Re: [sl4] Bayesian rationality vs. voluntary mergers

From: Wei Dai (
Date: Sun Sep 14 2008 - 22:43:56 MDT

Tim Freeman wrote:
> So after the coin flip, the utility function for the merged AI might
> be "51 for a universe of 60% staples, or 49 for a universe of 60%
> paperclips, or nothing if I don't get enough staples or enough
> paperclips". Swap the numbers if the coin flip comes out the other
> way.

I haven't made much progress on finding another example that clearly
supports my suggestion that the "period of irrationality" might not be
short, but one thing that puzzles me here: why 51/49? Why not 52/48, or
50.1/49.9? It seems that the original AIs would prefer 50.1/49.9 to 51/49 to
52/48, but if they go all the way to 50/50, things fall apart. That seems
quite strange.

I tried doing a literature search to see if there has been any academic
research that might apply here, and it turns out that the problems of
merging differing priors and utility functions have been noticed by
economists in the context of creating an aggregate prior/utility function
for purposes of government policy and the like. There are several recent
papers on merging priors, which all pointing to a 1955 paper by Harsanyi [1]
on the issue of merging utility functions. These works seem to show that
merging priors is a worse problem than merging utility functions: whereas
merging utility functions can only make some individuals worse off, merging
priors can make everyone worse off. This is reflected in my examples as

What Harsanyi showed was that if we assume the following postulates:

A. Social preferences can be represented by expected utility maximization
B. Individual preferences can be represented by expected utility
C. Society is indifference between two outcomes A and B whenever all
individuals are indifferent between them

then the social utility function must be a linear combination of individual
utility functions. It apparently wasn't considered that postulate A should
be false.

In [2], the authors show the possibility of merging differing priors, but
only by giving up the "Pareto condition" (similar to postulate C above) that
when all individuals in society agree on preferences between two
alternatives, so should society. Again I didn't see any consideration that
perhaps social preferences should not take the form of expected utility

I wonder where the assumption came from, that groups as well as individuals
should be guided strictly by expected utility maximization? Is it just that
no one has proposed a viable and mathematically worked out alternative? I
didn't see anything in the literature similar to the "flip a coin" solution
that several people have suggested here.

[1] "¡°Cardinal Welfare, Individualistic Ethics, and Interpersonal
Comparisons of Utility"
[2] "Utilitarian Aggregation of Beliefs and Tastes"

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