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neq1 comments on Bayes' Theorem Illustrated (My Way) - Less Wrong

126 Post author: komponisto 03 June 2010 04:40AM

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Comment author: neq1 03 June 2010 02:49:38PM 1 point [-]

It seems to me that the standard solutions don't account for the fact that there are a non-trivial number of families who are more likely to have a 3rd child, if the first two children are of the same sex. Some people have a sex-dependent stopping rule.

P(first two children different sexes | you have exactly two children) > P(first two children different sexes | you have more than two children)

The other issue with this kind of problem is the ambiguity. What was the disclosure algorithm? How did you decide which child to give me information about? Without that knowledge, we are left to speculate.

Comment author: JenniferRM 03 June 2010 06:14:09PM *  4 points [-]

This issue is also sometimes raised in cultures where male children are much more highly prized by parents.

Most people falsely assume that such a bias, as it stands, changes gender ratios for the society, but its only real effect is that correspondingly larger and rarer families have lots of girls. Such societies typically do have weird gender ratios, but this is mostly due to higher death rates before birth because of selective abortion, or after birth because some parents in such societies feed girls less, teach them less, work them more, and take them to the doctor less.

Suppose the rules for deciding to have a child without selective abortion (and so with basically 50/50 odds of either gender) and no unfairness post-birth were: If you have a boy, stop; if you have no boy but have fewer than N children, have another. In a scenario where N > 2, two child families are either a girl and a boy, or two girls during a period when their parents still intend to have a third. Because that window is relatively small relative to the length of time that families exist to be sampled, most two child families (>90%?) would be gender balanced.

Generally, my impression is that parental preferences for one or the other sex (or for gender balance) are generally out of bounds in these kinds of questions because we're supposed to assume platonicly perfect family generating processes with exact 50/50 odds, and no parental biases, and so on. My impression is that cultural literacy is supposed to supply the platonic model. If non-platonic assumptions are operating then different answers are expected as different people bring in different evidence (like probabilities of lying and so forth). If real world factors sneak in later with platonic assumptions allowed to stand then its a case of a bad teacher who expects you to guess the password of precisely which evidence they want to be imported, and which excluded.

This issue of signaling which evidence to import is kind of subtle, and people get it wrong a lot when they try to tell a paradox. Having messed them up in the past, I think it's harder than telling a new joke the first time, and uses similar skills :-)