Not if you consider that the 1:5 figure constrains that ONLY one person among the six has a crush on you. If you learn for a fact one does, you’ll also immediately know the others all don’t. Which is not true for a random selection of students—you could randomly pick six that all have a crush on you.
Bob belongs to a group in which you know for a fact five people DON’T have a crush on you. So you have evidence lowering Bob’s odds relative to a random winker.
Either that, or it doesn’t matter how many actually have a crush on you, you’re looking for the specific one you have definite evidence about. For thisy, a random winker is not qualified to enter the comparison at all—if they’re not one of the six, they’re not the person you’re looking for. So Bob might have a crush on you AND not be the person you’re looking for, although his odds are higher than those of the other five you don’t have any evidence about.
That’s the interpretations that make the math not wrong, anyway. If you only know that “at least one of them has a crush on me” and more than one could potentially satisfy your search criteria, the 1:5 figure is not the right odds.
“you’ll also immediately know the others all don’t”
No. Receiving an anonymous love note from among the 6 in NO WAY informs you that 5 of the 6 DON’T have a crush on you. All it does is take the unspecified prior (rate of these 6 humans having a crush on you), and INCREASE it for all 6 of them.
@irmckenzie is right. There’s no way you get < 10:1 with MORE positive (confirmatory) evidence for Bob than a random stranger. All positive evidence HAS TO make a rational mind MORE certain the thing is true. Weak evidence, like the letter, which informs that AT LEAST 1 in 6 has a crush, should move a rational mind LESS than strong evidence, like the wink, but it must move it all the same, and in the affirmative direction.
Not if you consider that the 1:5 figure constrains that ONLY one person among the six has a crush on you. If you learn for a fact one does, you’ll also immediately know the others all don’t. Which is not true for a random selection of students—you could randomly pick six that all have a crush on you. Bob belongs to a group in which you know for a fact five people DON’T have a crush on you. So you have evidence lowering Bob’s odds relative to a random winker.
Either that, or it doesn’t matter how many actually have a crush on you, you’re looking for the specific one you have definite evidence about. For thisy, a random winker is not qualified to enter the comparison at all—if they’re not one of the six, they’re not the person you’re looking for. So Bob might have a crush on you AND not be the person you’re looking for, although his odds are higher than those of the other five you don’t have any evidence about.
That’s the interpretations that make the math not wrong, anyway. If you only know that “at least one of them has a crush on me” and more than one could potentially satisfy your search criteria, the 1:5 figure is not the right odds.
“you’ll also immediately know the others all don’t”
No. Receiving an anonymous love note from among the 6 in NO WAY informs you that 5 of the 6 DON’T have a crush on you. All it does is take the unspecified prior (rate of these 6 humans having a crush on you), and INCREASE it for all 6 of them.
@irmckenzie is right. There’s no way you get < 10:1 with MORE positive (confirmatory) evidence for Bob than a random stranger. All positive evidence HAS TO make a rational mind MORE certain the thing is true. Weak evidence, like the letter, which informs that AT LEAST 1 in 6 has a crush, should move a rational mind LESS than strong evidence, like the wink, but it must move it all the same, and in the affirmative direction.