GuySrinivasan comments on Let's split the cake, lengthwise, upwise and slantwise - Less Wrong

43 Post author: Stuart_Armstrong 25 October 2010 01:15PM

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Comment author: sketerpot 25 October 2010 07:54:18PM 7 points [-]

In your Romantic Dinner / Battlestar Galactica example, it's not really clear what it means for one person to translate or scale their utility function. I'm going to take a newbie stab at it here, and please correct me if this is wrong:

Scaling: This is where the outcome matters more to one party than to the other party. For an extreme example, one person stands to gain between 0 and 10 minutes of extra life from the bargain, and the other person could gain between 0 and 500 years of extra life. And these are totally selfish people, who genuinely don't care about each other's utility; they just want to reach a bargain that optimizes their own utility. The total-utility-maximizing answer would favor the person who has the most to gain, and either person could turn this to their advantage by claiming to really, really care about the outcome. "I'll literally die if we don't watch Battlestar Galactica!", or some such thing.

Translation: This just adds or subtracts a constant amount of utility to any person's utility function. "I would love to watch BSG, but I'm so happy just being with you! ♥". If one person will be disgruntled if they don't (e.g.) have a romantic dinner, and the other person will be at least fairly cheerful either way, then this could influence the bargaining -- and if so, it gives a selfish person a way to game the system, by acting unhappy when they don't get their way.

The way to take advantage of people using the naive egalitarian or utility-sum-maximizing decision methods is to exaggerate how much you care about things, and sulk when you don't get your way. Also known as "acting like a toddler", which our society frowns on, probably for exactly this reason.

Is this reasonably accurate?

Comment author: GuySrinivasan 25 October 2010 09:27:27PM 4 points [-]

It doesn't mean anything to translate or scale a utility function. A utility function is just a mathematical way to encode certain relative relationships between outcomes, and it turns out if you add 42 to every value of the function, it still encodes those relationships faithfully. Or if you multiply everything by 9000.

This is why comparing two individuals' utility functions in any naive way makes no sense: their functions are encoding relative preference relationships, but it doesn't matter if one of them multiplies everything by 9000. So any comparison that breaks when one of them multiplies everything by 9000 or adds 42 to everything but the other doesn't isn't actually making correct use of the underlying relative preference relationships.