Vladimir_Nesov comments on Fair Division of Black-Hole Negentropy: an Introduction to Cooperative Game Theory - Less Wrong

26 Post author: Wei_Dai 16 July 2009 04:17AM

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Comment author: Vladimir_Nesov 16 July 2009 10:58:58AM *  5 points [-]

The procedure for "fair division" is presented as more or less arbitrary. At least some rationale should be given explicitly. Black holes weaken the post; I think it'll be better if you take them out right away and rename the post (links won't break).

Comment author: Wei_Dai 16 July 2009 11:41:01AM 4 points [-]

You're the second person to not like to black hole example. It happens to be something I was thinking about, and found a solution for in cooperative game theory. Maybe it's not ideal for pedagogy, but it does have the advantage of being a "real-world" example.

For other examples, as well as the theoretical considerations that led to Shapley Value, see chapter 5 of the book I linked to, or the Wikipedia entry on Shapley Value.

Comment author: RichardKennaway 16 July 2009 12:26:21PM 5 points [-]

it does have the advantage of being a "real-world" example.

Harvesting negentropy by dropping mass into black holes is not a real world example, it is a far future sci-fi example.

Comment author: Eliezer_Yudkowsky 16 July 2009 12:59:10PM 8 points [-]

I'd have to disagree with that. It's a far-future science example and an obvious default one given the current model of physics for anyone who understands thermodynamics. Okay, it may take some explaining before it's equally obvious to everyone, but it is, in fact, obvious. Especially if you want value that scales nonlinearly with material. I find it difficult to put into mere words just how obvious this is - it far exceeds the obviousness of, say, using gold to talk about inflation, when the choice of those particular atoms is completely arbitrary in a grand physical sense.

Comment author: Wei_Dai 17 July 2009 12:24:35AM 9 points [-]

Yes, in some sense it's an obvious default, which seems to go largely unrecognized (even by those who understand thermodynamics), maybe due to a bias towards thinking that value scales linearly with material. But I don't want to claim too much. There are a number of caveats I didn't mention in my post:

  • Some space-time geometries may have better entropy dumps than black holes. In an open universe without dark energy, for example, the cosmological background temperature goes to 0 and negentropy is essentially infinite.
  • Why make negentropy the object of fair division, instead of value created from using up negentropy, which might not be a linear function of it?
  • Why should individuals own matter? If they don't, then our intuition about what constitutes fair division would change drastically.
Comment author: Douglas_Knight 16 July 2009 05:32:03PM 5 points [-]

may take some explaining before it's equally obvious to everyone

That doesn't seem like a partly useful meaning of "obvious."

The real issue is that most people don't believe in the future. Do you want that as a prereq for game theory? does it have positive propaganda value? (I'd guess that it has negative propaganda value, but I'd also guess that the people complaining are incorrect about how distracting it is.)

Comment author: HalFinney 16 July 2009 06:21:55PM *  3 points [-]
Comment author: RichardKennaway 16 July 2009 06:40:49PM 1 point [-]

Beat me to it. Link.

Comment author: Eliezer_Yudkowsky 16 July 2009 06:57:08PM 2 points [-]

See also: "Trivial".