# Re: [sl4] Bayesian rationality vs. voluntary mergers

From: Eliezer Yudkowsky (sentience@pobox.com)
Date: Mon Sep 08 2008 - 08:39:08 MDT

On Sun, Sep 7, 2008 at 3:36 PM, Wei Dai <weidai@weidai.com> wrote:
>
> The problem here is that standard decision theory does not allow a
> probabilistic mixture of outcomes to have a higher utility than the
> mixture's expected utility, so a 50/50 chance of reaching either of two
> goals A and B cannot have a higher utility than 100% chance of reaching A
> and a higher utility than 100% chance of reaching B, but that is what is
> needed in this case in order for both AIs to agree to the merger.

The obvious solution is to integrate the coin into the utility
function of the offspring. I.e., <coin heads, paperclips> has 1 util,
<coin tails, paperclips> has 0 utils.

Obvious solution 2 is to flip a quantum coin and have a utility
function that sums over Everett branches. Obvious solution 3 is to
pick a mathematical question whose answer neither AI knows but which
can be computed cheaply using a serial computation long enough that
only the offspring will know.

Of course, just because something is obvious doesn't mean it can't be flawed.

> The second example shows how a difference in the priors of two AIs, as
> opposed to their utility functions, can have a similar effect. Suppose two
> AIs come upon an alien artifact which looks like a safe with a combination
> lock. There is a plaque that says they can try to open the lock the next
> day, but it will cost \$1 to try each combination. Each AI values the
> contents of the safe at 3 utils, and the best alternative use of the \$1 at 2
> utils. They also each think they have a good guess of the lock combination,
> assigning a 90% probability of being correct, but their guesses are
> different due to having different priors. They have until tomorrow to decide
> whether to try their guesses or not, but in the mean time they have to
> decide whether or not to merge. If they don't merge, they will each try a
> guess and expect to get .9*3=2.7 utils, but if they do merge into a new
> Bayesian AI with an average of their priors, the new AI will assign .45
> probability of each guess being correct, and since the expected utility of
> trying a guess is now .45 * 3 < 2, it will decide not to try either
> combination. The original AIs, knowing this, would refuse to merge.

I presume you're localizing the difference to the priors, because if
the two AIs trust each other's evidence-gathering processes, Aumann
agreement prevents them from otherwise having a known disagreement
about posteriors. But in general this is just a problem of the AIs
having different beliefs so that one AI expects the other AI to act
stupidly, and hence a merger to be more stupid than itself (though
wiser than the other). But remember that the alternative to a merger
may be competition, or failure to access the resources of the other AI
- are the differences in pure priors likely to be on the same scale,
especially after Aumann agreement and the presumably large amounts of
washing-out empirical evidence are taken into account?

I haven't read this whole thread, so I don't know if someone was
originally arguing that mergers were inevitable - if that was the
original argument, then all of Wei's objections thereto are much
stronger.

```--
Eliezer Yudkowsky
Research Fellow, Singularity Institute for Artificial Intelligence
```

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