I would’ve expected heterosexuality (&c.) to be an exception. You want your complements to underestimate the odds they can find someone better than you, which suggests pushing the narrative that you’re rare (and they’re abundant).
Suppose that I’m a redhead, along with 10% of the female population, and I want the most attractive possible man to date me (assuming for the sake of the simplicity that everyone agrees on who the most attractive people are, and everyone knows how attractive they are too, etc. etc., as is typical in matching problems). I’m a 50th percentile woman myself. Say that 10% of men near-exclusively want to date redheads, they know this, and the rest don’t at all. Men rate women with their preference of hair higher than all women without it (but otherwise match the general attractiveness rankings; i.e. a man who prefers redheads prefers me to 95% of other women). In the equilibrium with full knowledge for all participants, everyone matches with their counterpart at precisely their level of attractiveness and kind of hair/hair preference (I think this strategy is the only rationalisable strategy by weak dominance, but it’s not the only NE; at the very least the silly equilibrium with all players matching on the first round is a NE).
If I meet a man in the most attractive 1%, and I can convince him that redheads are extremely rare, say 0.1% of the population, I would be able to convince him to date me (since 0.1% of the male population is both more attractive than him and attracted to redheads, and he should expect them to snatch up the female redhead population; a 50th percentile redhead is much better than he can hope for). So it seems like convincing such men that I’m rare would benefit me. But let’s suppose instead that I can press a button to make every man think that redheads are 0.1% of the population. Does this help me? Well, again, if I meet a man in the most attractive 1% who is still single, I’ll be able to convince him to date me. But the chance I will ever meet such a man is very low, since any other redheaded woman can also convince such a man to date them! By a symmetry argument (ie, any strategy I can take, other women can too: the expected quality of dates among all redheads can’t be improved by this and my 50th percentile attractiveness dooms me to a median expected payoff) we can see that my expected match can’t be improved by pressing this button. And indeed my expected match becomes worse: 9.9% of men prefer redheads but believe that they cannot date one, so will consent (if they see a non-redhead of the appropriate attractiveness) to match with a non-redhead. Thus the expected quality of dates among redheaded women decreases, and my expected date quality is worse (also, some non-redhead-prefering men will never match).
So I don’t think it usually helps me to make men falsely believe that I’m rare, since my competition benefits just as much as I do and it makes the average outcome worse for all of us (there are probably ways you can make the numbers work out for the button being better, but I think you’d have to try moderately hard).
On the other hand, if I somehow convince all men that 99.9% of women are redheaded, then my position is improved, since the position of non-redheaded women is made worse (some non-redhead-preferers will accept a redheaded woman, and no redhead preferers will accept a non-redheaded woman) and my position is made better in equal proportion. This is assuming that traits are entirely immutable; if we reverse it and talk about a redhead-preferring man pressing a button that convinces all women that all men like redheads, then the same logic applies and also some women may dye their hair. This effect (people changing their presentation to match what they perceive as common tastes) is the one I wrote the post about.
I would’ve expected heterosexuality (&c.) to be an exception. You want your complements to underestimate the odds they can find someone better than you, which suggests pushing the narrative that you’re rare (and they’re abundant).
I’m not sure this holds.
Suppose that I’m a redhead, along with 10% of the female population, and I want the most attractive possible man to date me (assuming for the sake of the simplicity that everyone agrees on who the most attractive people are, and everyone knows how attractive they are too, etc. etc., as is typical in matching problems). I’m a 50th percentile woman myself. Say that 10% of men near-exclusively want to date redheads, they know this, and the rest don’t at all. Men rate women with their preference of hair higher than all women without it (but otherwise match the general attractiveness rankings; i.e. a man who prefers redheads prefers me to 95% of other women). In the equilibrium with full knowledge for all participants, everyone matches with their counterpart at precisely their level of attractiveness and kind of hair/hair preference (I think this strategy is the only rationalisable strategy by weak dominance, but it’s not the only NE; at the very least the silly equilibrium with all players matching on the first round is a NE).
If I meet a man in the most attractive 1%, and I can convince him that redheads are extremely rare, say 0.1% of the population, I would be able to convince him to date me (since 0.1% of the male population is both more attractive than him and attracted to redheads, and he should expect them to snatch up the female redhead population; a 50th percentile redhead is much better than he can hope for). So it seems like convincing such men that I’m rare would benefit me. But let’s suppose instead that I can press a button to make every man think that redheads are 0.1% of the population. Does this help me? Well, again, if I meet a man in the most attractive 1% who is still single, I’ll be able to convince him to date me. But the chance I will ever meet such a man is very low, since any other redheaded woman can also convince such a man to date them! By a symmetry argument (ie, any strategy I can take, other women can too: the expected quality of dates among all redheads can’t be improved by this and my 50th percentile attractiveness dooms me to a median expected payoff) we can see that my expected match can’t be improved by pressing this button. And indeed my expected match becomes worse: 9.9% of men prefer redheads but believe that they cannot date one, so will consent (if they see a non-redhead of the appropriate attractiveness) to match with a non-redhead. Thus the expected quality of dates among redheaded women decreases, and my expected date quality is worse (also, some non-redhead-prefering men will never match).
So I don’t think it usually helps me to make men falsely believe that I’m rare, since my competition benefits just as much as I do and it makes the average outcome worse for all of us (there are probably ways you can make the numbers work out for the button being better, but I think you’d have to try moderately hard).
On the other hand, if I somehow convince all men that 99.9% of women are redheaded, then my position is improved, since the position of non-redheaded women is made worse (some non-redhead-preferers will accept a redheaded woman, and no redhead preferers will accept a non-redheaded woman) and my position is made better in equal proportion. This is assuming that traits are entirely immutable; if we reverse it and talk about a redhead-preferring man pressing a button that convinces all women that all men like redheads, then the same logic applies and also some women may dye their hair. This effect (people changing their presentation to match what they perceive as common tastes) is the one I wrote the post about.