Most Likely Wealth Distribution

Sa huling post, I gave vent to all my left-wing righteousness against the growing income disparity. Pagkatapos ay naganap ito sa akin — a totally uniform wealth distribution is stochastically unlikely. Sa katunayan, it is over seven billion times less likely than one person in the whole world holding all the wealth in the world. That brings me to the topic of this post – what is the most likely wealth distribution?

How do we attempt to answer this question? Ayos lang sa iyo, it is a mathematical question, not a moral one. The most moral distribution, one might think, would be to take all the wealth in the world and divide it equally among the 7.4 billion people. Borrowing the concept of phase space from statistical mechanics, this particular distribution will correspond to just one point in a 7.4 billion dimensional space. The other extreme situation – any one person holding all the wealth in the world, at ang iba na may wala sa lahat – corresponds to 7.4 billion points, and is so much more likely, which is the statement I made in the first paragraph. Ngunit dapat na isang partikular na pamamahagi sa pagitan ng mga dalawang magpakalabis na ito ay pinaka-malamang na mayroong. So I sat down in front of my trusted iMac, trying to figure it out.

Ang pagsagot sa tanong na ito na bumabagsak sa pag-uunawa ng mga bilang ng mga paraan ng paghahati n bagay sa upang grupo (ang tinatawag na mga bituin at mga bar problema), and then sorting and counting the number of points in the phase space, nang paulit-ulit. Not a very hard problem, maliban diyan n at upang ay masyadong malaki, and the combinatorics involves factorials of large numbers. So you have to use Stirling’s approximation. Mahusay, I will spare you the mathematical details and get straight to what I found.

What I found was quite surprising. The most likely situation seems to be the one in which the wealth distribution is highly skewed. The richest person would own more than 60% of the wealth, and the top 50 people would own practically everything!

So any wealth redistribution effort will have to fight the tremendous stochastic pressure in addition to our innate reluctance to part with the green stuff. Does this constitute a mathematical proof that socialism cannot work? I guess the right-wingers might take it that way. Akin, it shows a couple of other things: As the total wealth grows, the inequality will grow faster. Pangalawa, those who find themselves on the right side of the income divide should thank their stars more than their so called talent, hard work etc. Oo naman, ito ay tumatagal ng lahat na sa lungga ang iyong paraan sa kanang bahagi (unless you were born there, which is statistically quite unlikely), but talent, proclivity for hard work, soft kasanayan, mahirap kasanayan etc. ay ang lahat ng mga aksidente ng mga pangyayari. By the same token, if you do find yourself on the right side, diyan ay hindi masyadong maraming dahilan upang maglakad sa paligid sa isang Problema budhi — hey, somebody had to be here. Better you than somebody else, karapatan?

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