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Wednesday, March 09, 2005

Bathroom Justice! 

Ok, I've blogged enough about politics and religion. It's time for a really controversial issue...

If a bathroom is shared among male(s) and female(s), should the toilet seat always be put down, or should it stay where it was after its last use?

(Let's assume this is a private bathroom; so the issue is one of practicality, rather than presentability. Even if it isn't, it's easy enough to change the policy when entertaining.)

The first question that comes to my mind when considering which policy is best is "Which policy requires people to adjust the seat position the most?"

Let's call one policy AD (Always Down) and the other candidate policy CWN (Change When Needed). There are other potential candidates, but I think these are the main interesting ones.

Even without going through the gory details of the math, I think you can see that the answer is that AD requires more seat adjustments.

In AD, all of the seat adjustments are driven by a male urinating. Whenever this happens the seat must be raised before use, and lowered afterwards. So the number of seat adjustments in a day is twice the number of male urinations in a day (let's call M1 the event and m1 the average number of M1 events in a day); so we have 2m1.

At first, I suspected that CWN would be better unless the ratio of females to males rose above a certain point, and then AD would be better. But, that turns out not to be the case.

In CWN, the worst case is also 2m1 (two adjustments for each M1, but at different times). But, if there are ever consecutive M1 events, we save two adjustments (one after the earlier M1 and another before the later one) In most cases, I think CWN will yield a number significantly below 2m1, but as we change the scenario (e.g. by adding females to the environment) to increase the frequency of non-M1 events (F1, F2, M2), consecutive M1s will become less and less frequent and we approach 2m1 as a worst case limit.

Note also that the answer to another interesting question: "On whom does the burden of adjusting the seat fall under each policy?" is that under AD the entire burden falls on the male(s), and under CWN at least half of the burden falls on the male(s) (because it will always be a male who raises the seat, and it will sometimes be a male who lowers it), and some falls on the females.

So, it seems that CWN is superior to AD with respect to both seat-adjustment effort, and a more equitable sharing of the seat-adjustment burden. AD imposes the entire burden on the males, and the burden is higher than what CWN divides between the genders.

"OK" I can hear some women saying, "But the issue isn't just seat-adjustment effort. It's also the effort to remember to check the seat before using the toilet. How does that compare?"

I'm glad you asked.

Under AD, the remembering burden is also proportional to 2m1 (the male(s) remember to check and raise (sounds like poker!) the seat before M1 and remember to lower it after M1). Once again, the entire remembering burden falls on the males. Females can just sit down with confidence.

Under CWN, everyone has to check before each use, but nobody has to remember to make an adjustment afterwards. So for males the number of checks is m1+m2 and for females it's f1+f2. Since I think it's fair to assume that m1>m2, this is better for the males than 2m1. And, the burden is similar for the females (compared to males) assuming that they use the toilet approximately the same number of times throughout the day. Admittedly, under CWN, the total number of rememberings will be more than under AD if 2m1<(m1 + m2 + f1 + f2), which will probably happen whenever there are more females than males, but the burden will be shared and it will be better for each person under CWN than for the average male under AD.

So, in conclusion, it seems clear to me that CWN is superior, in terms of both efficiency and burden-equity, to AD.

So, ladies, will you do the reasonable thing and agree to a CWN policy?

Or, will you stubbornly insist on AD?

UPDATE: Glen Whitman applies some Coasean analysis to the problem...