Discussions of how to aggregate values and probabilities feel disjoint. Jeffrey-Bolker formulation of expected utility presents the preference data as two probability distributions over the same sample space, so that expected utility of an event is reconstructed as the ratio of the event’s measures given by the two priors. (The measure that goes into the numerator is “shouldness”, and the other one remains “probability”.)
This gestures at a way of reducing the problem of aggregating values to the problem of aggregating probabilities. In particular, markets seem to be easier to set up for probabilities than for expected utilities, so it might be better to set up two markets that are technically the same type of thing, one for probability and one for shouldness, than to target expected utility directly. Values of different agents are incomparable, but so are priors, any fundamental issues with aggregation seem to remain unchanged by this reformulation. These can’t be “prediction” markets since resolution is not straightforward and somewhat circular, grounded in what the coalition will settle on eventually, but logical induction has to deal with similar issues already.
Discussions of how to aggregate values and probabilities feel disjoint. Jeffrey-Bolker formulation of expected utility presents the preference data as two probability distributions over the same sample space, so that expected utility of an event is reconstructed as the ratio of the event’s measures given by the two priors. (The measure that goes into the numerator is “shouldness”, and the other one remains “probability”.)
This gestures at a way of reducing the problem of aggregating values to the problem of aggregating probabilities. In particular, markets seem to be easier to set up for probabilities than for expected utilities, so it might be better to set up two markets that are technically the same type of thing, one for probability and one for shouldness, than to target expected utility directly. Values of different agents are incomparable, but so are priors, any fundamental issues with aggregation seem to remain unchanged by this reformulation. These can’t be “prediction” markets since resolution is not straightforward and somewhat circular, grounded in what the coalition will settle on eventually, but logical induction has to deal with similar issues already.