[EM] Heitzig consensus and brinkmanship

[Kevin Venzke]

 Hi Kristofer, I have a feeling that in a setting so contentious that a faction would considermaking 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 picturean informal pre-vote debate about where the consensus should be. The mechanismmight push selection towards the median voter (unless in practice the mechanism hasso little chance of operating that people forget about it), but people wouldn't agree wherethe median is. So I think people would assume consensus is impossible.
If the number of voters is small and known, maybe it would be different. But I'm reallynot 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 thevoter 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 consensusand hanging on to a chance to win.
Maybe I've overlooked something though.
Going off topic, the idea I like here is to require each voter to nominate a majority ofthe voters (as though they would form a government). The most-nominated voterdetermines the outcome of the question. In this way, defection requires a potentiallydangerous form of burial.
Kevin

    Le dimanche 5 juillet 2020 à 18:28:44 UTC−5, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit :  
 
 The other day, I was thinking about the Heitzig consensus mechanism --
the one where you submit a favorite ballot and a consensus ballot, and
if there's unanimity in favor of the consensus, then it wins, otherwise
you run Random Ballot on the favorites.

I had a thought: is this method susceptible to a sort of brinkmanship
strategy? Suppose a faction wants to pull the consensus in its
direction. It declares that unless it gets a concession on the
consensus, it will dishonestly set its favorite option to something
extremely damaging, so as to make the random ballot option all the worse
for everybody involved. Like in a standoff, the faction doesn't actually
want the worse option to be chosen, it just wants the threat to be credible.

There's a typical defection dynamic to this, too. Any given faction can
amplify its influence by threatening disaster if it doesn't get what it
wants. However, if every faction does so, then the result is certain
destruction.

But then again, perhaps the problem only exists if the favorite votes
are public. Suppose they are anonymous. Then a faction may declare that
it is willing to risk disaster to pull the consensus in its direction.
However, since the faction doesn't want disaster to strike, it's better
to declare such a threat but not follow up on it, because when the vote
happens, the faction can only lose by voting something disastrous as its
favorite. But the other factions know this, so they won't consider the
threat to have any force, and so the problem disappears.

Is it that easy?

-km
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