You probably already like imprecise probabilities
"The chance of rain is 0.50496847", said no one
The idea that our beliefs ought to be imprecise or indeterminate is potentially a big crux for how we should make altruistic decisions. Many people seem to deny that imprecision in our credences is ever rationally permissible, or at least required. But I think that, with a bit of reflection, most people would agree that it would be unreasonable to have arbitrarily precise beliefs about many real-world propositions. This is important because it means that all of the in-principle arguments against imprecision can be set aside, and all there is to argue about is how imprecise our beliefs ought to be in a specific circumstance. In particular, it opens the door to severe imprecision in beliefs about the effects of our actions on cosmos-wide welfare.
You ask your friend: “What do you think’s the chance that it will rain tomorrow?”
Your friend thinks for a moment and says: “That’d be 0.50496847.”
I’d guess that most readers will think that their friend has said something silly. How could they possibly have a probability to eight digits? It doesn’t seem like we should have precision greater than, say, one in a thousand at the very most. Specifying decimals beyond that is totally arbitrary.
Here are some arguments your friend might give in defence of all those decimals:
“People who guess more decimals perform better on average than people who don’t.”
“I’m throwing away information if I don’t use all the decimals that occur to me.”
“If your credences aren’t precise, you’re liable to be money-pumped.”
“If you don’t have arbitrarily-precise beliefs, you end up a radical skeptic / everything becomes permissible.”
“Not guessing more decimals is just giving up!”
Are you persuaded?