June 30, 2012

Small gods: why you should not believe in powerful gods

A boy and his godHere is a hilarious game theory argument against standard theism: [1206.6752] God exists with probability 1/(H+1)

The basic idea is that is a rational (but imperfect and finite) human plays a "game" against God, who is rational and perfect. The human can choose between being good or bad, and God can choose to exist or not (presumably in the sense of interfering with the universe or not). Being good has a cost of -1 to the human if God doesn't exist and a reward H (heaven) if God exists, and being bad has a human reward of +1 or -H (hell). But God also has some preferences: if it exists it gets +X for having the human being good and -X for being bad. If God choses not to exist there is zero payoff.

For this game there are three equilibria: humans being good and God existing, humans being bad and God not existing, and a mixed strategy where the human has a 50% chance of being good and God choses to exist with with probability 1/(H+1). Since humans are imperfect they cannot play the pure strategies, and hence they must play the mixed strategy. God must also do so, since otherwise the rationality assumptions break down.

Hence the higher the claim H is, the less likely we should regard the existence of God. Preachers arguing it is infinite are inadvertently implying that God doesn't exist or doesn't intervene. On the other hand, really wussy Gods with H close to 1 have a high chance of existing by this argument. Terry Pratchett was clearly onto something in Small Gods:

There are billions of gods in the world. They swarm as thick as herring roe. Most of them are too small to see and never get worshiped, at least by anything bigger than bacteria, who never say their prayers and don’t demand much in the way of miracles.

They are the small gods-the spirits of places where two ant trails cross, the gods of microclimates down between the grass roots. And most of them stay that way.

The rational choice for the human with a prior with a bounded support is hence to believe in a fairly weak god.

Posted by Anders3 at June 30, 2012 08:39 PM