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Saturday, April 01, 2006

On subjective probability and behavioral economics

I recently ran into an interesting, but an almost too general article, 'The marketplace of perceptions' (Craig Lambert, Harvard Magazine, March - April, 2006). What surprised me is that there was no mention of Frank P. Ramsey and his work on subjective probability that has had a profound impact on Economics since he first published his 1926 essay, 'Truth and Probability'. (Don't let the math in the essay scare you, even if you're not the math types, the essay is fascinating and certainly recognized as one of the most revolutionary works in probability theory.) To add to Craig Lambert's essay, here are excerpts from Ramsey's essay:

"...Thirdly, it sometimes means that if his mind worked according to certain rules, which we may roughly call 'scientific method', he would have such a degree of belief. But fourthly it need mean none of these things for men have not always believed in scientific method, and just as we ask 'But am I necessarily reasonable," we can also ask 'But is the scientist necessarily reasonable?' In this ultimate meaning it seems to me that we can identify reasonable opinion with the opinion of an ideal person in similar circumstances. What, however, would this ideal person's opinion be? As has previously been remarked, the highest ideal would be always to have a true opinion and be certain of it; but this ideal is more suited to God than to man."


"Let us take a habit of forming opinion in a certain way; e.g. the habit of proceeding from the
opinion that a toadstool is yellow to the opinion that it is unwholesome. Then we can accept the fact that the person has a habit of this sort, and ask merely what degree of opinion that the toadstool is unwholesome it would be best for him to entertain when he sees it; i.e. granting that he is going to think always in the same way about all yellow toadstools, we can ask what degree of confidence it would be best for him to have that they are unwholesome. And the answer is that it will in general be best for his degree of belief that a yellow toadstool is unwholesome to be equal to the proportion of yellow toadstools which are in fact unwholesome. (This follows from the meaning of degree of belief.) This conclusion is necessarily vague in regard to the spatio-temporal range of toadstools which it includes, but hardly vaguer than the question which it answers

And of course the famous example that explained degree of belief

"I am at a cross-roads and do not know the way; but I rather think one of the two ways is right. I propose therefore to go that way but keep my eyes open for someone to ask; if now I see someone half a mile away over the fields, whether I turn aside to ask him will depend on the relative inconvenience of going out of my way to cross the fields or of continuing on the wrong road if it is the wrong road. But it will also depend on how confident I am that I am right; and clearly the more confident I am of this the less distance I should be willing to go from the road to check my opinion. I propose therefore to use the distance I would be prepared to go to ask, as a measure of the confidence of my opinion; and what I have said above explains how this is to be done."

Also, it is quite apparent that Ramsey's use of bets to measure partial belief can be extended into measuring change in the utility of certain goods over time (going back to Lambert's essay where he brings up the notion of discounting both cost and benefit in the future). I'll see if I can find some work on use of betting principle in determining variation in utility over time because I'm sure someone would have done that by now. Maybe someone reading this blog who has an idea can leave me a comment to simplify my search.


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