[EM] Heitzig consensus and brinkmanship

[Kristofer Munsterhjelm]

On 07/07/2020 03.20, Kevin Venzke wrote:
> Hi Kristofer, I have a feeling that in a setting so contentious that
> a faction would consider making such threats, the odds of achieving a
> consensus result are already really small. I think factions would
> always doubt that the other factions are giving up enough. I picture 
> an informal pre-vote debate about where the consensus should be. The 
> mechanism might push selection towards the median voter (unless in
> practice the mechanism has so little chance of operating that people
> forget about it), but people wouldn't agree where the median is. So I
> think people would assume consensus is impossible.

You are probably right. If there is an easy consensus to be had, (and
the participants are honest,) then nobody would feel the need to make
threats like that.

I was thinking about the possibility of using the mechanism to direct a
government or organization to act in a minmax manner: one that intend to
make the worst off best off, rather than improve the condition of the
median voter. From what I remember, Jobst and Forest were originally
trying to find a method to avoid a majority dictatorship, so my idea is
in a way to consistently take that to its logical conclusion. If the
state or the organization must pay attention to every voter, or to a
supermajority of them, then it can't afford to leave some of them badly off.

But if it's to be used as a part of normal operating procedure, then it
has to resist strategy to some degree, and it can't take the whole
organization or state down with it at the first sign of trouble. So if
the brinkmanship scenario is a problem, then either the mechanism has to
be augmented to stop it being a problem, or the assembly has to somehow
be able to keep the peace enough that politics will never become that
contentious to begin with.

> If the number of voters is small and known, maybe it would be
> different. But I'm really not sure... Suppose via PR the voters elect
> five representative voters to play this game. Five seems like enough
> where a spectrum of views might be represented, where the voter on
> one extreme really doesn't want to see his counterpart win. But it's
> easy to imagine that the median option of the five offers the same
> utility to the extremes as rolling the dice. I could also imagine
> political value to refusing to endorse the consensus and hanging on
> to a chance to win.

Yes, that is a possibility - that a way out is to make the consensus
option at least as good on expectation as the roll of the dice,
discounted by whatever risk aversion exists.

That's an important point, I think. The consensus option doesn't have to
be extremely good. For it to be chosen, it just has to be preferred to
rolling the dice by everyone. If it's barely better, that's still good
enough to make it pass.

> Maybe I've overlooked something though.
> 
> Going off topic, the idea I like here is to require each voter to 
> nominate a majority of the voters (as though they would form a
> government). The most-nominated voter determines the outcome of the
> question. In this way, defection requires a potentially dangerous
> form of burial.

Wouldn't that give a coordinated majority the ability to control the
outcome? Or am I missing something?