You are right. Seems like there is an error in this example and a main problem is not with a prior 1:5 odds, problem is with a bad phrasing and confusion between “crush when winked” odds and “wink likelihood ratio”.

you get winked at by people ten times as often when they have a crush on you

Is a statement about likelihood ratio (or at least can be interpreted that way) - P(wink|crush):P(wink|!crush)=10:1

And in final calculation likelihood is used and its correct according to Bayes Rule

To change our mind from the 1:5 prior odds in response to the evidence’s 10:1 likelihood ratio, we multiply the left sides together and the right sides together

While a statement

the 10:1 odds in favor of “a random person who winks at me has a crush on me”

is a statement about odds P(crush|wink):P(!crush|wink)=10:1 and to apply a Bayes rule to it as if it is ratio would be a mistake, but i’m guessing it’s just an author’s error in phrasing of this statement.

You are right. Seems like there is an error in this example and a main problem is not with a prior 1:5 odds, problem is with a bad phrasing and confusion between “crush when winked” odds and “wink likelihood ratio”.

Is a statement about likelihood ratio (or at least can be interpreted that way) - P(wink|crush):P(wink|!crush)=10:1

And in final calculation likelihood is used and its correct according to Bayes Rule

While a statement

is a statement about odds P(crush|wink):P(!crush|wink)=10:1 and to apply a Bayes rule to it as if it is ratio would be a mistake, but i’m guessing it’s just an author’s error in phrasing of this statement.