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A game theoretic approach to the toilet seat problem

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Re: A game theoretic approach to the toilet seat problem

#42
Sometimes, when you apply real-world numbers, a single forcing function overwhelms any other subtleties in the analysis. The analysis in this case fails to address the extraordinarily high cost of nagging John must endure when Marsha is inconvenienced N(J) as opposed to the other way around. Since N(J) = K * N(M), and K is never less than 50 IMO, strategy M will be the winner. Always.

Re: A game theoretic approach to the toilet seat problem

#43
This analysis misses a very important point - Marsha benefits from John lifting the seat since this avoids it getting dirty (assuming they take turns using the toilet and John is not a very accurate shooter).

Moreover, John is probably going to perform #1 more frequently then #2 - by a factor of 3-4? Thus, we can further stipulate that his default state should be 'seat up' and ask whether Marsha should be made to lift the seat up after she is done.

Re: A game theoretic approach to the toilet seat problem

#44
post #43

This analysis misses a very important point - Marsha benefits from John lifting the seat since this avoids it getting dirty (assuming they take turns using the toilet and John is not a very accurate shooter). Moreover, John is probably going to perform #1 more frequently then #2 - by a factor of 3-4? Thus, we can further stipulate that his default state should be 'seat up' and ask whether Marsha should be made to lif…

I think you need to reread the article:

1) The analysis assumes that John ensures the seat is in the up position before #1; if the seat is up he pays cost 0 and if it is down he pays cost C. Furthermore if John performes #1 with the seat down, the question of the final position of the seat is moot compared to the question of "why is John gross?"

2) The article takes the probability p of #1 for John. It notes that if p < 1/2 then Marsha's strategy is actually good, but this is clearly not the case

Re: A game theoretic approach to the toilet seat problem

#46

Heh. My simpler solution is to just always sit (I'm a guy). It's more comfortable, requires less concentration and removes any possibility of missing. The only time I stand is for proper urinals.

I grew up with three brothers and my mom enforced this rule because she was sick of cleaning the toilet and bathroom and four boys had been in and out all day.

Re: A game theoretic approach to the toilet seat problem

#47
post #9

Or place a coin near the toilet and flip it after use (and washing your hands). Use the coin to determine a new random seat position thus causing randomized nuisance for everyone.

The cost of coin flipping is probably more than the cost of seat position transfer.

Re: A game theoretic approach to the toilet seat problem

#48
post #47
post #9

Or place a coin near the toilet and flip it after use (and washing your hands). Use the coin to determine a new random seat position thus causing randomized nuisance for everyone.

The cost of coin flipping is probably more than the cost of seat position transfer.

Simple: Install a random number generator and a light, connected up to the handle. When you flush, if the light goes on, put the seat in the down position, if it's off, put it in the up position.

Re: A game theoretic approach to the toilet seat problem

#49
post #6

"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." I thought it was a pity that he skipped this one. He was otherwise really quite thorough!

My observations also hold, I have never once had evidence that a woman has raised the seat. Leaving out this possibility is on the same level as assuming that things fall downward or that the sun rises in the east.

(Honestly, though, who doesn't check the state of the seat before commencing operations? What sort of fairyland would you have to be living in?)

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