Most Likely Wealth Distribution

In the last post, I gave vent to all my left-wing righteousness against the growing income disparity. اس کے بعد یہ مجھ سے واقع ہوئی — a totally uniform wealth distribution is stochastically unlikely. اصل میں, 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? تم برا, 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, اور کچھ بھی نہیں کے ساتھ باقی بالکل – corresponds to 7.4 billion points, and is so much more likely, which is the statement I made in the first paragraph. لیکن سب سے زیادہ امکان ہے کہ ان دو انتہاؤں کے درمیان میں ایک خاص تقسیم نہیں ہونا چاہئے. So I sat down in front of my trusted iMac, trying to figure it out.

اس سوال کے جواب میں تقسیم کرنے کے طریقے کی تعداد باہر figuring فوڑے (ن) میں اشیاء کرنے کے لئے گروپوں (نام نہاد ستاروں اور سلاخوں مسئلہ), and then sorting and counting the number of points in the phase space, اور اس سے زیادہ. Not a very hard problem, اس کے علاوہ (ن) اور کرنے کے لئے بہت بڑے ہیں, and the combinatorics involves factorials of large numbers. So you have to use Stirling’s approximation. ٹھیک ہے, 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. میرے لئے, it shows a couple of other things: As the total wealth grows, the inequality will grow faster. دوم, 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. اس بات کا یقین, یہ سب اس کے دائیں طرف سے اپنے راستے بل کرنے کے لئے لیتا (unless you were born there, which is statistically quite unlikely), but talent, proclivity for hard work, نرم مہارت, وغیرہ مشکل مہارت. حالات کے تمام حادثات ہیں. By the same token, if you do find yourself on the right side, ایک کے ساتھ کے ارد گرد چلنے کے لئے بہت زیادہ کی وجہ سے نہیں ہے شورش زدہ ضمیر — hey, somebody had to be here. Better you than somebody else, حق?