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Do men or women have more brothers?

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Re: Do men or women have more brothers?

#21

Post by stcredzero »

hinkley wrote: post #16
serge2k wrote: post #3

Classic stack overflow, top answer is a giant mass of "look how awesome I am!" sensible answer is 3 down with half as many upvotes.

That's one of my productivity secrets. Always read the top 4 answers before deciding on a course. Answer #3 is right far too often for my liking. And sometimes answer #4 brings up corner cases the others missed.

I think the above structure is eerily reflected in large corporations and in government. The actual work/know-how resides in tier 3 and 4, with the top two tiers actually just being better at politics and self promotion.

Re: Do men or women have more brothers?

#22

Post by rcar »

With the assumptions that 1) boy/girl is always random but 50/50, and 2) people are choosing to have 1-10 kids ahead of time and going for it (that's how people plan their families, right?), girls do have very slightly more brothers than boys.

The notebook below shows a simulation of 50k towns of 100 families. It also holds for different max numbers of children and more families.

https://gist.github.com/rcarneva/7baac666bd65f487df73378a90c...

Re: Do men or women have more brothers?

#23

Post by wernercd »

ewjordan wrote: post #13
tomp wrote: post #12

Earlier quoted context omitted.

Hm... I'm not sure you're answering the correct question. Assume you're a man and you have a sister. Your next sibling is about to be born. There is a 50% chance that it's a boy! In which case, he will have one brother (you), you will have one brother (him), and your sister will have 2 brothers. She wins. There is a 50% chance that it's a girl! In which case, both she and your other sister will both have 1 brother (y…

"Assume you're a man and you have a sister." You just put your finger on the scale. All you can assume is that you're a man, not that you have a sister.

4 siblings... 2 boys, 2 girls... 50/50...

The girls each have 2 brothers...

The boys each have 1 brother.

6 siblings, 3/3... 8 siblings, 4/4... etc

Re: Do men or women have more brothers?

#24

Post by tempestn »

dhimes wrote: post #9
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.

By assuming a starting family with equal numbers of males and females, you bias the result. You have to look at the distribution of all families. In families with similar numbers of boys and girls, the girls with have more brothers. But in families with significantly more of one gender, the boys will, on average, have many more brothers. When you combine all possible families of a given size, weighted by their likelihood, you find that males and females have the same number of brothers on average. (You can test this pretty easily with the n=1 and n=2 cases, and with a bit of work for the n=3 case.)

Re: Do men or women have more brothers?

#25

Post by tempestn »

serge2k wrote: post #3

Classic stack overflow, top answer is a giant mass of "look how awesome I am!" sensible answer is 3 down with half as many upvotes.

Absolutely. I actually upvoted #3[1] before coming here and seeing your comment.

[1] http://math.stackexchange.com/a/1794617/63267

Re: Do men or women have more brothers?

#26

Post by seccess »

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…

My question is: does the ratio of famale-to-male matter? What if the chance of a girl was 60% and male was 40%? My intuition is that it wouldn't, but I'm not sure.

Re: Do men or women have more brothers?

#27

Post by bradleyjg »

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…

If the simple model is in exact equipoise then the more complex considerations become very important for answering the question. If the a model taking into account all the complexities was still in equipoise than it would come down to noise. It is very unlikely that of the roughly 7 billion people on the planet the women have exactly as many brothers as the men. There's an empirical answer here.

Re: Do men or women have more brothers?

#28

Post by tempestn »

wernercd wrote: post #23
ewjordan wrote: post #13

Earlier quoted context omitted.

"Assume you're a man and you have a sister." You just put your finger on the scale. All you can assume is that you're a man, not that you have a sister.

4 siblings... 2 boys, 2 girls... 50/50... The girls each have 2 brothers... The boys each have 1 brother. 6 siblings, 3/3... 8 siblings, 4/4... etc

The problem is that you're not considering all the other cases. Here are the possibilities with 2 siblings:

    Gender:     B,B  B,G  G,B  G,G
    # brothers: 1,1  0,1  1,0  0,0
Average # of brothers for boys: 0.5

Average # of brothers for girls: 0.5

You can see that in the families with a mix of boys and girls, the girls do indeed have more brothers. But this is balanced out by the families with more (or in this case all) of one or the other.

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