# State credences as fractions to avoid suggesting false precision

I often find it helpful to think in probabilities and adopt a Bayesian mindset.

As part of that, I sometimes state my subjective probabilities in conversation.

Sometimes people respond skeptically, asking how can you possibly know that?”.

There are several reasons for this. Sometimes, the reason is that they’ve understood my credence to be much more precise than it is.

Two statements:

1. I think there’s roughly a 70% chance X will happen
2. I think there’s roughly a 2/3 chance X will happen

When I say (1), I usally intend to communicate a fairly imprecise credence. That’s to say, I mean something equivalent to (2) i.e. I think there’s something between a 60-73% chance X will happen. But, despite the word roughly”, I find people—especially people who aren’t familiar with the Bayesian mindset—often hear me as expressing a much narrower range, e.g. “68-72% chance”.

If I state the probability as a fraction rather than as a percentage, I am forced to specify the denominator, and this carries a clearer implication about the precision of my credence. It becomes more natural to think that, after a small positive update, I would round things off and state the same credence, rather than making a minor adjustment (e.g. “I now think there’s a roughly 71% chance) 1.

I’m writing this down because it’s a simple improvement I ought to have internalised by now. And also, because I’m starting to think this comms issue may have confused at least one eminent economist, and perhaps a lot of people in finance.

1. I’ve seen this effect in personal conversations with n ≈10 people who weren’t familiar with the Bayesian mindset. I think there’s about a 2/3 chance that it’s real. I would have thought that Tetlock or some science communication” people would have done studies on this, but I can’t quickly find them.↩︎