Most Likely Wealth Distribution

Trong bài viết cuối cùng, I gave vent to all my left-wing righteousness against the growing income disparity. Sau đó, nó xảy ra với tôi — a totally uniform wealth distribution is stochastically unlikely. Trong thực tế, 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? Tâm trí bạn, 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, và phần còn lại với không có gì cả – corresponds to 7.4 billion points, and is so much more likely, which is the statement I made in the first paragraph. Nhưng có phải là một phân phối đặc biệt ở giữa hai thái cực đó là có khả năng nhất. So I sat down in front of my trusted iMac, trying to figure it out.

Trả lời câu hỏi này nắm để tìm ra nhiều cách phân chia n các đối tượng vào để các nhóm (cái gọi là sao và quán bar vấn đề), and then sorting and counting the number of points in the phase space, hơn và hơn. Not a very hard problem, ngoại trừ việc nđể là khá lớn, and the combinatorics involves factorials of large numbers. So you have to use Stirling’s approximation. Cũng, 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. Với tôi, it shows a couple of other things: As the total wealth grows, the inequality will grow faster. Thứ hai, 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. Chắc chắn, phải mất tất cả những gì để đào hang theo cách của bạn để phía bên phải (unless you were born there, which is statistically quite unlikely), but talent, proclivity for hard work, kỹ năng mềm, kỹ năng cứng vv. là tất cả các tai nạn của tình. By the same token, if you do find yourself on the right side, không có quá nhiều lý do để đi bộ xung quanh với một lương tâm đang gặp khó khăn — hey, somebody had to be here. Better you than somebody else, đúng?

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