PART IV OF VI MAY 23, 2005
by Caitlin DowlingLEGAL RIGHTS AND THE MATERNAL-FETAL CONFLICT. By Linda TranINTRODUCTION TO PHYLOGENETICS.By Faride UndaELSEWHERE AND OVERHEARDby Caitlin Dowling | A GAME THEORETIC APPROACH TO THE TOILET SEAT PROBLEMBy Richard Harter The toilet seat problem has been the subject of much controversey. In this paper we consider a simplified model of the toilet seat problem. We shall show that for this model there is an inherent conflict of interest which can be resolved by a equity solution. The incremental costs (difference between pre and post habitation costs) are: John: ( p - 1/2)pCMarsha: pC/2 Total: (p^2)C John's incremental cost would actually be negative if p were less than 1/2. This is not the case; p>1/2. Note that Marsha's incremental cost is greater than than John's for p<1. Marsha objects. Consequences of strategy M: In strategy M the seat is always left down. When John performs operation #1 he lifts the seat before the operation and lowers it after the operation. The respective average cost of toilet seat transfer operations is: John: 2pCMarsha: 0 The incremental costs are: John: 2(p^2)CMarsha: 0 Total: 2(p^2)C In these strategy Marsha bears no cost; all of the incremental costs are borne by John. John objects. Note also that the combined incremental cost of strategy M is greater than that of strategy J. It is notable that John and Marsha each advocates a strategy that benefits them. This is predictable under game theory. However the conflict over strategies has a cost M in marital discord that is greater than the cumulative cost of toilet seat transfers. It behooves John and Marsha, therefore, to adopt a strategy that minimizes M. This is not simple. A common reaction is to advance sundry arguments to justify adopting strategy M or J. All such arguments are suspect because they are self serving (and often accompanied with the "If you loved me" ploy.) A sound strategy is one that is equitable and is seen to be equitable. In this regard there are three candidate criteria: (1) Minimize the joint total cost (2) Equalize the respective total costs (3) Equalize the respective incremental costs The argument for (1) is that John and Marsha are now as one and it is the joint costs and benefits of the union that should be considered. This principle is not universally accepted. It is readily seen that (see remark 5) that the joint total cost is optimized by strategy J which has already been seen to be suspect. Criterion (2) seems plausible. It 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. (But see remark 6.) Criterion (3) argues that the mututal increased cost of toilet seat operations should be shared equitably, i.e., neither party should bear a disproportionate share of the costs of cohabitation. A short calculation reveals that criterion (3) can be achieved if John leaves the seat up after performing toilet operation #1 with a frequency f = (2p-1)/p Since the value of p is seldom precisely measured and is variable in any event it suffices to use an approximate value of f. If we assume that p=2/3 then f=1/2. This suggests the following convenient rule of thumb: In the morning John leaves the seat up after performing #1. In the evening he puts it down. This rule may not be precise but it is simple and approximately equitable; moreover the use of a definite rule sets expectations. The seat is put down in the evening to avoid the notorious "middle of the night surprise". I expect that this analysis should settle the toilet seat controversey for once and for all - if John and Marsha are mathematicians. * * * 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.
| For those that prefer a print version, please download our beautiful pdf file. (part i pdf) (part ii pdf) (part iii pdf) home (again) about (us) archive (of stuff) submissions (or suggest) notes (on masthead) bioteach (.ubc.ca) THE SECRETS OF PARENTING THAT NO ONE WILL TELL YOU.By Russell Bradbury-CarlinA GAME THEORETIC APPROACH TO THE TOILET SEAT PROBLEMBy Richard HarterWHEN CELEBRITIES, WHO HAVE BEEN CLONED IN THE MOVIES, GET TOGETHER FOR A COFFEE.By David NgTHE CRAIGSLIST EUTHANIST THEORY.By Brian Sack PICK A NUMBER BETWEEN ZERO AND INFINITY...By David J. Chalmers |