Friday, June 17, 2016

Statistics of Pie

Pinker:

But each child should to want the parent to dole out twice as much of the investment to himself or herself as to a sibling, because children share half their genes with each full sibling but share all their genes with themselves. Given a family with two children and one pie, each child should want to split it in a ratio of two-thirds to one-third, while parents should want it to be split fifty-fifty.

Pinker, Steven. The Blank Slate: The Modern Denial of Human Nature (p. 248). Penguin Publishing Group. Kindle Edition.

If the reasoning here sounds a bit dubious to you, you aren't alone. Maybe Pinker needs a bit more stat work. Supposing the child in question really really wants to maximize the chance of the largest numbers of his genes surviving, then the computation is bound to be a bit more complicated. The real question is the dependence of each fitness function on the share of pie, and perhaps more importantly, the mutual dependence of the fitness functions of the siblings. In some societys, a boy's chance of survival might be increased by having lots of brothers - but for the son of an Ottoman Sultan, it's the reverse.