Friday, June 22, 2007

Return to Bathroom Arena

I’ve blogged about toilet-seat norms twice before. Now there is another contribution to the debate. However, I don’t think it’s especially helpful. Shorn of all the fancy game-theoretic jargon (like “trembling-hand perfect equilibrium”), the new article shows two things: (1) The change-when-necessary rule is more efficient than the always-down rule. But we already knew that. (2) If the woman can costlessly punish the man for leaving the seat up, then she can enforce the inefficient always-down rule anyway. The punishment in question is referred to as “yelling,” though we might imagine other punishments.

This is really a “duh” proposition. Everyone knows that female disapproval is what preserves the always-down rule in some households. The question, from the inception of the debate, has been whether such disapproval is warranted.

Moreover, the assumption (implicit in the article) of costless punishment is not justified. Yelling involves an expenditure of effort and time. Alternative punishments might involve the woman placing an embargo on certain activities that she, too, finds enjoyable.

The article says that always-down necessarily prevails, but that’s no longer true once punishment is costly. The analytical question is whether the woman can make her threat to punish credible. This can be difficult, since the punishment will always have to be imposed after the seat has been left up. Yelling thus imposes a cost on the woman (as well as the man) without making her life any easier at that moment.

In a one-shot game – say, if the woman is only a one-night visitor – imposing the punishment is simply not rational, because she will impose a cost on herself with no future benefit. So for the threat to be credible, the man must believe the woman is irrational (and not just broadly irrational, but irrational on this particular matter). She must be willing to yell even if it won’t do a bit of good.

In a repeated game, as occurs during long-term cohabitation, the threat can be credible even if the woman is rational. This is where the game theory gets more complicated. But put very simply, future interactions mean that yelling can indeed affect future benefits, thereby justifying the cost. But the logic breaks down if the end of the repeated game is in sight – for instance, in the event of an impending break-up or divorce. In such cases, the credibility of female threats will crumble, so we should expect the change-when-necessary rule to emerge. This is an empirically testable proposition. Any takers?

UPDATE: Hello, Economist readers! Maybe-Megan-McArdle disputes the argument for the efficiency of the change-when-necessary rule. A few responses:

First, MMM emphasizes the costliness of checking the lid’s position. In the daytime, the cost of checking is negligible – it happens instantaneously upon seeing the toilet. So if MMM’s case for always-down rests upon night-blindness and midnight surprises, then she should immediately concede that change-when-necessary is the efficient daytime rule.

Second, about those midnight surprises. Honestly, I’m just incredulous that women are blindly backing up to their toilets without at least sticking out a hand to locate the seat! I would suggest that this is an inherently dangerous activity, irrespective of the rule for seat-position. In any case, the whole problem can be obviated at a low fixed cost ($3.65) and near-zero marginal cost (about 2 cents/year) by installing a nightlight. With low enough wattage, night blindness is not an issue. Plus, a nightlight has ancillary benefits. Walking around in pitch darkness carries many dangers worse than the midnight surprise.

Third, about gender equity. MMM notes that seat-checking costs are borne almost entirely by women. This is true (unless men pony up for the nightlight – which I, for one, would happily do). But under the always-down rule, the seat-adjustment cost is borne entirely by men. So if men’s advocacy of change-when-necessary is tainted by self-interest, so is women’s advocacy of always-down.

More importantly, as I emphasized in a prior post, there is no necessary conflict between efficiency and equity here. If change-when-necessary is indeed the more efficient rule, then side-payments in the form of cash or foot-rubs could be used to compensate women for acquiescing to the socially optimal rule.

P.S. My interest in this issue is purely intellectual, since in my lone-bachelor household the operative rule is always-down. This is an ingrained but inefficient habit, a consequence of having internalized oppressive gender-biased norms. It being too late for me, I speak only for the benefit of future generations.


Anonymous said...

I don't have any comment on this particular issue, but I can vouch for the accuracy of the principle in other arenas. Specifically, when living together, the tidier partner will pretty much always shoulder the entire cleaning burden, except where she can provide an incentive to her sloppy partner to meet certain minimum standards (e.g., avoidance of yelling, sulking, or other forms of punishment that are only effective in an iterated game). And sure enough, now that my partner doesn't live with me, but only visits, he can easily avoid most of this kind of punishment by not being there, and his tidiness standards have fallen rather dramatically.

Ran said...

Now reading the previous posts: these arguments all make theoretical sense, but there's definitely something irrational going on. I (a man) always put the lid down after I go (well, not in public restrooms, which don't have them, but then, they generally are separated by sex anyway), and no one has ever seemed to mind. No one, so far as I know, has ever accidentally sat on the lid without noticing it was down.

That said, I think there might be a fairness argument for always leaving the lid down. Men don't need to raise the seat to pee: we can sit. (It's horrid to contemplate, but since women have no choice but to do it, it's not surprising that they don't have sympathy.) Alternatively, we can try to aim better, but I don't think anyone would like the result of that approach. :-) Further, it's less gross to put down the seat right before washing one's hands - especially if one has already touched the seat to put it up - than to put it down right before using the toilet. (Of course, this doesn't solve the problem of its being gross to put up the seat before peeing, but I don't see any solution that does.)

Marshall Bolton/Zig said...

I think all you economic guys and girls have got it wrong. Another academic discipline cracked the code a long time ago.

Two sweet words. Penis and Envy.

Small economic matters such as cost and benefit have no influence on the nefarious and varied expressions of this "resentiment".

AD or CWN are just sub-routines in the more general game of attrition. As such there is only temporary appeasement or temporary surrender.

But let me propose two more radical solutions - Cotton Wool or Scissors.

Anonymous said...

Ran: Check out this video.

The English Libertarian said...

I think this article ignores the possibilty of punishments imposed by the male player upon the female player in retaliation for punihshments imposed upon him. If, for instance, the male player were to reduce the female player's monthly shoe budget every time she yelled at him for leaving the seat up, this would incur a cost upon the female player for yelling, thus perhaps making it an irrational course of action, even if there is some benefit to be gained.

Anonymous said...

Wait a minute, how are only women susceptible to the midnight surprise? Isn't the situation symmetrical? If the seat is down, can't men get a "midnight surprise" of their own?

Gil said...

I'm not surprised that women argue for the policy that's in their interest.

But, I'm amazed at how indignant they can get that men have the nerve to challenge it, and to consider whether it's efficient or equitable.

They often (as in the article) make it seem like it reveals an unreasonable bias in men that they do this type of analysis.

The last paragraph in the Economist article is an example of this, and I made a comment there about it.

Anonymous said...

As I mentioned during one of the previous discussions of this topic, "midnight surprises" seem most likely to occur in households that (imperfectly) attempt to follow the Always Down rule. Members of households that don't try to adhere to the Always Down rule are unlikely to attempt a blind sit-down. (Although Glen's suggestion of separate day/night strategies would probably be even worse at this.)

Helen said...

The approach that's worked for us (35 years of marriage) is for everyone to lower not just the seat, but also the lid (seat cover), after every use. It's the same motion to lift either the lid only or the lid plus seat before each use. It's the same motion to lower the seat plus lid, or just the lid after use. No one finds the toilet in position for immediate use. The big advantage is that the toilet is always covered when not in use, so items like hairbrushes, razors, and bars of soap won't fall into it. Avoiding that hassle surely has considerable value.