Inspired by a trip to see Faust shortly before Christmas.
Selling your soul to the Devil is a mug’s game. Not only is the expected outcome (in a mathematical sense) infinitely bad, it is definitely going to be infinitely bad. From the Devil’s perspective, this makes it a fairly poor offering: only a very small number of people are going to be foolish enough to take such a bad deal.
But what if instead the Devil offered a deal in which he bought a chance at taking your soul? The person got the usual benefits: wealth, success, fame, love and so on for a certain number of years, and at the end of it the Devil got a certain probability at taking that person’s soul. For example, if the chance was 10%, 1 in 10 times the person concerned would go to hell for eternity; for the other 9, the normal course of events would occur(1). We will assume, as is usually the case in these scenarios, that either due to his nature or due to the intervention of a higher power the Devil will always keep his word.
This changes the nature of the equation. Mathematically speaking, the expected outcome is still infinitely bad (even a small chance of an eternity in hell outweighs any number of pleasurable mortal lifetimes) but now the bad outcome is not certain. Indeed, depending on what probability is chosen, it may actually be quite unlikely. Given we know that humans have a psychological tendency to treat unlikely outcomes as impossible, and assuming the Devil cannot adopt differential pricing, what probability should he set in order to tempt the maximum number of humans into such deals?
Some further points worth considering:
- We can presume that the Devil gets some souls anyway. And quite possibly the souls he was going to get belong to people who are more likely to be tempted by such deals. Any such souls are dead-weight loss – the key thing for him is the number of souls he wouldn’t otherwise get.
- On the flip side, the person making the deal might also take this into consideration: if they think they may end up in his clutches anyway, a deal seems even better.
- What are the implications of doing such a deal? One friend suggested that regardless of the nominal probability, anyone entering into such a deal would have their soul damned, due to the very fact of having been willing to do the deal combined with the presumed corrupting influence of the Devil’s gifts.
- Is there an opportunity cost to the Devil? We may assume that, like Screwtape, he is indifferent to whether humans are happy or sad on earth – souls are all that matters. But if fulfilling the deals imposes a non-zero cost – Faust, for example, gets his own personal devil, Mephistopheles, to follow him around for 24 years – then this becomes relevant.
- The ideal situation for the Devil, presumably, is to establish a new societal norm in which almost everyone has made such a deal. After all, you might be happy with the house you can afford and your promotion prospects, now, but what if a third of your colleagues have made devilish deals, what then? Given a large number of human desires are positional goods, in such a situation the Devil could presumably gain a chance at a very large number of souls without really making anyone happier.
Note: this post is intended as fiction and humour, using real-world economic concepts to play off the well-known literary trope in which a person makes a deal with the Devil involving their soul.
(1) A variant of this involves the Devil leasing the soul rather than purchasing a certain probability of acquiring. If the person dies within the span of the lease, the Devil keeps their soul; if not, they get it back. This is functionally equivalent, but has the disadvantage of requiring the Devil to use actuarial tables.