# Are you going to Hell?

One often hears Bible-thumpers declaring that anyone who does not adhere to (a rather narrow) religious tradition will be going to Hell when he or she dies. Often, their theology includes a God that is entirely good. Thus, when pressed why such a good God would institute such an awful thing as Hell, they claim that the purpose is to discourage people from deviating from the appropriate religious path. Since, if one does not adhere to the aforesaid religion, one will end up having very bad things happen, one will have incentive to actually do what is right.

We can write out a game tree to express this idea:

Here, $H>L$, and $C,R>0$. We illustrate God’s preferences of how the world should be through the “payoff” He gets; this is independent of the (much more controversial) thesis that God somehow enjoys certain states of the world in a hedonistic fashion.

The problem here with this reasoning for the existence of Hell is that it does not constitute a subgame-perfect Nash equilibrium. We’ve assumed that God only does something bad (sending people to Hell) to prevent worse things from happening (mass sinning). Consider the possibility that 100% of people adhere to the proper religion, and then God decides to send all those who acted righteously to heaven (100% of all people), and all those who sinned (egregiously?) to Hell (0% – no one). Then God is indeed doing what He prefers most by sending all sinners to Hell; since all sinners go to Hell, it is actually a Nash equilibrium for God to send all sinners to Hell.

The thing is, if someone actually did sin, God would have to consider what to do then and there. Since, once one is dead, sending you to Hell won’t (retroactively) prevent one from sinning, doing so would not serve its purported purpose. Moreover, Hell is unobservable to those who are still living, so it does not serve to deter the others who are alive from sinning – the conditional beliefs on those still alive are the same, regardless of what God actually does to the sinner. Thus, even if 100% of the world’s population would be sin-free, this scenario would not be a subgame-perfect Nash equilibrium, and thus the optimal thing for people to do would be to live it up. Given that the sinners would have already committed all of their sins, and there would be nothing possible to do about it after their deaths, the optimal thing for God to do would not be to send them to Hell. Indeed, since I don’t think there is any religion which doesn’t think somebody has existed who deserves to go to Hell, this isn’t a Nash equilibrium, either – the past sinners who should’ve gone to Hell under this worldview would not, since God would prefer to not send them to Hell (since He is good).

If one is then to posit the existence of Hell, one will have to address the issue that it cannot be based upon some purpose of deterrence where God acts completely rationally. It will probably have to be instead based on something else, such as a deontological framework, which may include a notion of just deserts.