# 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!

# Jewesses in Skirts

Let me explain. Among Orthodox Jews, many of the women refuse to wear pants – they will only wear skirts of knee length or longer. Yet the reason for this practice is not so clear. Many reasons are given by different people. I’ll list a few, along with a sentence about why I don’t think they make so much sense:

(i) Modesty: Pants are immodest because they are form-fitting to the leg. Yet there are many other parts of the body for which clothes that are just as form-fitting are fine, yet are equally not allowed to be uncovered under Orthodox Jewish law. Besides, no one said you had to be wearing skinny-jeans.

(ii) Men’s clothing: Under Biblical law, women may not wear men’s clothing. Yet by now, it is normal for women to wear pants. Indeed, most Orthodox rabbis agree that this is not the main reason.

(iii) Suggestive: Certain parts of the pants might be sexually suggestive. If this is a problem for women, this would then definitely be a problem for men.

You might be asking yourself at this point: “What the heck does this have to do with game theory?” Well, I actually have a good reason for why many Orthodox Jewish women wear skirts, and it involves a perfect Bayesian equilibrium of an extensive form game.

We divide Orthodox Jews into two classes, each of which holds different communal standards. The first group adheres to a rather stricter standard, which may include certain norms about interactions with men, more stringencies regarding keeping kosher, etc. The second group is a little bit more laid back, though they may also be fully observant according to what they believe is necessary. I’m not making any claims about which one is better – I don’t want to go there – just bear with me.

Orthodox Jewish women in each class prefer others to recognize that they are in the correct class. This is perfectly understandable – one in the first class would not like others to offer food that didn’t meet their standards of keeping kosher, or would not appreciate certain advances from men; one in the second class might not appreciate being pressured into adhering to (from their perspective) unnecessary strictures. We therefore assign each class a payoff of C for being correctly labeled, and W for being incorrectly labeled, where C > W. For similar reasons, other Orthodox Jews would want to correctly label Orthodox Jewish women into these two classes.

To complete the model, we condition the beliefs of other Orthodox Jews on the signal of whether a given woman will wear only skirts (we assume that they can tell if they only wear skirts some of the time). If yes, they place her in the first class; if no, they place her in the second. Since having to only wear skirts is a restriction on the fashion choice of women, we’ll assign a modest loss of payoff (S) for only wearing skirts, where C – W > S.

Given their belief structures, other Orthodox Jews will assume that if you wear a skirt, you’re in Class #1; if you sometimes wear pants, you’re in Class #2. Knowing that others have this belief, the best strategy for Orthodox Jewish women is to actually always wear a skirt if they are in Class #1, while to not bother if they are in Class #2. In this way, the beliefs of others are self-fulfilling in the dress code of Orthodox Jewish women.

Of course, this model isn’t always true – I’m sure there are some people who have strong reasons (aside from those mentioned here) to choose to deviate from the equilibrium path described in this model. Yet I think this actually, to a large extent, gives the most compelling, and most credible, reason for why this dress code exists.

# Bidding up blood

Mexican drug cartels, which control the tremendously lucrative flow of drugs into the US, have over the past several years begun to kill civilians with impunity. Bodies are displayed in public, severed limbs have been tossed onto dance floors, and the total body count continues to rise.

Until recently, civilians and children were off limits in the cartels’ informal codes of honor. The willingness to kill civilians was a signal of ruthlessness, to inform citizens and each other who is winning the war[1].

As of 2010, the Mexican drug cartels have formed two tenuous alliances against each other, one composed of the Juárez Cartel, Tijuana Cartel, Los Zetas Cartel and the Beltrán-Leyva Cartel, and the other, the Gulf Cartel, Sinaloa Cartel and La Familia Cartel [2].

To see how the two alliances might be bidding up the violence, we can first model the civilian killings as an all-pay auction. After all, the cartel incurs some cost for each civilian it kills regardless of whether it wins, and the alliance that has the most kills at the end of each period becomes the more feared of the two among civilians.

In the classic War of Attrition game, the only Nash equilibrium outcomes are that one player bids 0 and the other bids V, the value of the territory under dispute for the period. This implies that we should see in any given time period a large number of killings by one alliance and none by the other, and perhaps the territory would switch hands from period to period (as is one solution for repeated Battle of the Sexes). The expected utility for each alliance should be 0. Alternatively, each cartel has a probability distribution over [0,N] for when it will stop killing civilians. If this is a good model, then the increase in killings might be explained by the decrease in cost of killing civilians (law enforcement is getting less effective).

In the war of attrition game, once both players have made a positive bid, any victory will be a Pyrrhic victory — the expected payoff will be negative. Consider the classic example of the all-pay auction for a $20 bill — if one player bids$20 and the other, $0, they both get a payoff of 0. If one bids$20 and the other, $2, then the player who bids$2 will be forfeiting $2 anyway and might as well bid$22 and win the money. But, now the first player is out $20 — he would lose less if he could get by with winning with a bid less than$40. At some point one player should just take the hit and exit with a negative payoff.

So, the body count continues being bid up as long as both alliances continue to kill civilians on every turn — and this is in fact the case. One explanation might be that the killings are not simply a signal to the civilian population, but also a signal to the other alliance.

We can consider a three-period game:

1. Each alliance finds out whether it is strong or weak
2. Given the first, each sends a signal (kill many or kill few)
3. Each decides whether to attack the other, or to defend. Nonaggression only occurs when both defend.

Each alliance must assert that it is “Strong” type rather than “Weak” type in order to maintain a foothold on the piece of territory. If a strong alliance believes the other alliance is weak on a period, it should attack and take over, since the weaker alliance cannot afford to retaliate.

 Alliance j is strong Attack Defend Attack -2,V -2,V Defend -2,V 0,0 Fig. 1: If Alliance i is weak, j is strong
 Alliance j is weak Attack Defend Attack -1,-1 -1,-1 Defend -1,-1 0,0 Fig. 2: If both are weak
 Attack Defend Attack -2,-2 -2,-2 Defend -2,-2 0,0 Fig. 3: If both are strong

We see that if you are weak, your subgame perfect equilibrium strategy in the last stage is to defend regardless of your opponent’s strength. What signal should you send? Since killing might be costly for a weak alliance, a strong alliance will never send a signal that it is weak (killing few people). Therefore, if the opponent receives the signal that few civilians were killed, he knows that this is a credible signal of weakness.

A weak alliance might signal from the set {many kills, few kills}. Since the players are in identical situations at t=0, their probability p that each will be strong or weak, the probability q that they will give a false signal if weak, and the additional cost c to a weak player giving a high kill signal will be the same. Expected payoff for the weak alliance if it sees a high kill signal is

(q)[mi(strong|many)U(strong, many, defend)+mi(weak|many)U(weak, many, defend)-c]+(1-q)(-2)

= (q)mi(strong|many)[mj(strong|many)(0)+mj(weak|many)(-2)-c]+mi(weak|many)(0)+(1-q)(-2)

= (q)mi(strong|many)[mj(weak|many)(-2)-c]+(1-q)(-2)

It turns out that if sending a false signal is costless, then q is maximized at 1 and we have a pooling equilibrium. If it is costly enough, then there is a separating equilibrium (weak alliance sends low signal, strong sends high signal). What it means for our cartels is that as long as there is a pooling equilibrium, both sides will definitely enter a war of attrition and bid up the body count even beyond their valuations for the territory. It is when the cost of killing just one civilian becomes high enough that it creates a separating equilibrium that the weak alliance doesn’t kill anyone, and the strong alliance kills one[3]. Needless to say, without an honor code to raise this cost, and given the state of Mexican law enforcement, this is quite unlikely.

Thanks to Jeffrey Kang for bouncing ideas around with me.
————————-
[1] http://www.washingtonpost.com/world/mexican-drug-cartels-targeting-and-killing-children/2011/04/07/AFwkFb9C_story.html
[2]”Violence the result of fractured arrangement between Zetas and Gulf Cartel, authorities say”. The Brownsville Herald. March 9, 2010. Retrieved 2010-03-12.
[3] Why one? Because people are discrete. If the separating equilibrium were at 2 kills, then 1 kill might be a possible low signal, in which case the players may enter a war of attrition anyway.