Reading Time: 3 minutes

This is a strengthened version of Pascal’s wager which typically has said that “even if there is the smallest chance Christianity is true, you should believe it”. This wager places the value that if Christianity is at least 50% true, you should follow it. The wager can be summed up in this sentence:

It is rational to seek a relationship with God and live a deeply Christian life, because there is very much to gain and relatively little to lose.

We have updated information from the time of Pascal to defend his wager more sufficiently. Michael Rota who wrote the new book “Taking Pascals Wager” lays out a premise argument like so:

1. If Christianity has at least a 50% chance of being true, then it is rational to commit to living a Christian life
2. Christianity does have at least a 50% chance of being true
3. It is rational to commit to living a deeply christian life

In order to appreciate this Wager, we need to explore decision theory

Decision theory

This is basically about how to make good decisions in circumstances of risk or uncertainty. This can be applied to mundane tasks such as taking a taxi vs taking a bus or significant events like career choices. There are three foundational concepts: states, strategies and outcomes 

States — A possible way things might be

Strategy — A possible action the decider might take

Outcome — The resulting situation when taking a strategy and a certain state is actual 

Decision theory offers 2 principles to guide you when taking risks

1. Try to maximise your expected value
2. Pick a strongly dominant strategy if possible. If not, pick a weakly dominant strategy 

What does it all mean?

1. Say I offer you a bet. We ask a trusted friend to flip a fair coin but not tell us whether it came up heads or tails. Then I ask you to decide whether to play or pass
2. If you choose to play it will cost you £1. 
   1. If the coin came up heads, you will get your £1 back and I will give you £2 of my own. So you’d gain a £3 total
   2. If you choose to play and the coin comes up tails, I’ll keep your £1
   3. If you choose to pass, no money will be changed either way

Would you take the bet? Decision theory says you should because of the first principle (maximise your expected value).

So let’s workout the probability using this table.

A coin: ½ 

(£2 x ½ ) + ( -£1 x ½) = 0.5 (Strategy play)

So if you played this bet a number of times every time you would win on average 50p.

Now compare that to passing

(£0 x ½ ) + ( £0 x ½) = 0 (Strategy play)

Since playing has a greater value than passing, you should play, every time.

We don’t usually have precise-like probabilities like this to assign to states. But we have scenarios like “I should do this because it might help or there’s no harm in doing it anyway” or “I’ll do that because there’s nothing to loose and everything to gain”. This is called a weakly dominant theory.

Say you borrow a bicycle of your friend and you drive to the store to buy some snacks. As you begin to lockup your bike you think “this part of towns pretty nice, no one is likely to steal my bike and I will be able to see it from the shop window”. Should you lockup the bike? It’s clear enough you should lockup the bike. Here’s why.

If a thief strolls past, locking is obviously far better. If a thief doesn’t pass buy, locking is no worse than not locking. So locking is a weakly dominant strategy.

Weakly dominant strategy — yields a better or at least equally good outcome

In decision theory, always pick this unless there is a strong dominant strategy.

Strongly dominant strategy — yields a better outcome in every possible state

So Decision theory is how to make good decisions in circumstances of risk or uncertainty. 3 foundational concepts, 2 guiding principles.

Buy this book: Taking Pascal’s Wager