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

[Jobst Heitzig]

Hello Kristofer,

you wrote:
> 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.

That's true. Methods in which a group can suppress the rest are
certainly bad, even more so when the group can be small...

> 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.

The hard point is, I think, to define what actually a potential
consensus option is. And here the idea was to say everything unanimously
preferred to some benchmark outcome qualifies as potential consensus.
The benchmark then cannot be any feasible option but must be a lottery
of some options, otherwise the supporters of the single option would
block the consensus. But which lottery you take as a benchmark could be
discussed. I chose the Random Ballot lottery since it seems the most
fair one and has all nice properties (strategy-freeness, proportional
allocation of power).

> 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.

Although I can hardly imagine real-world situations in which no
consensus option can be found (maybe be combining different decisions
into one, or using some kind of compensation scheme if necessary).

> 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? 

This sounds interesting, but what exactly do you mean by Random Pair?
Pick a randomly chosen pair of candidates and elect the pairwise winner
of them? I will think about this...

> 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.

I'm not sure I know what you mean here.

Yours, Jobst