AlanCrowe comments on Unknown knowns: Why did you choose to be monogamous? - Less Wrong

48 Post author: WrongBot 26 June 2010 02:50AM

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Comment author: AlanCrowe 28 June 2010 07:48:46PM 4 points [-]

I disagree with the first sentence. Since my disagreement hinges on the difference between partial and total derivatives I hope it is broadly interesting.

When Milton Friedman titled one of his books Free To Chose his underlying model was that happyness was a function both of the number of choices and the quality of the choices: . His theory is that q is a dependent variable: . When choices, c, are few, then producers offer consumers poor choices, on a take-it or leave-it basis. When choices are many, producers compete and consumers are offered good choices. is positive and large. is positive and large. What of ? Presumably it is negative, all that comparison shopping is a chore, but in this analysis it is seen as small. Choice is good,meaning .

I see the consumerist position, that choice is good, meaning , as a crude vulgarisation of the argument above.

Trying to apply this to a 30 year old American contemplating polyamory, my assumption is that he has experience of how the inner dynamics of the modern American monogamous romance play out. Unhappy experience. Now he is wondering about the dynamics implicit in polyamory. He wants to know whether changing the rules produces a better game, and he knows that he cannot find out via the simple equation: more choice = better. He must consider how the players respond to the changed incentives produced by the new rules.

Comment author: Blueberry 28 June 2010 08:04:41PM *  0 points [-]

I disagree with the first sentence. Since my disagreement hinges on the difference between partial and total derivatives I hope it is broadly interesting.

If q is a function of c, then h becomes a function of one independent variable, and your use of partials here doesn't make sense, because you can't hold c constant while changing q or vice versa.

Comment author: AlanCrowe 28 June 2010 08:37:55PM *  2 points [-]

You are making me feel old. My notation was orthodox in 1958. Indeed, in A Course Of Pure Mathematics, Tenth Edition, section 157, Hardy writes:

The distinction between the two functions is adequately shown by denoting the first by and the second by , in which case the theorem takes the form though this notation is also open to objection, in that it is a little misleading to denote the functions and whose forms as functions of x are quite different from one another, by the same letter f in and .

Comment author: cupholder 28 June 2010 09:20:12PM 0 points [-]

I think your notation is still orthodox, or at least fairly common, nowadays. Wikipedia uses it on its total derivative page, for example, and it seems familiar to me.

Comment author: cupholder 28 June 2010 09:23:21PM 1 point [-]

If q is a function of c, then h becomes a function of one independent variable, and your use of partials here doesn't make sense, because you can't hold c constant while changing q or vice versa.

I thought that this was the kind of situation partial derivatives are there for. AlanCrowe's just applied the multivariable chain rule, if I'm getting it right.

Comment author: Blueberry 28 June 2010 09:53:10PM 0 points [-]

Thanks, you (and Alan) are right. Sorry, it's been a while.