An outstanding challenge for ‘Bayesian’ decision theory is to extend its norms of rationality from individuals to groups. Specifically, can the beliefs and values of several Bayesian decision makers be amalgamated into a single Bayesian profile that respects their common preferences over options? If rational parties to a negotiation can agree on collective actions merely by considering mutual gains, is it not possible to find a consensus Bayes model for their choices? In other words, can their shared strict preferences over acts be reproduced with a Bayesian rationale (maximizing expected utility) from beliefs (probabilities) and desires (utilities) that signify a rational compromise between their rival positions?

Whatever else is to be required of a compromise, we suppose that a consensus Bayes model for the group preserves those strict preferences which the individuals already share. That is, we impose a weak Pareto condition on compromises. Whenever all parties to a decision have a common strict preference for one option over another, then any proposed Bayesian group model for their choice – any ‘neutral’ position – must reflect this preference and assign higher expected utility to the Pareto dominating option.

Of course, the probabilities and utilities of any one of the agents satisfies this weak Pareto condition. That is, each agent on her own meets this condition – whatever strict preferences they all have, each has. But it is hardly a compromise always to make the group decide all questions based on the preferences of a single member.