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steven0461 comments on Harsanyi's Social Aggregation Theorem and what it means for CEV - Less Wrong Discussion
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I'd be curious to see someone reply to this on behalf of parliamentary models, whether applied to preference aggregation or to moral uncertainty between different consequentialist theories. Do the choices of a parliament reduce to maximizing a weighted sum of utilities? If not, which axiom out of 1-3 do parliamentary models violate, and why are they viable despite violating that axiom?
Can you be more specific about what you mean by a parliamentary model? (If I had to guess, though, axiom 1.)
This and models similar to it.
Interesting. A parliamentary model applied to moral uncertainty definitely fails axiom 1 if any of the moral theories you're aggregating isn't VNM-rational. It probably still fails axiom 1 even if all of the individual moral theories are VNM-rational because the entire parliament is probably not VNM-rational. That's okay from Bostom's point of view because VNM-rationality could be one of the things you're uncertain about.
What if it is not, in fact, one of the things you're uncertain about?
Then I am not sure, because that blog post hasn't specified the model precisely enough for me to do any math, but my guess would be that the parliament fails to be VNM-rational. Depending on how the bargaining mechanism is set up, it might even fail to have coherent preferences in the sense that it might not always make the same choice when presented with the same pair of outcomes...
An advantage of parliamentary models is that you don't have to know the utility functions of the individual agents, but can just use them as black boxes that output decisions. This is useful for handling moral uncertainty when you don't know how to encode all the ethical theories you're uncertain about as utility functions over the same ontology.
Let's say the parliament makes a Pareto optimal choice, in which case that choice is also made by maximizing some weighted sum of utilities (putting aside the coin flip issue). But the parliament doesn't reduce to maximizing that weighted sum of utilities, because the computation being done is likely very different. Saying that every method of making Pareto optimal choices reduces to maximizing a weighted sum of utilities would be like saying that every computation that outputs an integer greater than 1 reduces to multiplying a set of prime numbers.