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Do men or women have more brothers?

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Re: Do men or women have more brothers?

#31

Post by xadhominemx »

squidfood wrote: post #17
jakobegger wrote: post #6

Earlier quoted context omitted.

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.

Actually, if everyone has babies of sex A until you have a baby of sex B, you get a 50/50 mix. - Half the parents will have an only child of sex B. - One quarter will have one A, one B. - One eighth will have A, A, B. - One sixteenth A,A,A,B. This converges on 50/50!

Well if you assume some sort of practical limit to the number of children a couple can have, then you end up with more B.

Re: Do men or women have more brothers?

#32

Post by pklausler »

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

Sure. Limit families to four children.

There's one way to have zero daughters. In BBBB, each of the four boys has 3 brothers. Score 12 for the boys here.

There's four ways to have one daughter. In each of them, she's got 3 brothers, while the 3 boys each have 2 brothers. Score 12 for the girls, 24 for the boys.

There's six ways to have two daughters. In each of them, the 2 girls each have 2 brothers, while the 2 boys each have 1 brother. Score 24 for the girls, 12 for the boys.

There's four ways to have three daughters. In each of them, the 3 girls each have one brother, and the boy has none. Score 12 for the girls, zero for the boys.

There's one way to have four daughters, but obviously nobody has a brother.

Add up the scores, and you'll see a tie at 48.

(EDIT: Bogus expected value removed after re-reading.)

Re: Do men or women have more brothers?

#33

Post by mudbungie »

sp332 wrote: post #14
mudbungie wrote: post #2

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

I think you forgot to put quotes around "Girl" on line 46. Edit: Actually I'm not sure what the problem is but I'm getting 0 girls and a divide-by-0 error. Edit2: I don't remember why I was getting all girls, but the other issue was integer division. If boybrothers/boys truncates to 0, then (girlbrothers/girls)/(boybrothers/boys) will divide by 0.

Actually, line 46 is referencing the class Girl, so you wouldn't want quotes. Technically, you're supposed to use try/except duck-typing in Python, but I often find that clearer code comes out of assertions where you literally check the type of an object instead of handling errors. This was no exception. (Sorry, bad pun)

You might try throwing in a random seed. I just trusted that my system would iterate enough that it wouldn't matter, but if you're getting all boys (I'm not sure that's the case, but you said that you're getting 0 girls...), it could be that for whatever reason, the system might not be advancing the seed. Try inserting the following two lines immediately after import random:

from datetime import datetime

random.seed(datetime.now())

Re: Do men or women have more brothers?

#34

Post by kbenson »

rcar wrote: post #22

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/7baa…

> that's how people plan their families, right?

That's probably how they begin planning them, but plans change. Also, there's likely quite a few unintended births.

Or, the alternative reply, if you prefer:

You sarcasm is far too understated to do well on a forum like this. ;)

Re: Do men or women have more brothers?

#36

Post by squidfood »

xadhominemx wrote: post #31
squidfood wrote: post #17

Earlier quoted context omitted.

Actually, if everyone has babies of sex A until you have a baby of sex B, you get a 50/50 mix. - Half the parents will have an only child of sex B. - One quarter will have one A, one B. - One eighth will have A, A, B. - One sixteenth A,A,A,B. This converges on 50/50!

Well if you assume some sort of practical limit to the number of children a couple can have, then you end up with more B.

Actually, no. If you have a hard limit, then some people will end up A,A, ... A with no B. That evens it up again.

Re: Do men or women have more brothers?

#37

Post by gweinberg »

squidfood wrote: post #17
jakobegger wrote: post #6

Earlier quoted context omitted.

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.

Actually, if everyone has babies of sex A until you have a baby of sex B, you get a 50/50 mix. - Half the parents will have an only child of sex B. - One quarter will have one A, one B. - One eighth will have A, A, B. - One sixteenth A,A,A,B. This converges on 50/50!

That's true, but it doesn't imply boys and girls have the same number of brothers. As a commenter in the op pointed out, if families keep having children until they have a son, no boys have any brothers and all girls have exactly one brother. I think if they keep having kids until they have a girl, though, for gors and boys you have a .5 chance no brother, .25 1 brother, and so on.

Re: Do men or women have more brothers?

#38

Post by millstone »

The question was phrased ambiguously as "do men or women have more brothers." Here's three possible interpretations.

One interpretation is "if I am the last born (or some other gender-neutral specifier), do I have more brothers if I am a man or a woman?" As paulmd answers, the chances are even.

But we can also interpret it at the aggregate level. Say we have a family with M men and W women, and we decide to count brothers by polling each person for how many brothers they have, and totaling the result up. If we poll men, we get M(M-1) brothers, and if we poll women, we get MW brothers. The result depends on the distribution, but at the expectation value (M = W), women have more. Same conclusion if we average instead of sum.

The third, most natural interpretation is to "deduplicate:" ask each person to list his or her brothers, take the count of the union. This is the familiar sense: we would say there are three Brontë Sisters, even though none of them individually had three sisters. Here the number of brothers equals the number of men, except when then there's only one man; then each women has 1 brother and each man has 0.

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