The value of life and zero utility
It is clearly possible to talk of negative holdings. We do so all the time. How much do you have for example? I give even odds that the answer will be negative. You have a current account balance of minus £800, or, if you are affluent, a mortgage of minus some much larger figure. But have you really got less than nothing? You seem to be clothed and fed, able to navigate around the capital, I've even seen you buying drinks.
Bernoullie counts the exhange value of our earning power and any other exchangeable goods as a part of our holdings, which seems to me to be eminently sensible and easily explains the above paradox. The reader with the overdraft is expected to be able to repay on future earnings. The reader with the mortgage likewise, but failing that can make up the debt by selling her house. So neither really has less than nothing.
We could work out the worth of a man as follows: [resale value of all goods + (expected earnings - minimum living expenses) multiplied by life expectancy] . Call this number L, then we could think of any citizen whose total debts exceeded L as being in possession of negative value. However this is not entirely realistic, since any person whose debts exceeded L could no longer be considered as a debtor, since they could be under no obligation to pay back their debts. They would flip over into being more a thief, beggar or charity case. Perhaps in earlier times it might have been thought possible to extract such debts through torture or other punishment. The logic of this, although eminently human, is, thank evolution, no longer considered rational.
So here's a thought: Perhaps at the moment of suicide we could conjecture that a person has completely nothing.
Now imagine this. We find a large sample of people on the point of suicide. (shouldn't be too difficult, its fast becoming one of the biggest killers, especially if they succesfully reclassify traffic accidents). We then offer them goods to see if we can tempt them to desist from suicide. The quantity of goods necessary to prevent suicide could then be consider equivalent to the negative utility of their holdings at the point of death. Their fate could be considered worse than death by a measurable amount, not just in utility, but in actual money. Since the moment of self slaughter must surely be counted as zero, then this would be a negative value.
Some may think this unromantic, but I think it opens up as yet unseen romantic vistas of great poetic power. Comparisons of value are the very constituents of romance and poetry. Fie on those who say that the most valuable thing in their lives is a two bedroom flat in Dulwich village. Surely the most valuable thing in most peoples lives is their union with their beloved. The greatest negative value at the point of suicide must have been that of Romeo when he thought his beloved Juliet dead. Had one of our hypothetical research team approached Romeo in his last soliloquy and offered him goods to prevent his suicide, what would have stayed his hand? Nothing but the sight of his Juliet alive. As it happens, quite an easy thing to acheive. But what else, had this been impossible? Nothing, (we romantics hope), not the wealth of kingdoms, nor the power of empererors, nor mastery of the seven seas. So now we have a measure of the negative utility of Romeo's holdings, and by comparison the positive utility of Juliet's life. The number we achieve is a kind of de facto infinity. For any sum of money, or office of power, there is something of higher value, and that is Juliet's life. And for any debt, however large, there is a greater possible debt, and that is the debt of someone who owed Romeo his life once Juliete was no more.
As a kind of punch line for affecionados of probability, if we offered Romeo the St Petersburg Game, then we could suppose that he was prepared to pay the ultimate price. But how many consecutive heads would Romeo have to toss before the casino would be obliged to ressurect his Juliet?