Most Likely Wealth Distribution

গত পোস্টে, I gave vent to all my left-wing righteousness against the growing income disparity. তারপর এটা আমার ঘটেছে — a totally uniform wealth distribution is stochastically unlikely. আসলে, 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? আপনি মনে করবেন না, 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, এবং কিছুই সঙ্গে বাকি সব – corresponds to 7.4 billion points, and is so much more likely, which is the statement I made in the first paragraph. কিন্তু সম্ভবত যে এই দুই চরম মধ্যে একটি বিশেষ বন্টন সেখানে উচিত. So I sat down in front of my trusted iMac, trying to figure it out.

এই প্রশ্নের উত্তর বিভাজক পদ্ধতির নম্বর figuring আউট boils নিচে এন বস্তু থেকে গ্রুপ (তথাকথিত বড় ও পানশালা সমস্যা), and then sorting and counting the number of points in the phase space, এবং উপর. Not a very hard problem, সেটি বাদে এন এবং থেকে বেশ বড় হয়, and the combinatorics involves factorials of large numbers. So you have to use Stirling’s approximation. ভাল, 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. আমার, it shows a couple of other things: As the total wealth grows, the inequality will grow faster. দ্বিতীয়ত, 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. অবশ্যই, এটা যে সব ডান পাশ থেকে আপনার উপায় গর্ত করা লাগে (unless you were born there, which is statistically quite unlikely), but talent, proclivity for hard work, নরম দক্ষতা, ইত্যাদি হার্ড দক্ষতা. পরিস্থিতিতে সব দুর্ঘটনার হয়. By the same token, if you do find yourself on the right side, একটি প্রায় পদব্রজে ভ্রমণ করতে খুব বেশী কারণ নেই অস্থির বিবেক — hey, somebody had to be here. Better you than somebody else, অধিকার?