Pascal’s Wager Revisited

Incorporating Pascal’s Lighthouse

In a Nutshell

It has become known as Pascal’s Wager.

You have to live your life one way or the other, so in that sense you have to make a bet. The bet is on the existence of God.  If God does not exist and you believe that he does, what have you lost? Something, perhaps, some time, some foregone plans and pleasures. But the loss is finite.

Now what if God does exist, and you have bet against him? Now the consequences could be devastating and they could be eternal.

So we have a small or at least limited cost on one side and a potentially infinite gain or loss on the other.

Pascal’s conclusion was that the sensible bet is obvious.

But is it?

What if we have the wrong God?

One of the best-known objections is usually called the many gods objection.

Human beings have believed in many different gods. Perhaps there is a god who rewards atheists and punishes believers. In that case Pascal’s calculation seems to fall apart.

There is something in this objection, but I don’t think it’s as strong as it first appears. After all, we don’t normally treat every conceivable possibility as equally likely. I can imagine almost anything. That doesn’t mean I should attach the same probability to everything I can imagine.

A conception of God which has been developed over thousands of years, has been examined by generations of philosophers and theologians, and is accepted by hundreds of millions of people surely has a different claim on our attention from a god somebody invented five minutes ago specifically to defeat Pascal’s argument.

We have to apply common sense and make judgments about probabilities.

And this is where Pascal becomes very interesting.

We aren’t very good at thinking about the future

Even if we put religion to one side, there is another reason I think Pascal’s argument is worth taking extremely seriously.

Human beings have a strong tendency to favour the present over the future. Economists call this discounting. Give me £100 today or £100 in twenty years and most people take the £100 today.There is a sense to this. But we often go further. Apparently distant consequences somehow seem less real simply because they are apparently distant or uncertain. When a small probability is attached to an enormous and uncertain future consequence, this can have devastating implications.

We also need to think about what happens if the event occurs at a dramatically different scale or more quickly than we might envisage. 

That takes us from Pascal to climate change.

Noah’s Law

Imagine that we are uncertain but that there is some possibility of a genuinely catastrophic and irreversible outcome to some process What should we do?

One answer is to wait until we know more. But by then, it may be too late to prevent it.

This idea is sometimes expressed as Noah’s Law.

If there is a reasonable chance that a flood is coming, you don’t wait to drown before building the ark. 

The Guardian Principle

Think of humanity as the temporary custodian of something enormously valuable – a planet, a civilisation and the possibility of a future stretching far beyond our own lifetimes. We don’t own that future. We are looking after it for the people who come next.

That, for me, is the essence of what I term the Guardian Principle.

Climate change, a devastating pandemic, technologies capable of causing destruction on a scale we cannot reverse. Sometimes the sensible precautions may be expensive, sometimes surprisingly cheap. But the underlying question is the same.

How much should we be willing to do now to reduce even a small chance of something truly terrible happening later?

Pascal’s Wager gives us one way of thinking about that question.

There is a snag, though.

Pascal gets mugged

I receive an extraordinary offer. Give a stranger £10 and he will somehow arrange for me to receive an unimaginably large fortune tomorrow. Or give him £10 or he will somehow destroy the world.

The probability that he can or will do either is effectively zero. But the consequence is so enormous that multiplying a tiny probability by an astronomical gain or loss can still produce an uncomfortable answer.

This is Pascal’s Mugging.

So something is missing. Yes – there has to be a credible risk. And there will rarely be a neat formula that tells us this or exactly what to do.

But we can’t afford to underestimate the problem nor to underestimate our responsibilities. 

Pascal’s lighthouse

So should we accept Pascal’s Wager?

Well, belief  is not something we can simply switch on because a calculation tells us it would be prudent to do so. But Pascal saw something very important – that we are not always good at dealing with a small probability attached to an enormous consequence. Sometimes we concentrate too much on the small probability and not enough on what happens if we are wrong.

At other times, as Pascal’s Mugging shows, we make the opposite mistake and allow a fantastic consequence to overwhelm an almost nonexistent probability.

The sensible position lies somewhere between the two.

That is where the Guardian Principle comes in. And it seems to me the lasting lesson of Pascal’s Wager – not a command telling us what to believe, but a lighthouse. Not telling us precisely where to steer, but a bright beacon to illuminate the rocks we are foolish to ignore.