ESRogs comments on Gains from trade: Slug versus Galaxy - how much would I give up to control you? - Less Wrong

33 Post author: Stuart_Armstrong 23 July 2013 07:06PM

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Tags: blackmail power moral_uncertainty utility decision

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Comment author: ESRogs 20 July 2013 06:56:38PM 6 points [-]

To a first approximation, it isn't too bad an idea to assume that one is equally likely to face a certain situation as it's symmetric complement. Using the KSBS, you'd expect to get a utility of h (same in both case); under the MWBS, a utility of (x+y)/2 (x in one case, y in the other). Since x+y ≥ h+h = 2h by the definition of the MWBS, it comes out ahead in expectation.

Not sure I'm understanding fully, but it sounds like this reasoning might fall prey to the two envelopes paradox.

The assumption about situations and their symmetric complements seems like it implies that you're equally likely to trade with an agent with twice or with half as much power as yourself. In which case, drawing the conclusion that MWBS comes out ahead in expectation is analogous to deciding to switch in the two envelopes problem.

So it seems like you can't make that assumption. Is that not the case?

Comment author: Stuart_Armstrong 20 July 2013 07:05:32PM 0 points [-]

You can face both situation A, and complement A, against agents weaker and more powerful than yourself (not strictly true, but true if you don't look at options worse than the default point, which you don't care about anyway).

Comment author: ESRogs 21 July 2013 05:26:25AM 0 points [-]

Hmm, okay. I guess what I really want to know is whether your relative level of power compared to other agents you expect to meet affects whether you'd want to employ the MWBS vs something else.

Based on my naive understanding, it sounds to me like an agent who believes themselves to have low expected relative power might prefer the h utility of KSBS versus the ~min(x,y) utility of MWBS. I'm not sure whether the details actually work out that way though.

Comment author: Stuart_Armstrong 21 July 2013 07:01:29AM *  0 points [-]

I believe that is incorrect (low relative power is a high risk-high reward situation). But we'd have to analyse it properly, with prior probs, etc... Which I have no time for now! :-(

Comment author: ESRogs 22 July 2013 12:39:18AM 0 points [-]

Ah, yeah, I was thinking the high risk, high reward thing might be the answer, based on other statements in your post. Fair enough. Thanks for taking the time to respond!

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