Good point! The formula indeed assumes a base probability of zero. That's actually why I put "The best cafe ever" in there and that it is called an "exceptionally awesome cafe". I got a bit lax later in the text just calling it "awesome".
For a cafe aficionado, who spends most of their time in cafes, reading HN and thinking about formulas, the probability that some random cafe becomes their new favorite is virtually zero.
In other words: The more cafes you already know, the closer to zero the chance that a random one will be the best of them all.
So yeah, it is a formula for cafe lovers. Not for the casual person who is happy with a random filtered coffee swill from the vending machine. Those would have to add a base probability, turning the formula into something like b+n/(n+x)*(1-b).
I think Laplace's Rule of succession [1] could be better here. It assumes there are binary "successes" and "failures" (e.g. thumbs up/down). Let s be the number of "successes", n be the total number of data points (successes+failures), and 1/x the prior probability of a success. Then the probability that the next data point will be a success is:
(s + 1)/(n + x)
E.g. for prior probability 1/2 (success and failure initially equally likely), x=2, so
Interesting philosophical question: is awesomeness intrinsic or extrinsic (a matter of perception)? Can anything be intrinsic?
If it's intrinsic, then yes, the probability that it is awesome should not be zero if you've never heard of it. It's awesomeness exists independently of any measurement. But, by definition, you can't know it's awesomeness until you measure it, so awesomeness quotients only matter after they've been measured. And a measured value value must be expressible/observable outside the system (i.e. extrinsic).
Perhaps you only define the trust function from n=1+