In the last post, we saw that the choices we make aren’t free. That is, our choices (like how to get to work) are influenced by other things. Sometimes these things are obvious, like the weather or how quickly we need to get somewhere. Sometimes they are more subtle, like whether we had a good sleep. This was a problem when we tried to measure the best outcome of our choice, because whatever influenced our choice might have also affected its outcome.

I noted we could avoid problems with non-free choices by choosing at random. For example, you can flip a coin to decide whether to walk to work or go by bus. If you did that, this would happen:

All of the other influences on your choice would be cut, and replaced by the single influence of the coin toss.¹In the language of Bayesian networks, this is a (perfect) intervention. This solves your problem of trying to measure how long each way to work takes on average, because while something like weather affects both how to get to work and travel time, the coin toss only directly affects how to get to work.

But how do we know the coin toss isn’t also related to travel time in some other way? Maybe something affects the coin toss (and hence how you get to work) as well as travel time. We can even propose something plausible here: maybe your mood and energy affect your coin toss as well as your travel time.

In fact, they almost certainly will affect the coin toss in some way. Worse still, we can never rule out these common background influences, because they are always there. So why isn’t this a problem?

It’s not a problem for our measurement because the coin toss is random. You might be thinking this is a contradiction — aren’t things that are random by definition not influenced by anything? Actually, no. It’s just that the influences don’t affect the probabilities of a random thing. We’ll provide a definition of randomness in the next post to hopefully make this clearer.