First of all, this question is not about the convergence of the distribution. It's about human behavior. So we'll put that discussion aside.www.ddhw.com To understand this paradox, we have to understand utility function. Money has nomination value, but it's not equal to its utility. For example, $200 may be about twice as valuable as $100, but $20,000,000 might not be twice as valuable as $10,000,000. Mathmatically, we say a normal human being has concave utility function, which means the marginal increment of utility is decreasing as the nomination value increses. The paradox uses a hidden assumption, i.e., the utility of money equals to its face value U(x) = x. And it calculates expection based on this identity utility function. Therefore, it's not normal human behavior, and the paradox is created. www.ddhw.com Consider this scenario, you picked an envelop and it has $10,000 inside, you expect to get more money if you switch based on the expection. But your decision is based on your utility function at the moment. Let's assume, you have $9,000 debt and it's due today. So identity utility function is not for you, because, the utility of $1000 is way less than $10,000, the utility of $20,000 is not much better than $10,000 in hand. Now the expectation of the utility of the outcome of swiching is less than the utility of $10,000 at hand. So you'll not switch. www.ddhw.com
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