Jeff’s post last Sunday on Jewesses in Skirts got me thinking, how is it that we have Orthodox Jewish communities that are tolerant of pants-wearing by women, and communities that are not tolerant of pants-wearing, but rarely a community with large factions of each type? The question, of course, applies to more than just skirts worn by Jewish women – we can talk about many aspects of our culture, such as our changing views on LGBT people, or miscegeny, or a gold standard vs. silver standard using the same language.
We’ve established that, assuming that the types of women in the previous post are static (that is, Nature or Circumstance assigned you to one group and you can’t change allegiances), that it is optimal for the more conservative group to adhere to skirt-wearing, and the other group not to bother. Those static proportions of types in the population affect how the “others” in Jeff’s game form their prior beliefs about which type a woman is based on her choice of clothing. But, what if the women could choose or change their ideology, and what if we consider the effects of judgement and peer-pressure?
In the following model, we can look at a scenario where the proportion of each type of player in the population is endogeneous. Suppose that a new community forms, consisting of some random number of “conservative,” skirts-only types (Jeff puts them in class 1) and some number of “progressive” types who sometimes wear pants (Jeff puts them in class 2). This represents what we would expect to happen if everyone formed their own opinions and ideologies totally independently of everyone else. Each person will randomly encounter other members of the community on a one-on-one basis, and receive social payoffs from the encounter. If she encounters a likeminded person, they both feel validated in their choices, and if not, they feel judged. As before, we assume some disutility for a restriction on wardrobe.
Now, say that the population starts out with a percentage of progressive types and of conservative types. Then, assuming that the population is large, if you are one of the members, then of the people you meet, will be progressive and will be conservative. Therefore, if you are a woman who chooses to be conservative and wear only skirts, your expected utility is and if you choose to wear pants, then your expected utility in any one encounter is . You would be indifferent if — that is, if (the fraction of progressive types) is 1/3.
Maintaining is incredibly difficult, because it is so sensitive to shocks. If for any reason becomes a little more or a little less — say, a contingent of pants-wearers suddenly move in — the balance would tilt and one of the ideologies would start providing the better payoff, the whole population would start snowballing in that direction, and it would become the predominant convention (or evolutionarily stable state) . That may be why these larger faction groups tend not to exist in real life: they are a lot like a flipped coin that lands on its edge.
So what kinds of things affect what is? The payoff matrix, obviously, and how I’ve assigned the payoffs. No one said that I must assign those particular numbers (and indeed, I don’t. The numbers that go into those matrices don’t really matter. What matters is their order of size and relative distance to each other. Try it: multiply all of the numbers by a constant, or add a constant to all of them. The solution should be the same.) What if the inconvenience of wearing only skirts is very large? (Imagine replacing the 2s with, say, 5s.) Then, (the tipping point) could be much smaller, and it would take a much smaller group of rebels to send the equilibrium going the other way. Issues like women’s suffrage are like this — they are so significant that a grassroots movement picks up momentum very quickly. If the inconvenience is less, then p would be greater, and if the existing equilibrium is skirts-only/conservative, it would be harder to change. Equivalently, we can think about the effects of mutually judgemental behavior (making the 0s in the matrix more negative). If people are less tolerant when they meet the other type, conventions are harder to change. If they are more tolerant, change is easier.
If you enjoyed the ideas in this post, you may also enjoy When in New York, do as the New Yorkers do, which describes a special, symmetrical case of the kind of game we’ve discussed here.
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.