On The Uses And Abuses Of Game Theory For Life

by hilzoy

Via Crooked Timber, an excellent study: The social norm of leaving the toilet seat down: A game theoretic analysis (pdf). From the intro:

"The issue of whether the toilet seat should be left up or down after use seemingly generates a lot of passion among the parties concerned, however, scientific inquiries into the matter are almost non-existent. Notable exceptions are Choi (2002) and Harter (2005). Choi (2002) argues that the rule of leaving the toilet seat down after use is inefficient in the sense that there is at least one other rule that outperform this rule. The unit of analysis in Choi (2002) is the household and the efficient rule is defined as one that minimizes the total cost of toilet seat operations per household. Choi (2002) does not model the issue as a situation of conflict, hence ignores the game theoretic aspects of the problem. Harter (2005) models the situation as a cooperative game and proposes a contract that splits the costs of toilet seat operations evenly among the parties. Both papers agree that the social norm of leaving the toilet seat down in inefficient in the sense that it does not minimize the total cost of toilet seat operations per household. However, both papers fail to address an important concern: If a female finds the toilet seat in a wrong position then she will most probably yell at the male involved. This yelling inflicts a cost on the male. Based on this omission, women may argue that the analysis in these papers is suspect.

In this paper, we internalize the cost of yelling and model the conflict as a non-cooperative game between two species, males and females. We find that the social norm of leaving the toilet seat down is inefficient. However, to our dismay, we also find that the social norm of always leaving the toilet seat down after use is not only a Nash equilibrium in pure strategies but is also trembling-hand perfect. So, we can complain all we like, but this norm is not likely to go away."

From the body of the study:

"Assume that the inconvenience cost of changing the seat position is C. Further assume that the need for #1 arises with a probability p. Let’s look at the average costs to John and Marsha:

The average cost to John as a bachelor

Doing #1 this time when he did #2 last time + Doing #2 this time when he did #1 last time = p x (1 x p) x C+ (1 x p) x p x C= 2 x p x (1 x p) x C (1)

The average cost to Marsha as a bachelorette

Obviously 0 since she performs everything with the seat in the down position."

There are lots more equations where those came from.

Back in grad school, I decided that there were two vital facts that philosophers needed to engrave in their minds and recall on a regular basis:

(1) Occasionally, Wittgenstein was wrong

(2) There are some situations to which game theory cannot usefully be applied.

I leave it to the reader to decide which bears most directly on the matter at hand.

Comments

[Ugh]

Do they factor in the costs from the fact that most men neglect to wash their hands and so a second, post-urination touching of the toilet seat increases the likelihood of germ dissemination?

Why are you looking at me like that?

[Bernard Yomtov]

I promise never to mention game theory again.

[Dantheman]

"(2) There are some situations to which game theory cannot usefully be applied."

This is one of them. Apparently, it is more work for a female to place the toilet seat done before use than the male to do so. As a result, the male must perform the task of putting the toilet seat down.

[Sebastian Holsclaw]

Real answer: in a relationship you have to decide if the value of complying with your partner's wish to avoid their annoyance is worth the annoyance it will cause you to comply.

Is that game theory? Cost weighing? Whatever. :)

[LizardBreath]

I've seen this before, and no one seems to address the real cost of toilet seats left up -- the risk that, in a small bathroom, a woman will enter and attempt to sit without facing the toilet, and will thus run the risk of splashing down.

[hilzoy]

LB: for some of us, it has come perilously close to not being just the risk. That's what comes of living alone in a house where you assume that the policy that suits your needs is the one that will prevail, and don't reckon with the odd visitor.

I take the neglect of this vital issue to show that these papers were all written by guys, since it's pretty obvious to the testosterone-challenged.

[cleek]

Sebastian is right.

men lift it up, euphemize, then put it back down. women just euphemize. nobody gets yelled at. nobody falls in.

[st]

The previous two comments, of course, assign some value/cost to the operation of actually looking at the toilet to see if the seat is up or down. I am not a woman, but even I must occasionally sit on a toilet, and however small the bathroom, I have never found myself opening the door and backing in an spirit of blind hope and pure entitlement.

But that's just me; I understand the laws of game theory are against me.

[Ugh]

the risk that, in a small bathroom, a woman will enter and attempt to sit without facing the toilet, and will thus run the risk of splashing down.

This I never understood, you don't, you know, look before sitting down? I mean, the toilet seat might be up and how will you know without looking? ;-)

[OCSteve]

I've seen this before, and no one seems to address the real cost of toilet seats left up -- the risk that, in a small bathroom, a woman will enter and attempt to sit without facing the toilet, and will thus run the risk of splashing down.

And this would be were I learned once and for all to leave the seat down. Total dark, she was trying to be polite by not turning on the light and waking me up.

The cost was high.

[st]

OCSteve - hmmm. Valid and vividly illustrative example. I may have to reconsider my position.

[Nombrilisme Vide]

H'm. My approach to this quandry would be stereotypically leftist; i.e., it imposes additional (and arguably unnecessary) burdens upon all parties involved, but in an equitable manner: I put the seat and lid down. Thus, any subsequent access to the facility will require equal effort on the part of would-be users of either sex.

[hilzoy]

st: like I said: I live alone. Most of my male friends leave the seat down. I didn't acquire a brother until I was nearly ten, and he didn't run around leaving the seat up either. Therefore, the idea that one might need to look was a late acquisition.

[Nell]

This may be my most heartfelt agreement ever with OCSteve in comments, so let it be recorded. Excellent, on-point anecdote.

[Gromit]

In our home we leave seat and lid down after every use, on account of the cats and dogs. But count me among those who would never place their bare behinds on anything without looking first. After all, what if the male never lifted the seat in the first place?

[liberal japonicus]

Can I mention that these things are the bees knees?

[Anarch]

The previous two comments, of course, assign some value/cost to the operation of actually looking at the toilet to see if the seat is up or down.

Or, in one very memorable case, sobriety.

[Sebastian Holsclaw]

"And this would be were I learned once and for all to leave the seat down. Total dark, she was trying to be polite by not turning on the light and waking me up.

The cost was high."

This is an illustration of one of the most enduring facts about interpersonal relationships: often in avoiding a minor problem we cause a major version of that same problem. Turning on the lights, mildly annoying at worst. I suspect that splashing down caused you to become much more awake.

[bob mcmanus]

In my house, we leave the seat down but lid up, as the dogs require a fresh supply of drinking water.

"Occasionally, Wittgenstein was wrong"

Wittgenstein was never right or wrong, only obscure or passed over in silence.

[Gromit]

Can I mention that these things are the bees knees?

Looking at the "gentle massage feature with cycling motion" I can safely say I'd never turn my back on that contraption.

Also, who is Chloe, and what did she do to deserve having a toilet named after her?

[Ugh]

Can I mention that these things are the bees knees?

lj - in the 5th grade I visited Japan on a two week student exchange program. The first week I stayed with a family who basically had old style squat toilets, but had purchased a sit down top for me and the other student to use during our stay.

During the second week, I had my first, and to this date last, encounter with a high tech toilet. It had a heated seat and everything. When I got up and turned around to flush, it squirted water all over my pants.

[Steven Donegal]

This article is more evidence that as a society we have way too much time on our hands.

[John Thullen]

OCSteve: "..she was trying to be polite by not turning on the light and waking me up."

Yes, but why does make you sleep in the bathroom?

So, I'm over at my sister's-in-law (she's single) at Thankgiving and she has a knitted Santa cover on the toilet seat, which made it heavy in an unbalanced way, and the seat kept slamming down, thwack, mid .... um.... stream.

I had to put my drink down to hold the seat up.

I gained a certain appreciation for the female condition, most notably Marie Antoinette on the way to the guillotine.

I don't know about game theory, but if my experience could be made into a game, we could call it "Flinch", not to mention, "Whoops".

Was Wittgenstein circumcised?

I backed OUT of the bathroom.

[OCSteve]

This may be my most heartfelt agreement ever with OCSteve in comments, so let it be recorded. Excellent, on-point anecdote.

I suspect that splashing down caused you to become much more awake.

Well it gets worse. The cost? She screamed bloody murder. Can’t blame her, being nice to me she did not turn on the light. It was a bit of a uhmm, shock? She screeched like a banshee, followed by a string of curses that would make a sailor on shore leave blush.

A concerned neighbor called 911. Two cops showed up 10 minutes later expecting a domestic violence situation. By the end, the two cops were crying, they were laughing so hard. This was like 3AM. They tried to be serious with laugh tears streaming down their faces.

I am sure the story is still retold in that neighborhood.

Gentlemen, put the damned seat down.

[OCSteve]

So, I'm over at my sister's-in-law (she's single) at Thankgiving and she has a knitted Santa cover on the toilet seat, which made it heavy in an unbalanced way, and the seat kept slamming down, thwack, mid .... um.... stream.

That is just wrong. I have a sister in law that does that. It makes me want to go in the back yard (after dark of course).

[Amanda]

I just moved in with my fiancé this week. We have previously come to what seems the perfect compromise: all parties put both the seat and lid down after toilet use. The problem is that I am the one constantly forgetting this rule and leaving the lid up.

The joys of cohabitation. At least there hasn't been any yelling yet.

[Steve]

Men shouldn't go to the bathroom standing up, not at home anyway. You inevitably splash outside the toilet bowl, whether imperceptibly or otherwise. It's a bad practice.

[Dantheman]

"who is Chloe, and what did she do to deserve having a toilet named after her?"

I am willing to bet it is not someone who remembers the Spike Jones version of the classic song, although in his stage show, after singing the "When I hear the call, I've gotta go" line, the singer would dash to an on-stage outhouse.

[damon]

There's a real movement afoot in Germany to have men sit down to urinate (I almost wrote "ruinate").

My own "logical" proposal, years ago, was that if I (a male) have to put the seat down when I'm done, the female should have to put the seat up when she's done. This imposes a similar burden on all parties, which seemed to me to be an equitable solution. However, the proposal was not well received.

Re the danger of sitting on a bowl with the seat up, I think Wittgenstein was right when he said, "Don't think -- look!"

[Bernard Yomtov]

So, I'm over at my sister's-in-law (she's single) at Thankgiving and she has a knitted Santa cover on the toilet seat, which made it heavy in an unbalanced way, and the seat kept slamming down, thwack, mid .... um.... stream.

I think we have the makings of a deal. Even though I live alone I would personally promise to never leave the seat up if those damn toilet seat covers were outlawed.

[cleek]

In our home we leave seat and lid down after every use, on account of the cats and dogs.

ditto. except, cat.

[Ara]

The real solution is for men to pee like girls.

[bob mcmanus]

"Men shouldn't go to the bathroom standing up"

If it weren't for posting rules, this could approach an Unfogged thread.

As a dude who must celebrate his dudeness by standing tall, I am in a quandary about when and how often to wash my hands. Should I wash before flushing and lowering the seat? But then should I wash the faucet handles?
Maybe surgical gloves and Purex alcohol before and after? Cooties everywhere.

[John Thullen]

The Indian subcontinent has this quandry of the washing of the hands down cold.

Eat with one, take care of the other business with the other. Case closed. Except that I can't ever remember which is which, being ambidextrous.

I once had a respite meal in a swanky hotel in India, after losing most of my body mass to dysentery while traveling about, and I watched the Indian patrons ignore the four forks, three spoons, and three pieces of cutlery on either side of their plates in favor of the hand.

I also spent considerable time squatting over dank holes in cement block "powder rooms", knees locked up, wondering which hand to balance myself with, while hallucinating from various intestinal misunderstandings and wondering when my viscera would give out.

That'll be enough about me.

[John Thullen]

Maybe "quandry" should be "quandary".

If I had hand free, I'd look it up.

[oenophile]

Obviously, none of y'all have little kids running around. Toilet seats and lids are left down so that an unsupervised kid doesn't accidentally fall in. (Their heads are proportionally very heavy, so a curious child could, in fact, fall in head-first.) It's a good habit, considering that even the voluntarily childless will either have children visitors at their own homes or visit homes that feature toddlers.

Furthermore, when a toilet flushes, minute drops of spray are scattered for several feet in all directions. My toothbrush is in that radius. Call me prissy, but I don't want pre-flush toilet bowl contents on it!

[Jackmormon]

Another factor: if one is insomniac and lives with roommates, then putting down the lid entirely muffles the noise of the toilet flush.

[Ugh]

If it weren't for posting rules, this could approach an Unfogged thread.

I had the exact same thought.

[KCinDC]

I'm a lid-down person, but I have to agree with those who are mystified by the idea of sitting down without looking. I wonder whether women are more likely than men to, say, sit on sunglasses left in the front seat of a car.

[Slartibartfast]

I wonder whether women are more likely than men to, say, sit on sunglasses left in the front seat of a car.

I think we just might revive The Age Of The Whoopie Cushion, if true.

[booger]

I just like the fact that the equations used the variables "P" and numbers "1" and "2." That's funny.

[damon]

Hilzoy, just curious: what's something that Wittgenstein was wrong about?

[Ugh]

I think we just might revive The Age Of The Whoopie Cushion, if true.

The fact that there is even such a thing as a whoopie cushion goes to show that the "not looking before sitting" phenomenon is more widespread than might be thought.

[JakeB]

I have a female friend who enjoys throwing the seat down before she sits down. But she is the only woman I've met who says that.

As oenophile points out, any bathroom in which you regularly wash your hands, brush your teeth, etc., is one where you want to flush with the lid down as well. Thus in our household, the seat is always down before usage.

It also seems to me that it's not necessarily that game theory cannot be usefully applied, but I am skeptical that the work of the analysis is worth the results. The amount of physical work involved in shifting the seat position is miniscule, unless you've got severe back problems or no arms or something like that. I find the whole idea of attempting to calculate costs and finding a NE in this case to be asinine. In fact, I'd sort of like to pee on Choi's leg.

[Prodigal]

Ever since I learned that a toilet will, when flushing, fling tiny droplets of water out of the bowl to a distance of up to six feet, the fact that I keep my toothbrush in the same room as one was enough to make me shut the lid before every flush.

[Sebastian Holsclaw]

Ah, but Prodigal, there is the medicine cabinet. Aren't you keeping that closed? Oh, the humanity.

[Radical Centrist]

John Thullen: Eat with the right, clean with the left.

Ditto on the toilet spray thing. Ew.

By the way, this thread has had myself and my coworker in tears of laughter. Thank you all.

[hilzoy]

Damon: Just about all of ethics, for starters.

[Slartibartfast]

As oenophile points out, any bathroom in which you regularly wash your hands, brush your teeth, etc., is one where you want to flush with the lid down as well.

Hm. Well, in the spacious Slartibartfast estate, the toilet is a long, long way from the sink. Sometimes I have to stop and rest halfway.

[Nombrilisme Vide]

I'm a lid-down person, but I have to agree with those who are mystified by the idea of sitting down without looking.

Having lived in a household with young males of the uncoordinated and imperfectly responsible variety (i.e., the sorts who might not even worry about whether the seat is up or down), I too shall chime in my agreement that blind sitting seems a rather bold and potentially messy policy...

[Prodigal]

There's only the medicine cabinet if you've got a bathroom that has one installed, Slarti. Sometimes they just give you the sink cabinet to work with.

[KCinDC]

Oh, come now, if you don't have a medicine cabinet, then where do you put the slot that allows you to stuff razor blades into the wall? (Actually I don't remember the last time I lived in a place with one of those -- probably before I could have needed it.)

[jakebob]

Feng Shui sez: Keep the lid closed when not in use, keep the unclean spirits where they belong.

Sure makes life boring. sigh.

[radish]

Lid down to flush, always, and pee sitting down at home. Aerosolization is inevitable, to paraphrase my fluid dynamicist friend. If you want to pee standing up (maybe just because you can ;-) you go outside in the bushes. Of course we're a lid-down-always household anyway because we don't want the cats drinking out of the toilet.

I've had reason to believe that there's another, subtler, gender issue though. I originally decided to start peeing sitting down when I started having to clean my own @#%! bathroom! When I was little my mom used to take care of it. Then for a while I lived in a house where somebody at some point may have cleaned the bathroom. Or maybe not. But eventually I figured out that the less often you pee standing up the less often you have to clean the toilet.

[TickleMe]

In my pre-teen years, my younger brother and I (I am female) shared our very own bathroom and came to an impass on seat up / seat down.

He posited that it was unfair that he had to do all the work, all the raising and lowering of the seat.

I admitted that he had a point, but told him the, um, "splashing," on the bowl was just nasty to look at.

We, at very tender ages for both of us, came to a consensus (not a compromise) - we agreed that we would each put the lid down when finished.

From that moment on we never had a potty issue with each other.

Cheers.

[Slartibartfast]

pee sitting down at home

Sitzpinkler!

[tzs]

Anyone feel the quoted article will end up as one of this year's IgNobel nominees?

And damn it, I want to see the calculations done 1) with cat in house, 2) kiddies getting toilet-trained in house, 3) large dog in house who has figured how to nudge up the seat to get a drink anyway....

[Prodigal]

Never having had one, KC, I cann't answer the question with anything other than "That sounds cool, whatever it is."

[KCinDC]

Prodigal, here's a bit about it.

[dutchmarbel]

. I originally decided to start peeing sitting down when I started having to clean my own @#%! bathroom!

I actually gave my husband the choice between sitting with me cleaning the toilets or standing and cleaning them himself. I even explained that it is much better, healthwise, to sit (empties the blatter better). He's getting very good at cleaning :)

I try to raise our boys with the rule that they stand in public places, but sit in houses where people live. Results are mixed so far :)

[Slartibartfast]

BTW, and completely not off-topic, has anyone else encountered the cleverly designed urinal that backspatters on you no matter where you're aiming?

Another argument for sitzpinkling, right there.

[Ugh]

Another argument for sitzpinkling, right there.

Everytime you write "sitzpinkling" I think of Mister Mxyzptlk.

[KCinDC]

Not to be confused with Joe Btfsplk.