[EM] Heitzig consensus and brinkmanship

[Kristofer Munsterhjelm]

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