain way can get what it wants, too; all that's required is that 
the majority does not vote Approval style (either max or min) and that 
the minority does, and that the minority is not too small.

It is in that respect I mean that Range is more radical, because it 
permits a minority to overrule a majority that otherwise agrees about 
which candidates it prefers. For those who mean that elections have to 
be, at least, majoritarian, Range may contain a surprise.

>I conjecture that at least when the nomination of additional options
>is allowed, the method SEC described recently is a hot candidate for
>this award, since it seems that SEC will lead to the election of the
>option at the *mean* (instead of the median) voter position, and I guess
>that in most spacial utility models the mean position is in many senses
>"better" and will in particular have less Bayesian Regret than the
>median position. (Recall that in a one-dimensional spacial model where
>additional options can be nominated, all majoritarian methods likely
>lead to median positions being realized and are thus basically all
>equivalent.)

You could probably devise a whole class of SEC-type methods. They would 
go: if there is a consensus (defined in some fashion), then it wins - 
otherwise, a nondeterministic strategy-free method is used to pick the 
winner. The advantage of yours is that it uses only Plurality ballots.

I suppose the nondeterministic method would have to be "bad enough" to 
provide incentive to pick the right consensus, yet it shouldn't be so 
bad as to undermine the process itself if the voters really can't reach 
a consensus.

Assume (for the sake of simplicity) that we can get ranked information 
from the voters. What difference would a SEC with Random Pair make, with 
respect to Random Ballot? It would lead to a better outcome if the 
consensus fails, but so also make it more likely that the consensus does 
fail. Or would it? The reasoning from a given participant's point of 
view is rather: do I get something *I* would like by refusing to take 
part in consensus -- not, does *society* get something acceptable.