And so we get a lognormal distribution where small positive differences (arguably ultimately due to luck; genes, environment, continent, family network etc) combine to give enourmous advantages.

That said, regardless of your starting point it pays to try to position yourself to gain as many positive points as you can - with luck you can ride that same multiplicative unfairness to achieve better than linear progress.

Power law (Pareto distribution), not lognormal.

But you're partly right. Simulate random exchanges at random prices and the wealth distribution will come out Pareto.

However, we cannot conclude that because [a] random exchanges lead to a power-law dist and [b] we observe a power-law in reality, that [c] the real wealth distribution is tantamount to random.

As far as I'm aware the debate of lognormal vs power law distribution on wealth is unsettled.

EDIT: google search suggests power law tail - log normal bulk.

You are maybe thinking that it is difficult to identify powerlaws? (EDIT: s/identify/statistically verify/; s/powerlaws/TRUE powerlaws/)

But look: http://globalrichlist.com/how.html The bulk is indeed powerlaw.

Maybe you are thinking that a sufficiently winsorised US income distribution is lognormal.

To the contrary I think people are too eager to find scale free and power law phenomena.

There are several papers discussing log-normal bulk and then power law tail.

http://physicsworld.com/cws/article/news/2002/feb/26/the-phy...

http://fmwww.bc.edu/ec-p/wp671.pdf and more

For what it's worth my initial statement was meant to hold beyond income and wealth and generalize to say achievement and productivity and so a lognormal assumption was fitting as the distribution to pick. It also chimed well with grandalf's statement on how advantages multiply.

To paraphrase William Gibson: everything is here, it's just unevenly distributed.

The universe tends toward clumpiness.