What are the odds at any given moment that the feeling is mutual?

100% Now go break the ice.

There is a way to work it out mathematically, although it required a BIG assumption and would probably require a lot of research to get an accurate figure.

Let’s assume that the average person will think that 10% of the people he/she meets are attractive enough to be interesting. The other 90% are too old, too young, not their type or just plain ugly. Let’s also assume that the second person thinks the same.

This makes a 10% x 10% = 1% chance that any two random people sitting together on the bus are going to find each other mutually attractive.

I’ve heard it is 100% when a touch of MDMA is involved.
The next morning it is still 100%. Unfortunately the feeling is usually “revulsion”.

@downtide There is no way they are independent. If X is Y’s age range, there is a higher chance that Y is in X’s age range. So, if
Pr(Y likes X) = 10%
we can be fairly sure that
Pr(Y likes X | X likes Y) > 10%.

@roundsquare While it may be true that @downtide‘s equation is overly pessimistic, yours seems overly optimistic. One confounding factor is the fact that there are small sets of people towards whom a lot of attraction is felt but who return little, if any, of that attraction. Think of the set {Jessica Alba, Megan Fox, Angelina Jolie, Keira Knightley, Natalie Portman}, for example, or the set {George Clooney, David Duchovny, Johnny Depp, James Franco, Brad Pitt}.

If you’re talking about strangers sitting next to one another than the chances of having the feeling of attraction are pretty good. Once the people speak, move, share details of themselves then that initial attraction can super quickly rise or go down or away.

@CunningLinguist Just to be sure… are you sure you read my equations correctly? The reason I ask is because the two statements ” @downtide‘s equation is overly pessimistic” and “yours seems overly optimistic” cannot, in fact, both be true. My equations would imply that the probability of mutual attraction is over 1% (using @downtide‘s premise for there being a 10% chance of attraction).

To be clear: I did not write that the probability of mutual attraction is 10%.

Pr(Y likes X | X likes Y) means “the probability that Y likes X given that X likes Y.”

@roundsquare Your statement says that the probability of the feeling being mutual is greater than 10%, while @downtide‘s equation says the probability of the feeling being mutual is 1%. Was ”>10%” a typo?

My 10% figure was a wild guess. But I do see @roundsquare ‘s point too – if B is within A’s preferred age-bracket then A is more likely to be in B’s age-bracket too.

I’m going to say 50% for this reason. You, me and everybody else are either attracted to, or not attracted to every person that we meet. And so is everybody else.

A bit better than 50%, especially in summer.

@CunningLinguist “Your statement says that the probability of the feeling being mutual is greater than 10%, ”
Not true. You are misreading my notation. The vertical bar between “Y likes X” and “X likes Y” means “given that.” So, I’m saying that if X likes Y then the probability that Y likes X is greater than 10%. Maybe its 11%. Then, the probability of mutual attraction is 1.1% (greater than 1%).

@Kardamom That does not actually make sense. It’s actually a very common logical fallacy that confuses the binary of actuality with the more complicated notion of probability.

@roundsquare But the feeling is only mutual when X likes Y and Y likes X. So the probability that Y likes X if X likes Y is the probability that the feeling is mutual. This is the trouble with word problems: what the English actually means and what mathematicians think it means are often not the same thing.

@CunningLinguist I wasn’t really trying to put the answer into a real mathematical formula, because with human attraction, it just doesn’t work that way. That’s all. I was just saying that you have just about as good of a chance of the other person being attracted to you, as not. All things being equal, which that is never the case anyway.

@CunningLinguist Okay… lets break this down.

1) Mutual attraction between X and Y = “X likes Y” AND “Y likes X”
2) The OP is asking for Pr(Mutual attraction between X and Y)
2a) So, the OP is asking for Pr(“X likes Y” AND “Y likes X”)
3) @downtide stated as an assumption that Pr(“X likes Y”) = 10%.[1]
3a) Thus, Pr(“Y likes X”) = 10%
3b) So, says @downtide (originally)
Pr(“X likes Y” AND “Y likes X”) = Pr(“X likes Y”) * Pr(“Y likes X”) = 10% * 10% = 1%
4) My point is
4a) Pr(“X likes Y” and “Y likes X”) = Pr(“X likes Y”) * Pr(“Y likes X” | “X likes Y”) The difference between what I am saying and what @downtide originally said is in bold [2]
4b) Then, I said that Pr(“Y likes X” | “X likes Y”) > Pr(“Y likes X”) because of age range compatibility [3]
4c) Thus, Pr(“Y likes X” | “X likes Y”) > 10%. (For the sake of argument, say Pr(“Y likes X” | “X likes Y”) = 11%).
4d) Thus
Pr(Mutual attraction) = Pr(“X likes Y” AND “Y likes X”) = Pr(“X likes Y”) * Pr(“Y likes X” | “X likes Y) = 10% * 11% = 1.1% > 1%

At what point in this line of reasoning are you disagreeing or considering to be overly optimistic?

[1] This was just an assumption to show the method of calculating. I don’t think @downtide is particularly tied to this number.
[2] This is conditional probability
[3] One can reasonably disagree with this statement. But, as far as I can tell, this is the only part that can be disagreed with. In fact, debate about this statement here is the key to the OPs question.

What I was saying is that you should have made 4d explicit because it’s absence makes it look like you’re saying something other than you now say you are saying. Really quite simple.

Don’t underestimate common unconscious associative memory. So the odds are higher than you think.

@roundsquare I’m not particularly tied to that number at all, it was just a wild guess, based loosely on the proportion of people I find attractive when I’m out and about.

@mattbrowne what is common unconscious associative memory, and how does that have an effect?

@downtide That’s what I figured. Its so hard to come up with a single number anyway (though I suppose, in the end, one can do a weighted average).

@downtide – Here’s an example:

Picture a man and a women in a car talking about politics. They pass a building made of clay brick (which is kind of unusual in the area) without noticing it. Well, their conscious minds don’t notice it. All of the sudden the man says, hey, I’m hungry, how about some pepperoni pizza tonight. The woman turns, astonished. Hey, I just thought the same thing. Pepperoni pizza. Telepathy? Looks like it. But it’s not. Scientific explanation: associative memory. Both their unconscious minds noticed the building made of clay brick they just passed. Six weeks earlier they had a wonderful evening in a different town and ate pepperoni pizza in a nice building made of clay brick. The sex later that evening was great.