Do men or women have more brothers?

The question sounds like an elegant and abstract question straight out of a mathematical textbook, but to answer it you need to start making assumptions about the the distribution of family sizes, which leads you to family planning and cultural differences. There is no way to solve this problem on a napkin.

Why does everyone try to solve this problem from first principles? The best way to solve this problem would be to look at actual statistics!

So now I wonder: Is there any publicly available census data that's detailed enough to answer this question? Or are there any public genealogical databases that might be helpful in answering this?

Re: Do men or women have more brothers?

#5

Post by paulmd » Mon, May 23, 2016, 8:07 PM UTC

Seems like a straightforward Gambler's Fallacy situation. Assuming the chances of each sex are independent and equally probable, then each subsequent child has a 50% chance of each sex. Your previous streak is irrelevant (it doesn't matter whether you're male or female), the chance of having a brother is equal. As the number of families approaches infinity the number of brothers will even out.

Or to rephrase the question - after flipping a coin and getting 50 heads in a row, what's the chance of the 51st coin coming up heads? (answer: 50%)

Now in reality the chances of each sex may not be equal - some people have a genetic predisposition to have more sons than daughters or vice versa. And of course there's family planning and so on that may artificially alter the number of brothers/sisters (eg to carry on the fmaily name).

https://www.sciencedaily.com/releases/2008/12/081211121835.h...

Re: Do men or women have more brothers?

#6

Post by jakobegger » Mon, May 23, 2016, 8:11 PM UTC

paulmd wrote: post #5

Seems like a straightforward Gambler's Fallacy situation. Assuming the chances of each sex are independent and equally probable, then each subsequent child has a 50% chance of each sex. Your previous streak is irrelevant (it doesn't matter whether you're male or female), the chance of having a brother is equal. As the number of families approaches infinity the number of brothers will even out. Or to rephrase the ques…

Many people really want either a son or a daughter. So they'll keep trying until it works. An acquaintance of mine had four sons before the fifth one finally was a daughter.

I'm pretty sure that effect is a lot stronger than any genetic predispositions.

Re: Do men or women have more brothers?

#7

Post by micheljansen » Mon, May 23, 2016, 8:13 PM UTC

mudbungie wrote: post #2

I chose to answer the question empirically. http://pastebin.com/1g1bAEPt Turns out it's equal.

While that's a nice way to approach a mathematical problem, it does not take into account the social aspects of the problem. For example, it used to be (and perhaps still is?) quite common for families to aspire to have a boy and therefore have another child when they have a girl, but not when they have a boy.

Interestingly, these sort of things are much easier to model empirically the way you did (all you would need is a small tweak to the "haveAKid" condition in the while loop around line 35), whereas the math gets pretty complicated fast.

Re: Do men or women have more brothers?

#8

Post by acbabis » Mon, May 23, 2016, 8:13 PM UTC

jakobegger wrote: post #4

What a great example of a seemingly simple question that can't be answered. The question sounds like an elegant and abstract question straight out of a mathematical textbook, but to answer it you need to start making assumptions about the the distribution of family sizes, which leads you to family planning and cultural differences. There is no way to solve this problem on a napkin. Why does everyone try to solve this…

> Why does everyone try to solve this problem from first principles?

Trying to solve the problem from first principles is probably how a lot of the posters came to the conclusion that it wasn't possible. If the problem were possible to solve from first principles, it would have been a waste of time to find/create data, so trying to solve it from first principles is the correct approach given no prior knowledge of the answer.

Re: Do men or women have more brothers?

#9

Post by dhimes » Mon, May 23, 2016, 8:14 PM UTC

paulmd wrote: post #5

Seems like a straightforward Gambler's Fallacy situation. Assuming the chances of each sex are independent and equally probable, then each subsequent child has a 50% chance of each sex. Your previous streak is irrelevant (it doesn't matter whether you're male or female), the chance of having a brother is equal. As the number of families approaches infinity the number of brothers will even out. Or to rephrase the ques…

But by the wording, however, it seems different. (I really, really suck at this stuff though.) If I have 50 men and 50 women in a family, the men each have 49 brothers, and the women each have 50. The coin-flip comparison would be "how many heads are there not counting a particular head" or something.

Re: Do men or women have more brothers?

#10

Post by tracker1 » Mon, May 23, 2016, 8:16 PM UTC

jakobegger wrote: post #6

paulmd wrote: post #5

Seems like a straightforward Gambler's Fallacy situation. Assuming the chances of each sex are independent and equally probable, then each subsequent child has a 50% chance of each sex. Your previous streak is irrelevant (it doesn't matter whether you're male or female), the chance of having a brother is equal. As the number of families approaches infinity the number of brothers will even out. Or to rephrase the ques…

Many people really want either a son or a daughter. So they'll keep trying until it works. An acquaintance of mine had four sons before the fifth one finally was a daughter. I'm pretty sure that effect is a lot stronger than any genetic predispositions.

My mom was one of four daughters (no sons), their mom was one of three daughters (no sons), two of my cousins only have girls, and my sister only has girls... my brother is the only one of myself and cousins that have any sons.