Pascal's wager

This was taken from: http://kinsman.is-a-geek.net/blog/

Game theory is a concept in applied mathematics. Like any branch of mathematics, it throws around big sounding terms such as pay-off matrix and Nash equilibrium, but at its heart game theory is really very simple.

Game theory is about winning.

In any game where the rules are clearly defined, game theory can be used to try and find the best strategy. Take a classical game of chicken for example, where two drivers accelerate towards a head-on collision, the one who swerves being the chicken. A traditional pay-off matrix for chicken looks like this:

	bob swerves	bob goes straight
fred swerves	tie	bob wins
fred goes straight	fred wins	crash

The matrix is fairly easy to understand; if both players swerve, the game is a tie. Neither player is the chicken and neither player dies. If both players stay the course, they both die - the worst possible outcome. If one player swerves, only their pride will be hurt, while the other gains the honour of winning.

So what is the best way of winning? If you don’t swerve you could die - so you’d better swerve. The other guy will be thinking that as well though, so if you don’t swerve they probably will. But wait - what if he is thinking the same thing! Then you will both die!

Analysing the game in this way, trying to work out the right decisions to achieve the best outcome - most people call this strategy. Mathematicians call it game theory.

Blaise Pascal was a French mathematician who was also very religious. He used game theory’s sibling, decision theory, to try and tell the world that belief in God is the right decision. This is now known as Pascal’s Wager.

The wager states that belief in God is the correct decision because the pay-off is infinite, while the punishment is infinitely painful. The pay-off matrix as proposed by Pascal would look like this:

	no god	god exists
atheism	oblivion	hell
christianity	oblivion	heaven

It would seem Pascal is right. Time to throw away all my years of scepticism - praise be to God the almighty! I see the light! But wait, something tells me the matrix isn’t quite complete. That’s the problem with game theory (and decision theory): it can appear very authoritative until you realise that you haven’t accounted for all the variables.

Take my initial example of chicken. The analysis of the game looks complete, it looks like I have thought of every possible scenario. But what happens if both players swerve in the same direction. There’s a chance that if they both chicken out, they could actually swerve into each other and be killed. Taking this into consideration, the pay-off matrix now looks like this:

	bob swerves left	bob swerves right	bob goes straight
fred swerves left	tie	crash	bob wins
fred swerves right	crash	tie	bob wins
fred goes straight	fred wins	fred wins	crash

In the initial matrix, there was a 25% probability of winning and a 25% probability of crashing. In the new matrix there is only a 22% probability of winning and a 33% probability of crashing. Clearly it could lead to disaster if you base your decisions on the original matrix.

Pascal’s wager is equally flawed. For starters it doesn’t take other religions into account. Let’s add Islam:

	no god	god exists	allah exists
atheism	oblivion	hell	hell
christianity	oblivion	heaven	hell
islam	oblivion	hell	heaven

Or what about a God / Allah that doesn’t punish wrong choices in belief, and only judges based on how good you have been throughout your life?

	no god	god exists	allah exists
good atheist	oblivion	heaven	heaven
good christian	oblivion	heaven	heaven
good muslim	oblivion	heaven	heaven
bad atheist	oblivion	hell	hell
bad christian	oblivion	hell	hell
bad muslim	oblivion	hell	hell

And what if God / Allah exists, but actively punishes belief? What if God / Allah wants us to think for ourselves?

	no god	god exists	allah exists
atheism	oblivion	heaven	heaven
christianity	oblivion	hell	hell
islam	oblivion	hell	hell

As you can see, decision theory isn’t very useful if you don’t know all the rules behind the game, and we know nothing of the rules behind the afterlife, or even whether it exists. This makes the wager an unconvincing argument.

Sorry Pascal, but I’m sticking with atheism.

Taken from: http://kinsman.is-a-geek.net/blog/index.php/2007/12/27/pascals-wager/