Prior Beliefs, Unlikely

Here is a Big Red Button:

Don’t press it, wait till the very end of this post.

What do you think the red button does? You might not know what to expect. Still, you will have some ideas, and you will assign more weight to some than others. These are your prior beliefs. Essentially, the ideas plus the degree of belief that you have in those ideas before you go collect more evidence.

For example, you might believe the following. The button very likely prints or displays something; maybe it makes a sound, but that’s less likely, especially if your sound is off; it’s unlikely to cause your computer (or mobile) to catch fire — maybe so unlikely you’d be happy to say that it’s impossible; and yet, I’ll hazard a guess and say you think it’s even less likely that pressing the button will start a world war. (But if it does either of those, don’t blame me.)

Since something can’t be less probable than impossible, you have two options: you can say that it’s impossible for the button to either cause the computer to catch fire or for it to start a world war; or you can assign a higher probability to the computer catching fire. It doesn’t have to be a big probability. Maybe 1 in a quadrillion.

But does it make sense to say that it is more likely to cause the computer to catch fire than to start a world war at all? *

It will depend on your background beliefs, but for most people, the answer is a clear yes. That’s because we can think of more plausible situations in which (say) the red button is the last straw that leads to fire rather than war. For example, perhaps it runs an extremely intensive compute process that causes your compute chips to heat up to extremes, and those chips happen to be extremely dusty and improperly cooled. Improbable but still possible. Common enough for How to Geek to think the following advice necessary: “If you’re reading this because your computer is on fire right now, evacuate immediately.” All that’s needed is for the red button to be the last straw.

But even world wars have last straws, and it is possible, even if incredibly improbable, that the red button would cause a world war — say, by sending a forged email from one dictator to another, disparaging the other’s fashion sense in a particularly haughty tone. So not impossible, just less probable. Let’s say 1 in a septillion, which is pretty unlikely. If this prior belief is a reasonable estimate, and you could find and press ten similar red buttons every second, it would take about 200,000 times the age of the universe before you’d have much chance of one of them causing a world war.

We always assign some probability, no matter how tiny, to some physically possible outcome — that’s just what “physically possible” means. We just might not be explicit about it. So what probability do you think you would give for the red button causing our sun to implode?

But enough about improbable prior beliefs. Now you can go ahead and see for yourself: What does the Big Red Button do? Don’t worry, I know you already pressed it a long time ago.

* We’re dealing with things that are very, very unlikely, so in any realistic decision making situation, we wouldn’t need to spend time weighing up these options; they both fall below the threshold of “useful to spend time and resources thinking about”. But that doesn’t answer the question of whether it makes sense.

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