Wednesday, October 15, 2008

Um, honey?

One problem that I have and that I see others having is just what the concept of probability is supposed to be doing for us.  My lawyer gf was reading me some statistics from a survey on divorce the other day and two of the (paraphrased) questions were 

1) What percentage of marriages end in divorce?

2) What is the probability that your marriage will end in divorce?

The answers to 1) were pretty accurate; median answer around 40%.  However, the median answer to 2) is 0%.  Now, one of the points of the survey was that people can't realize their own potential for getting divorced, but I was struck by the view of probability that was inherent in the way the question was asked.  Usually, when I am thinking about probability, I think in terms of properties of empirical data, i.e. what is the probability that a rich male from Connecticut votes Republican?  Probability is here just a simple proportion; those who do, over the total. There is another step to be made, extrapolating from the data you have to the whole population.  This is not really the same idea that is inherent in question 2).  Part of the idea here, as I see it, is that probability is an epistemological property.  So, if I don't know whether something is going to happen, I can theoretically estimate whether it is going to happen or not by thinking about the possible things that could happen and then putting the amount of possible worlds in which the outcome obtains over the total amount of possible worlds.  So, if we think about re-running history, maybe sometimes we would get divorced, and maybe sometimes we wouldn't.   

How would we go about thinking about this?  One way to get a grip on what possible worlds there are, is that we can look at other existing situations as an approximation of how our lives might go.  But this is a different enterprise from thinking about our own lives being re-run again and again.  If history was run again, it would be exactly the same (I make no apology for being a causal determinist - quantum mechanics be damned), so the probability (as an ontological concept) that I will get divorced is 1 (if I do) and 0 (if I don't).  I don't know whether I will or not and my best guess as to whether I will is by using other people's experiences.  So, it is inconsistent to say that on average 40% of people get divorced but that my own probability of getting divorced is anything other than 40%.  

My girlfriend was not best pleased with this discussion.

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