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Towards a theory of drama [Oct. 8th, 2012|02:43 pm]
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Imagine a couple who usually have a personal assistant walk their dog. One day the assistant doesn't show up, and late at night just as they're getting ready for bed they realize the dog hasn't been walked. Also, it's an atomic dog, and if it doesn't get walked it explodes, killing everyone in a several mile radius.
"Honey, the dog hasn't been walked. Would you mind walking her?"

"I'm really sorry dear, I've had a busy day and I'm really tired. Could you take care of it tonight?"

"Oh, I'd love to, but I have to go to work really early tomorrow for a big meeting. Can you walk her?"

"I've been up for twenty hours straight, I've had a terrible day, and I just want to go to sleep. Please walk the dog for me."

"It's already 11 and I have to be at the office at 6 AM tomorrow. You don't have to be up until 8. I think this is your responsibility."

Look around you. Yes, look around. Have you figured out what we're looking for yet? That's right. The answer is interpersonal utility comparison.

Interpersonal utility comparison is impossible in principle, but in practice it works pretty well. This couple is trying to determine who will be more inconvenienced by walking the dog. If it became super-clear that one of them would be worse off, the other would immediately concede defeat and agree to the task.
"Also, the flesh harvester is out tonight, so it would probably kill me and make a robe from my skin if I walked the dog."

"What about me? I don't want to be killed either!"

"Silly, the flesh harvester only attacks men. Women are perfectly safe."

"Oh, right. Grumble. I guess I've got to walk the dog, then."

This seems like a very healthy method of solving interpersonal problems. But it doesn't always work. First, it requires some minimal ability to discuss issues reasonably and without screaming. Second, it requires that both sides be rational and trustworthy. It is a notoriously common failure mode to unconsciously overestimate your own interests relative to other people. In fact, it seems like a form of Fundamental Attribution Error: I don't want to take the dog out because I've had a really busy day; you don't want to take the dog out because you're selfish and lazy.

Third, it can get bogged down in more general problems - the failure mode of missing the trees for the forest:
"But I always do all of the work around here! Just this once, you could walk the dog for me!"

"You always do all the work? I've been supporting this relationship singlehandedly from day one!

"Yeah? Well, remember how your 'investments' cost us half our net worth and if we'd kept that maybe we could have paid the personal assistant to come more often?"

"Oh, it's always about the investments with you. You wouldn't lift a finger to help manage our money, but when I do all the work and something goes wrong, you sure are happy to cast blame. And how was I supposed to know that a portfolio consisting solely of Enron, Solyndra, and the Syrian Tourism Board was a bad idea?"

In other words, in sufficiently unhealthy relationships, all conflicts merge into a single conflict about Who Is The Better Person and Therefore Should Get Zir Way On All Disputes. And this becomes vulnerable to self-serving bias, ie the reason that when couples are surveyed both people claim they do 75% of the housework.

I'd like to be able to make a blanket recommendation like "never escalate disputes to a more general principle". But it does seem fair to me that if I have done all the work in a relationship up to this point - I've made all the money, done all the chores, let my partner have her way in every important decision, and so on, whereas all my partner has ever done is screw up and leave messes that I need to take care of - that my partner owes me and it's her turn to walk the dog tonight. All I can say is that if you always have to escalate to the meta-level, that's probably not a good sign.

An economist would intervene here and suggest an auction as the "rational" solution: both sides bid money to have the other person walk the dog, until eventually a bid is accepted.

This has a couple problems. First, most couples are too boring to even consider the idea. Second, many couples share an account, so that whoever ended up with the chore would end out paid in her own money. But most important, it promotes gaming the system.

Suppose I knew that relationship disputes usually ended in auctions. Even if I was perfectly happy to walk the dog and in fact enjoyed it, I might fake not wanting to do so, so that it would end in an auction, I could artificially inflate the price, and end up getting a lot of money for something I would have done anyway.

alicorn24 has set her computer to "notify" her when she gets an IM, which means in practice that her computer irregularly emits very loud BLEEEEEPs every minute or two that frighten me out of my skin whenever I am near her. I asked her to turn this off, and promised that in exchange, she could point out anything I did that annoyed her and I would stop. She very properly expressed concern that this would incentivize me to develop annoying habits.

This same objection covers the proposal to solve the dog-walking problem with rewards, eg "If you walk the dog, I'll do all the chores for the next week." Once again, it incentivizes your partner to lie and feign unwillingness to help.

That leaves punishment. Although this starts off by seeming promising, there actually aren't a lot of good socially acceptable ways to punish each other. I cringe at just the thought of whichever partner makes more money saying "I'm going to cut off your spending money unless you walk the dog now"; no court on Earth would blame that other partner if he immediately filed for divorce. Threatening to pull a "strike" on doing chores and housework sounds less immediately legally dangerous but also super-childish and would probably also get you in trouble. Overall I'm really skeptical of punishment being a good option here either.

In practice, if simple interpersonal utility can't solve the dog walking problem, because the two parties can't trust one another's utility self-reports or because they just don't care, it usually heads to screaming and yelling:
"I can't believe I married a lazy selfish pig who won't even walk the dog!"

"Which of us was the idiot who wanted a @!$%ing atomic dog in the first place, huh? Oooh, it's got a green glow, that's so adoooorable. And I told you you were too irresponsible to take care of it but noooo, you had to have it now, just like you always have to have everything. Spoiled brat."

"Jerk. I hope the flesh harvester gets you!"

I'm not really sure if there's some kind of useful purpose to this, but it could be a pain auction that serves basically the same purpose as a regular auction.

(I want to note that as far as I know, I am the first person to call relationship drama "basically an auction" and the first person to use the term "pain auction")

Imagine an artist who wants to give her painting to the person who wants it most. Although most artists would auction it off using money, this just gets it to the person with the highest desire*money, which may not be the same (and in fact probably is not the same) as the person with the most desire full stop.

One solution is a pain auction. The artist puts all prospective buyers in a sauna, then gradually turns up the temperature until it is painfully, scaldingly hot. Prospective buyers may leave the sauna at any time, but the last person remaining in the sauna gets the painting. The person who wants the painting the most will stay in the sauna the longest and win (given the false assumption that everyone has the same heat tolerance; in reality, ari_rahikkala will get the painting).

Now this is a terrible idea. It shares two of the worst features of the dollar auction. First, everyone sacrifices, not just the final winner. Second, one may sacrifice much more than the prize is worth. Suppose the painting is worth 100 utils to you, and every minute in the sauna costs 10 utils. If you've been in the sauna ten minutes, and there's only one other person in, you may stay in the sauna an extra minute in the hope that he will drop out and you will win, ending up with -10 utils instead of -100.

But it does have some attraction for solving the dog problem. If being in the environment of screams and insults is painful just like being in the sauna, eventually whichever partner hates walking the dog less will break and go walk the dog.

If interpersonal utility comparison doesn't work, a pain auction might be a next-best (by which I mean vastly worse) alternative that solves the same problem.

Next in sequence: no, it's actually much more complicated than that.
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Comments:
[User Picture]From: cartesiandaemon
2012-10-08 10:01 pm (UTC)

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Also, it's an atomic dog, and if it doesn't get walked it explodes, killing everyone in a several mile radius

ROFL, I love the way you present your hypotheticals.

I think the idea for a shared household is something like sharing chores (sometimes including paid work) approximately equally; "trading" chores so each does the chores they're happy to do; with a large reservoir of good will such that there's a lot of scope for doing something nice for each other without needing to feel it's traded back right then; periodic rebalancings to ensure that one partner hasn't accidentally put a lot more work in without either party noticing.

For instance, when you mention trading "giving up habits that annoy the other one", that's a good idea, but I think for lots of reasons it works better if you accept that you're trading similar-sorts of habits, rather than trying to trade one person's "no annoying noises" for the other persons "doing dog walking", because that obscures how much people are actually giving up.

And this may just be how I think of it, but I often think of an ongoing relationship as an opportunity to maximise joint utility with the general hope that that will turn out to be win-win in the long term. For instance, sometimes I do nice things for my partner because I want them to be happy, but for mundane chore type stuff my reasoning is more like "I can do this in less time than they can, so it's a net benefit to do so -- I'm sure they'll reciprocate in similar situations" (although I still worry that more of that falls on them :().
[User Picture]From: marycatelli
2012-10-09 02:15 am (UTC)

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One things couples are warned about is not being willing to do more than 50%. Because you don't know what the other person is doing silently, and really, wouldn't it be worse to be carefully parading everything you do so you can tally them all up?
[User Picture]From: cartesiandaemon
2012-10-09 08:59 am (UTC)

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True: most people probably need to feel you're doing 90% of the work to actually do 50% because what your partner does is often less visible to you. (Although some people probably make the opposite mistake and discount what they do.)

I meant, that's ideally what you end up with as a result of doing things for each other, not that each party should stand around like a straw vulcan saying "You've only done 49.9% of the work so far, I'm not doing any" :)
[User Picture]From: ciphergoth
2012-10-09 09:13 am (UTC)

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I don't know if it is worse. I and my primary partner encourage each other to boast about these things - it's easy not to notice they've been done, and I'd rather give praise where it is due!
From: (Anonymous)
2012-10-08 10:25 pm (UTC)

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I like randomness. If the discussion is going to take longer than a few minutes, $PARTNER and I tend just to flip a coin. On average it probably comes out even, but more importantly we both believe it does.

-- random Firedrake
From: (Anonymous)
2012-10-08 11:49 pm (UTC)

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Same here. The coin toss doesn't allocate the task to the best cost-avoider like a utility comparison *could*, but it sure cuts down on wasted time when you can't allocate efficiently anyway.
[User Picture]From: avanti_90
2012-10-09 05:11 am (UTC)

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In situations without an obvious flesh harvester or a lot of goodwill, a coin toss does sound like a good way to decide. It definitely sounds better to me than a pain auction, which would be unnecessarily painful for everyone.
[User Picture]From: oscredwin
2012-10-08 10:25 pm (UTC)

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"Interpersonal utility comparison is impossible in principle, but in practice it works pretty well."

Can you elaborate on that? The first part would be news to me and the second part seems to disprove the first part.
[User Picture]From: squid314
2012-10-08 10:44 pm (UTC)

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See for example here or page 11 here.

Edited at 2012-10-08 10:50 pm (UTC)
[User Picture]From: oscredwin
2012-10-08 10:56 pm (UTC)

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Given those I would rate the problem unsolved, hard, and possibly unsolvable. Most of the time when I see someone claim that something is impossible in principle I assume that there's a proof somewhere.

BTW, if you think they're impossible in principle, what was your take on the dust specs vs torture question?
[User Picture]From: squid314
2012-10-08 10:59 pm (UTC)

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I feel like there might be a proof somewhere, but I don't know too much about this subject and can't point you to it.

Even if there is, I think it might be an epistemological problem but not an ontological one; that is, there are interpersonal utilities, we just can't quantify them. I feel pretty comfortable saying, for example, that if I have some kind of foot injury that makes it excruciating for me to walk, my partner loses less utility to walk the dog than I do.

As such, I have no particular objections to dust specks vs. torture beyond the obvious ones (I neither fully accept it nor really have a good answer to it)
[User Picture]From: oscredwin
2012-10-08 11:15 pm (UTC)

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The second link you gave me is a paper that's only five years old and doesn't reference a proof. I take that as strong evidence that there isn't a proof. I would expect that with a much better understanding of psychology and perfect brain scanning tech, it would be possible to directly compare two people's utility.

I'm having trouble understanding the idea of something that can't be measured, even in principle, but can be compared on large enough scales (outside of QM).
[User Picture]From: oscredwin
2012-10-08 11:55 pm (UTC)

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The reason I'm picking at this is that when I read it I noticed myself learning something. It confused me because it seemed very inconsistant with things i had been reading on LessWrong and Overcoming Bias in the last 4 years (eg CEV).

Could you edit it to make it clear that it's a popular conjecture that you endorse and not a proven fact?
[User Picture]From: lastconformer
2012-10-09 06:16 pm (UTC)

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The basic mathematical brick wall is that every preference aggregation scheme will have some very perverse properties according to Arrow's impossibility theorem. But of course people can always haggle about those properties not being so bad after all, which is not a strictly mathematical question. That kind of argument always looks extremely unimpressive to me, but then I'm just some dude on the Internet.
[User Picture]From: sniffnoy
2012-10-10 06:08 am (UTC)

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Well, hold on. Arrow's Theorem is for cases where all you have is a preference ordering. A utility function contains more information than a preference ordering, so you may be able to do better with it. Of course, it's equivalent to a preference ordering on gambles satisfying certain constraints, but my point is that we're talking about the base choices, not gambles. You could talk about applying it directly to the gambles -- but there are infinitely many gambles, and Arrow's Theorem requires finitely many candidates. There's a variant for infinitely many *voters*, but I don't know of any for infinitely many candidates. Also, if you took the gambles as "basis elements" and ignored the structure among them, you'd be disregarding important information. Which admittedly would be irrelevant if Arrow's Theorem applied, as even without that extra information you'd have heavily constrained it, but SFAICT it doesn't.
[User Picture]From: lastconformer
2012-10-10 07:34 am (UTC)

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Arrow's Theorem is for cases where I have a preference ordering. I don't see the requirement that that's all I have. Basically the utility functions on the base choices imply a preference ordering. Likewise your aggregate utility function. So you have the theorem on the implied preference orderings and that's enough to make the result absurd. Additional information doesn't help, because the problem is not locating the solution, the problem is that the preference orderings already rule out the existence of a solution.
[User Picture]From: sniffnoy
2012-10-10 05:22 pm (UTC)

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Arrow's Theorem assumes that the aggregation scheme can *only* depend on the preference orderings, though. If you have something that depends on the additional information -- so that from the perspective of someone blind to the additional information, it would appear non-deterministic -- then the space of possible solutions could maybe get larger?

It does seem plausible to me that this wouldn't actually accomplish anything (if we're putting preference orderings in and getting preference orderings out, why should allowing it to depend on additional information matter?), but I'm not sure it's obvious.

(There is of course also the possibility of just not worrying about Arrow's Theorem because once you have more information you can come up with conditions that make sense in that context and worry about satisfying those instead, like proponents of range voting do.)
[User Picture]From: lastconformer
2012-10-12 09:16 am (UTC)

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I don't think this particular kind of indeterminism helps. The way indeterminism would destroy proofs of Arrow's impossibility theorem is by making "the" result of alternative rankings undefined, so they can't be used in counter-factual arguments.

But now look at e.g. this proof.

You could simply translate it to cardinal language. Replace all preference orders with utility functions. Replace the social welfare function with one that maps many utility functions to one. And then replace every A >_x B with u_x(A)>u_x(B).

Then the "cardinalized" social welfare function is deterministic again, though the proof still doesn't use the additional information. And afaict the proof is still valid.

Your parenthetical statement actually looks like one way to do the haggling I alluded to in my original comment.

Taking the example of the range voters, they replace IIA with a significantly weaker criterion annoyingly also named IIA. Basically the result should only be independent of the scores assigned to irrelevant candidates. This looks reasonable at first, but the perfidy is that the same system forces you to rescale your preferences to a pre-established range. Isolatedly, this wouldn't be so bad either, because otherwise voting would simply turn into a contest to think of the biggest number. But it means the scores of the relevant candidates actually are dependent on your preferences or utility for the irrelevant ones. And then the IIA criterion gets weakened to ignore this very dependence!

As a voting system this just shoves the problem to the individual level where the ballots no longer record it. By that standard FPTP is perfectly fair too. If you want to look at it as an aggregation system for honest utilities it doesn't even do that much, because then the rescaling will be part of the aggregation scheme and an algorithm with two steps one of which is free of paradoxes doesn't look that impressive.

But yeah, at that point we're haggling about when exactly an aggregation scheme should be counted as absurd, which is not a mathematical question.
[User Picture]From: maniakes
2012-10-08 10:36 pm (UTC)

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If the cost to either person of conceding the argument is trivial compared to the cost of a deadlock (as per the cost of walking an atomic dog in a neighbourhood without flesh harvesters), my instinct would be to toss a coin.

An alternate solution that leaps to mind would be to take turns (on a weekly basis, perhaps) as Argument Dictator. Whoever is Argument Dictator this week has final say over all decisions in a certain pre-defined class. The Dictator is bound by relationship norms, valuing the other partner's happiness, and the possibility of retaliation next week to use his/her power responsibly and with consideration to their partner. However, this creates a meta-problem of avoiding a death spiral of escalating retaliation.
[User Picture]From: snysmymrik
2012-10-08 10:49 pm (UTC)

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Obviously, the solution is to let the flesh harvester meet the unwalked atomic dog. Two problems solved in one nuclear explosion.
[User Picture]From: xuenay
2012-10-09 08:01 am (UTC)

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I like the way you think.
[User Picture]From: hentaikid
2012-10-09 10:09 am (UTC)

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Or hire the flesh harvester to walk the dog.
From: kovacsa
2012-10-09 02:35 pm (UTC)

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This comment is just so marvelous when taken out of context.
[User Picture]From: maniakes
2012-10-09 01:41 am (UTC)

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On further consideration, it occurs to me that IUC as a conflict-resolution algorithm would fail horribly if you happen to be dating a Utility Monster.
[User Picture]From: pktechgirl
2012-10-09 04:09 am (UTC)

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Isn't it impossible to simultaneously prevent people from artificially bidding up chores they don't really mind and avoid the dollar auction problem? You could split the difference and charge people a portion of their bid if they lose, but ultimately bidding either is painless or it isn't.
[User Picture]From: squid314
2012-10-09 09:31 pm (UTC)

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I think so, that's why I disapprove of auctions as a solution here.
From: (Anonymous)
2012-10-10 07:29 am (UTC)

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Can we Vickrey it up? I can't figure out how to implement that with trading chores, but it looks possible.
[User Picture]From: Geoff Greer
2012-10-09 08:27 am (UTC)

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alicorn24 has set her computer to "notify" her when she gets an IM, which means in practice that her computer irregularly emits very loud BLEEEEEPs every minute or two that frighten me out of my skin whenever I am near her. I asked her to turn this off, and promised that in exchange, she could point out anything I did that annoyed her and I would stop.

This isn't related to your main point, but you probably could have gotten what you wanted by saying, "I can't concentrate with that beeping. Can you turn it off?"

By offering to reciprocate her sacrifice, you turned the conversation into a negotiation. That made it easy for Alicorn to respond with a counter-offer. If you had simply asked her to turn off the beeping, I doubt she would have even thought of negotiating with you.

Edited at 2012-10-09 08:29 am (UTC)
[User Picture]From: squid314
2012-10-09 09:32 pm (UTC)

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Makes sense, although I don't like the way it feels to ask someone to make an unreciprocated sacrifice for me.
[User Picture]From: torekp
2012-10-09 11:29 pm (UTC)

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Recommendation: get used to it.
[User Picture]From: lastconformer
2012-10-10 07:46 am (UTC)

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Or you could ask her to change the sound to something non-frightening like bird twitter. Probably she doesn't value the actual beep, just the information.

Of course that assumes there are non-frightening surprise sounds, but I'll just assume that because (a)bird twitter doesn't frighten me (b)bird twitter doesn't frighten anyone I know and (c) evolution-wise people who got frightened by bird twitter should be extinct.
From: siodine
2012-10-09 03:07 pm (UTC)

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A coin flip should be the go-to-solution for utility disputes, but when that fails you can simply have an auction where everyone sacrifices their bid to charity. You shouldn't lose much utility in such an auction, and you aren't creating much of an incentive for cheating your partner. Moreover, by having both party's bids go to charity regardless, you make the coin flip even more agreeable. And if they have a shared account, that also makes the coin flip more agreeable.

Edited at 2012-10-09 03:11 pm (UTC)
[User Picture]From: ikadell
2012-10-09 05:40 pm (UTC)

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That's why some households have what you may call a chore pact. I always do the dishes, you always do the laundry, no questions asked, no whines for help: weird chores coming up, the person with the best ability addresses them (a shelf fell off, you put it back, because you are tall, the boiler company arrives, I will meet them because I work from home today). So one partner ends up always walking the dog if it comes to that, and zip. In a rational household, it would probably be the woman, regardless of who wanted the dog, because flesh harvester only attacks men.

This begs the questions of shouldn't the person who wanted the dog in the first place always take care of it henceforth, as an additional task (not an addendum to the chore pact, since putting it on the list of the chore pack would, using Alicorn's logic, cause the other partner to suffer: I am now washing dishes as well because you wanted the dog and will be walking it?). My answer is unquestionably yes, and the other partner can participate and help if s/he feels like or takes pity on the loved one who has to work tomorrow - which would be appreciated and may be rewarded...
From: vilhelm_s
2012-10-09 09:49 pm (UTC)

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I'm not sure that pain auctions would be as disastrous as you describe (at least as a way of giving away artwork, I'm not necessarily endorsing them for household chores). You compare them to penny-auctions, but note that in real life, humans are generally smart enough to not take part in those! (At least not twice). So combined with some cheap talk, maybe it could work out.

In particular, how about modifying it to a "Vickrey pain auction"? Everyone submits a sealed bid for how many minutes they can stand, and the winner only gets into the sauna, and stays there for as many minutes as the second bidder specified. This way, all the participants at least get non-negative utility from the procedure.

Of course, this still has the drawback that lots of people will suffer "unnecessarily", just for the signalling value. I wonder if there is a connection between this problem, and the point someone else made that allocating dog-walking duties to the least inconvenienced party incentivizes everyone to turn into utility monsters. Viewed from the outside, a world full of sauna-suffering art lovers seems quite similar to a world full of gratuitously salmon-averse people.
[User Picture]From: squid314
2012-10-09 10:21 pm (UTC)

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The Vickrey auction is actually really clever, although it would probably also result in a few unnecessary deaths since people have to specify the time they're going to spend in the sauna beforehand instead of reacting to their physical sensations of danger.
[User Picture]From: michaelkeenan
2012-10-09 11:23 pm (UTC)

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You could fix that by being able to pay $X to get out of the sauna, and if you do, the auction is held again but you're not allowed to bid this time.
[User Picture]From: sniffnoy
2012-10-10 06:09 am (UTC)

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How about a Vickrey auction in something other than pain?