# Why do women (almost) never ask men on dates?

This is something I’ve asked a few of people about. It seems odd that in our modern, post-feminist age, it is almost always men who do the asking out. This is not so good for both men and women. For men, it puts a lot of pressure on them to make all of the moves. For women, I cite Roth and Sotomayor’s classic textbook on matching, which shows that, though the outcome from men always choosing partners is stable, it is the worst possible stable outcome for women. That is, women could get better guys to date if they made the moves.

I have a few hypotheses, but none of them seem particularly appealing:

1) Women aren’t as liberated as we think.

Pro: There doesn’t seem to be any point in history where this was any different, so this social practice may indeed be a holdover from the Stone Age (i.e. before 1960).

Con: If this is true, then it is a very bad social practice, and we should buck it! This is not a good reason to maintain it!

2) If a woman asks a man out, it reveals information about her. This could be a case of multiple equilibria. Suppose that a small percentage of “crazy types” of both men and women exists, and under no circumstances do you ever want to date one of them. The equilibrium in which we are is fully separating for women, where the “normal types” always wait for men to ask them out, while the “crazy types” ask men out. Since this is a perfect Bayesian equilibrium, men know that if they get asked out, the woman must be crazy, and so they reject. Knowing this, the “normal” women would never want to ask a man out, since it would involve the cost of effort/rejection with no chance of success.

Suppose the chance that someone is crazy is some very small $\epsilon > 0$. Consider the game tree:

Notice that the crazy women always want to ask the guy out, no matter what the beliefs of the guy are.

There are a few perfect Bayesian equilibria of this game, but I will highlight two. The first is that the normal women never ask guys out, and guys never accept. As $\epsilon \rightarrow 0$, this gives expected payoff to people of $(0,0)$. No one wants to deviate, because only crazy women ask guys out, and so a guy would never accept an offer, as that would give payoff $-10$ instead of $0$; knowing this, normal women will never ask men out, because that gives them payoff $-1$ instead of $0$.

Another equilibrium is that all women ask men out, and men always accept. As $\epsilon \rightarrow 0$, the expected payoff vector is $(2,2)$. Thus the former is a “bad” equilibrium, while the latter is a “good” one. In other words, we may be stuck in a bad equilibrium.

Pro: I think that there definitely some guys out there who think that women who would ask them out are “aggressive” or “desparate,” and so they wouldn’t go out with them.

Con: I don’t think the above sentiment is true in general, at least for guys worth dating! If a guy has that attitude, he’s probably an @#0!3 who’s not worth your time.

There may also be some elements of the problem with (1), but these would be harder to overcome, as the scenario here is an equilibrium.

Finally, while this might have some plausibility for people who don’t really know each other yet, I definitely don’t think this is true for people who know each other somewhat better, and therefore would already know whether the woman in question was crazy. That being said, I would expect it to be more likely that a woman who has known the man in question for longer to be proportionally more likely to ask him out (relative to the man), even if it is still less likely.

3) Women just aren’t as interested. If he’s willing to ask her out, then fine, she’ll go, but otherwise the cost outweighs the benefit.

Pro: It doesn’t have any glaring theoretical problems.

Con: I want you to look me in the eyes and tell me you think this is actually true.

4) They already do. At least, implicitly, that is. Women can signal interest by trying to spend significant amounts of time with men in whom they have interest, and eventually the guys will realize and ask them out.

Pro: This definitely happens.

Con: I’m not sure it’s sufficient to even out the scorecard. Also, this seems to beg the question: if they do that, why can’t they be explicit?

When I originally showed this to some friends, they liked most of these possibilities (especially (1) and (2)), but they had some additional suggestions:

5) Being asked out is self-validating. To quote my (female) friend who suggested this,

…many girls are insecure and being asked out is validation that you are pretty/interesting/generally awesome enough that someone is willing to go out on a limb and ask you out because they want you that badly. If, on the other hand, the girl makes the first move and the guy says yes it is much less clear to her how much the guy really likes her as opposed to is ambivalent or even pitying her.

ProThis is true of some women.

Con: Again to quote my friend, “There are lots of very secure, confident girls out there, so why aren’t they asking guys out?”

6) Utility from a relationship is correlated with interest, and women have a shorter window. This one is actually suggested by Marli:

If asking someone out is a signal of interest level $X > x$, and higher interest level is correlated with higher longterm/serious relationship probability, then women might be interested in only dating people with high interest level because they have less time in which to date.

Pro: It is true, women are often conceived to have a shorter “window,” in that they are of child-bearing age (for those for whom that matters) for a shorter period.

Con: This doesn’t seem very plausible. Going on a date doesn’t take very long, at least in terms of opportunity cost relative to the length of the “window.” As a friend put it in response,

Obviously one date doesn’t take up much time; the point of screening for interest $X > x$ is to prevent wasting a year or two with someone who wasn’t that into you after all. But then it would seem rational for (e.g.) her to ask him on one date, and then gauge his seriousness from how he acts after that. Other people’s liking of us is endogenous to our liking of them, it really seems silly to assume that “interest” is pre-determined and immutable.

So overall, it seems like there are reasons which explain how it happens, but no good reason why it should happen. I hope other people have better reasons in mind, with which they can enlighten me!

# Sketchy dating after breakups

(I thought I’d put this post up now, since it relates to a friend’s recent post elsewhere.)

Generally, when people end a long-term relationship, they want to take a bit of a break from dating to get their feet back on the ground. Break-ups can be very emotionally taxing, and recovery takes some time. There are several rules of thumb as to how long one should wait; I won’t go into those, since that’s not the point of this post. What is interesting, though, is that often these rules are not well-kept. The question is, why?

For starters, let’s model a person’s payoff for entering a relationship. Let’s assume for now the person is a woman (also, let’s call her Fiona). Obviously she doesn’t want to enter one immediately after the breakup; but how much she does not want to do so depends on how much time has elapsed. More specifically, the payoff increases, eventually approaching a certain (bounded) value, at which point she is totally over her ex.

(Formally, we assign her a utility function $U(t)$, where $U(0)=0$, and $lim_{t\rightarrow\infty}U(t)=B$, where $B$ is some positive number. For example, when $B=1$, we could have a function like this:)

Fig. 1: sample graph

The guy who wants to ask her out also shares the same payoff (and we’ll call him Scotty). After all, of course he would – he’s only happy if she is, right? Thus it’s better for both of them if they wait longer to start up the relationship.

The thing is, Scotty doesn’t know if other people will have their eyes on Fiona. So, if he wants to lock her up as his only, he’s got to act quickly (by some time $\tau$). Suppose, for simplicity, he’s the first one to arrive on the scene (the same reasoning will apply even more strongly if there are others already competing with him for Fiona’s attention). Other suitors can be expected to arrive at a pretty much constant rate ($r$) if she’s still single. If he’s willing to ask her out by time $\tau$, then they definitely will by a later time ($t>\tau$), since they get an even higher payoff. Fearing this competition, Scotty will ask out Fiona at exactly the point where the gains from waiting are balanced by the losses in potential competition. (That is, $U^{\prime}(\tau)=rU(\tau)\geq0$.)

As the model is set up now, Fiona still has no reason to accept Scotty’s request. But if we introduce a cost of rejection (C) into the model, things change, even if such a cost is small. We can account for this as a natural consequence of social interactions: for example, things might be awkward between them if she turns him down. And no matter what, she cannot get more than a payoff of $B$ later. Thus, she will certainly accept as long as $U(t)\geq B-C$.[1] Though she’d have a higher payoff if he asked later, accepting this request is the best response to his move.

To close things off, I should explain why I assumed initially that the person was a woman. Since even in this age of gender equality, guys are generally the ones doing the asking, women will encounter the possibility of being asked out, even if they are not yet looking around for new opportunities to date. Hence they incur the cost, $C$. By contrast, men might not look until they can get a payoff closer to $B$, without incurring the cost $C$. This makes it more likely that this situation will come up when woman have recently broken up with their boyfriends, rather than with the men.

Obviously, both sides in this equation would rather wait longer to start something up. But it’s just too risky to do so, since they might lose out altogether. So, we end up with much sketchiness. Haaaaaaai!

[1] That is, this is a sufficient condition; she might accept an even lower payoff depending on how frequently she expects guys to ask her out later.