Motl vs Landsburg 2

Pošto većina misli da je Landsburg u pravu, a ja nisam u stanju da nešto doprinesem raspravi Motl vs Landsburg dok mi intuicija kaže da je Motl u pravu (pošto obično biva), kontaktirao sam Motla sa molbom da za nas napiše kratak sažetak svojih gledišta, i evo šta smo dobili (disclosure - prema Lubosu ja imam odnos kakav Mankiw ima prema Bernankeu, da bih ako moram da odlučim iz datog domena (ekonomija vs fizika-matematika), pitao njega pa šta on kaže uradio to ili zauzeo takav stav. S tim što mislim da ja imam više osnova za moj izbor jer je čovek genijalan fizičar a Bernanke je bip bip.. recimo verovao da su "temelji solidnni" 2007, i da će tržište nekretnina nije u krizi 2005, ili pak da će 2008 da bude godina velikog rasta):

I didn't enter the bet because I agree with what he says about the problem added to his bet as a clarification: one gets 43% for that problem. It is trivial to calculate it.

But the whole point of his bet is that he invented a completely different problem than the original problem. The original problem has answer 50%.

Of course that if he would offer a bet about the original problem, I would be happy to earn some money. After all, I agree with 50% which is also the official answer by Google Corporation where the problem was used. ;-)

The problem is really trivial for anyone who knows some statistics and it's clear that he was imagining that it's some super complicated maths that needs to employ the world's best mathematicians and statisticians and programmers for a decade. ;-)

I wrote all the programs needed to numerically verify any of the claims within a minute and it's my understanding that he already knows everything just like I do and there's no longer any real disagreement between us (about any of the variations of the problem that may be formulated) - he's just unwilling to admit that he has simply solved the original problem incorrectly.

The real essence of the problem is really very simple: the question is whether parents may influence the composition of girls and boys in the population by selectively stopping when they get their first son. The answer is, of course, that they cannot: in the hospital, if they assist in 10 million births, 5 million of them will be sons and 5 million girls (in the idealized biological model where the sexes have the same odds) regardless of the wishes of the parents to stop or not to stop. If some parents no longer produce children because of other reasons, others will, but every new birth has 50% odds again. So whenever a population keeps on producing children, the proportion remains 50-50.

However, in a single family, the "average" proportion of girls may differ from 50% if the families have a plan to stop after the first son. That's a less trivial calculation than the 50-50 and both of us did it correctly - the answer is 1-ln(2) = 30.6% of girls. But he made a mistake in translating this result to the case of a whole nation. A nation, where new couples may start families at every stage of the history, the proportion remains 50%.

P.S. Ovo je "kratak, ne najsofistikovaniji i najkompletniji prikaz mojih gledišta" (Motl). Dužan sam to obrazloženje pošto je poruka pisana u prvom trenutku bez znanja da će biti objavljena. Više tehnička prezentacija ovde.