Ponzi schemes

With Madoff getting 150 years in jail, it's topical to say something about Ponzi schemes. So let me make this remark: There are possible worlds where there is nothing wrong with Ponzi schemes. For instance, there is nothing morally wrong with certain Ponzi schemes in certain worlds. What makes Ponzi schemes problematic in our world is that with a finite amount of total wealth (including future wealth), it is not possible to have a system of transactions that do not create wealth, increase the wealth of some, and do not decrease anyone's wealth. But in a world with an infinite number of investors having infinite total wealth, it is possible to have financial schemes that increase the wealth of some, without decreasing the wealth of any, and yet without any wealth being created, simply by shuffling wealth about.

For instance, if the investors are numbered 1, 2, 3, ..., one can have a scheme where 1 gets $1 from 2, 2 gets $1 from 3 and 4, 3 gets $1 from 5, 6, 7 and 8, 4 gets $1 from 9, 10, 11 and 12, and so on. If the transactions are somehow made to be simultaneous, then once the scheme is over, each investor is richer, none is poorer, and no wealth has been created--it's been "sucked in from infinity." Interestingly, this infinitary scheme makes folks further down the chain get more money than people closer to the head of the chain: 1 only gets a dollar, but 3 and 4 each get $3.

But what if the transactions are not simultaneous but sequential? This can still work in finite time if supertasks are possible. But if the transactions are sequential and supertasks are impossible, then at any given finite time in the procedure, some investors are better off, while others are worse off, and only in the infinite time limit has everybody benefited.