Proportional Chances Voting is basically equivalent to a mechanism where one vote is selected at random to be the deciding vote, as Newberry and Ord register in a footnote (they refer to it as “Random Dictator”; I’ve also seen it described as “lottery voting”). Newberry and Ord do say that Proportional Chances is supposed to be different because of the negotiation period, but I don’t see how Random Dictator is incompatible with negotiation.
Anyway, some of the literature on this mechanism may be of interest here, given footnotes 8-9. This paper proposes such a mechanism, defends its plausibility: Saunders, Ben. “Democracy, Political Equality, and Majority Rule.” Ethics 121, no. 1 (2010): 148–77. I haven’t read any good papers which offer interesting critiques of Saunders, but the paper seems to be influential, so maybe someone else knows of one?
As for calling new votes (footnote 9 of this post), votes could be scheduled by a separate body than that doing the voting, or could be scheduled by some regularised rule. For instance, in Kira’s Dinner, the thought experiment in the Newberry and Ord paper, votes on what Kira should eat are scheduled according to the regular rhythm of Kira getting hungry. The voters take the votes as given—I think there are usually similar ways to establish systems like this in real-world multi-person organizations.
Proportional Chances Voting is basically equivalent to a mechanism where one vote is selected at random to be the deciding vote, as Newberry and Ord register in a footnote (they refer to it as “Random Dictator”; I’ve also seen it described as “lottery voting”). Newberry and Ord do say that Proportional Chances is supposed to be different because of the negotiation period, but I don’t see how Random Dictator is incompatible with negotiation.
Anyway, some of the literature on this mechanism may be of interest here, given footnotes 8-9. This paper proposes such a mechanism, defends its plausibility: Saunders, Ben. “Democracy, Political Equality, and Majority Rule.” Ethics 121, no. 1 (2010): 148–77. I haven’t read any good papers which offer interesting critiques of Saunders, but the paper seems to be influential, so maybe someone else knows of one?
As for calling new votes (footnote 9 of this post), votes could be scheduled by a separate body than that doing the voting, or could be scheduled by some regularised rule. For instance, in Kira’s Dinner, the thought experiment in the Newberry and Ord paper, votes on what Kira should eat are scheduled according to the regular rhythm of Kira getting hungry. The voters take the votes as given—I think there are usually similar ways to establish systems like this in real-world multi-person organizations.