Tyler links to a paper by Michigan State's Jay Pil Choi that effectively demonstrates by way of game theory a point I have long argued by way of what seems to me perfectly common sense -- that there's no damned good reason it should be incumbent upon men to put the toilet seat down:
Imagine a situation in which the aggregate frequency of toilet usage is the same across genders, i.e., the probability that any visitor will be male is ½. With the down rule, each male visit is associated with lifting the toilet seat up before use and lowering it down after use, with the inconvenience costs being incurred twice. With the selfish rule, in contrast, the inconvenience costs are incurred once and only when the previous visitor is a member of different gender. The worst case under the selfish rule would occur when the sex of the toilet visitor strictly alternates in each usage. Even in this case, the total inconvenience costs would be the same as those under the down rule if the costs are symmetric. If there is any possibility that consecutive users are from the same gender, the selfish rule strictly dominates the down rule since it keeps the option value of not incurring any inconvenience costs in such an event.
Of course, in my solitary and hermetic bachelor existence, I can take advantage of the fact that there is a greater than 95% chance that a given toilet user will be male (and will, in fact, be me) to employ the selfish rule full-on. This also leverages another important fact of nature -- that Toilet Operation #1 (requiring an up seat) is roughly four or five times more frequent than Toilet Operation #2 (requiring a down seat.)
However, the grey lining of this silver cloud is that it underscores that the number of female visitors to my abode is small enough to be suboptimal in numerous other dimensions. Whether this is correlated with my failure to employ the down rule, I'll leave to others to determine.
ADDENDUM: Richard Harter offers one possible solution to the cohabitation problem may be to equalize the respective total costs borne by each party, but notes this "requires, however, that Marsha put the seat in the up position after performing a toilet operation some percentage of the time. No instance of this behaviour has ever been observed in recorded history; ergo this criterion can be ruled out."
He also contributes a few additional wrinkles to the puzzle that are worth pondering:
Remark 1: The toilet has an additional attachment called the toilet seat lid which can only be down if the toilet seat is down. When the lid is down the toilet is (or should be) non-functional for toilet operations. Some persons maintain the toilet seat lid in the down position when the toilet is not use. For these persons the analysis in this note is moot. Such persons pay a fixed cost in seat movement for all toilet operations.
Remark 2: Toilets are also used by domestic animals as a convenient source of drinking water unless the lid is down. (See remark 1)
Remark 3: Experimental evidence suggests that almost all bachelors optimize the seat transfer cost, the exception being those who put the seat up after performing a #2 operation.
Remark 4: Folklore has it that Marsha performs more toilet operations than John, hypothetically because of a smaller bladder. John, however, drinks more beer. We shall not discuss his prostate problem.
Remark 5: “Readily seen” in this context means “It looks obvious but I don’t know how to prove it; you figure it out.”
Remark 6: The toilet lid solution is to put the toilet lid down after all toilet operations. This solution imposes a cost of 2C on each party and is accordingly more expensive. It is, however, more esthetic. It also eliminates the “doggy drinking” problem.
All worthy points, but I see a frame of reference problem in #6. It would count as a benefit the reduced "ick" factor enjoyed by Fido's owners, but fails to account for the pooch's lost utility in having diminished access to a cool drink of water.
Being married and thus a victim of this atavism, I practice #6 for nothing more than a small and pathetic bit of vindication.
Posted by: mock | February 19, 2006 at 09:41 PM