cousin_it comments on Solve Psy-Kosh's non-anthropic problem - Less Wrong

34 Post author: cousin_it 20 December 2010 09:24PM

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Comment author: cousin_it 20 December 2010 10:48:09PM *  1 point [-]

If the decision of a group decider is "1/9th as important", then what's the correct way to calculate the expected benefit of saying "yea" in the second case? Do you have in mind something like 0.9*1000/9 + 0.1*100/1 = 110? This doesn't look right :-(

Comment author: red75 21 December 2010 09:39:32AM *  8 points [-]

Do you have in mind something like 0.9 * 1000/9 + 0.1 * 100/1 = 110? This doesn't look right

This can be justified by change of rules: deciders get their part of total sum (to donate it of course). Then expected personal gain before:

for "yea": 0.5*(0.9*1000/9+0.1*0)+0.5*(0.9*0+0.1*100/1)=55 for "nay": 0.5*(0.9*700/9+0.1*0)+0.5*(0.9*0+0.1*700/1)=70

Expected personal gain for decider:

for "yea": 0.9*1000/9+0.1*100/1=110
for "nay": 0.9*700/9+0.1*700/1=140

Edit: corrected error in value of first expected benefit.

Edit: Hm, it is possible to reformulate Newcomb's problem in similar fashion. One of subjects (A) is asked whether ze chooses one box or two boxes, another subject (B) is presented with two boxes with content per A's choice. If they make identical decision, then they have what they choose, otherwise they get nothing.

Comment author: cousin_it 22 December 2010 03:50:42PM *  7 points [-]

And here's a reformulation of Counterfactual Mugging in the same vein. Find two subjects who don't care about each other's welfare at all. Flip a coin to choose one of them who will be asked to give up $100. If ze agrees, the other one receives $10000.

This is very similar to a rephrasing of the Prisoner's Dilemma known as the Chocolate Dilemma. Jimmy has the option of taking one piece of chocolate for himself, or taking three pieces and giving them to Jenny. Jenny faces the same choice: take one piece for herself or three pieces for Jimmy. This formulation makes it very clear that two myopically-rational people will do worse than two irrational people, and that mutual precommitment at the start is a good idea.

This stuff is still unclear to me, but there may be a post in here once we work it out. Would you like to cooperate on a joint one, or something?

Comment author: red75 22 December 2010 06:16:45PM 0 points [-]

I'm still unsure if it is something more than intuition pump. Anyway, I'll share any interesting thoughts.

Comment author: cousin_it 22 December 2010 07:07:50AM 1 point [-]

This is awesome! Especially the edit. Thanks.

Comment author: jsalvatier 21 December 2010 10:25:16PM 3 points [-]

This kind of answer seems like on the right track, but I do not know of a good decision theory when you are not 100% "important". I have an intuitive sense of what this means, but I don't have a technical understanding of what it means to be merely part of a decision and not the full decision maker.

Comment author: GuySrinivasan 21 December 2010 11:34:27PM 1 point [-]

Can the Shapely value and its generalizations help us here? They deal with "how important was this part of the coalition to the final result?".

Comment author: datadataeverywhere 20 December 2010 11:17:45PM 2 points [-]

I think my answer is actually equivalent to Nornagest's.

The obvious answer is that the factors you divide by are (0.9 / 0.5) and (0.1 / 0.5), which results in the same expected value as the pre-arranged calculation.

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