Decision Auctions aka “How to fairly assign chores, or decide who gets the last cookie”
After moving in with my new roomies (Danny and Bethany of Beeminder), I discovered they have a fair and useful way of auctioning off joint decisions. It helps you figure out how much you value certain chores or activities, and it guarantees that these decisions are worked out in a fair way. They call it “yootling”, and wrote more about it here.
A quick example (Note: this only works if all participants are of the types of people who consider this sort of thing a Good Idea, and not A Grotesque Parody of Caring or whatnot):
Use Case: Who Picks up the Kids from Grandma’s?
D and B are both busy working, but it’s time to pick up the kids from their grandparents house. They decide to yootle for it.
B bids $100 (In a regular Normal Person exchange, this would be like saying “I’m elbows deep in code right now, and don’t want to break flow. I’d really rather continue working right now, but of course I’ll go if it’s needed.”)
D bids $15 (In a regular Normal Person exchange this would be like saying “I don’t mind too much, though I do have other things to do now...”)
So D “wins” the bid, and B pays him $15 to go get the kids from their grandma’s.
Of course.… it would be a pain in the butt to constantly be paying each other, so instead they have a 10% chance of paying 10x the amount, and a 90% chance to pay nothing, using a random number generator.
This is made easier by the fact that we have a bot to run this, but before that they would use the high-tech solution of Holding Up Fingers.
We may do this multiple times per day, whenever there’s a good that we have shared ownership of and one of us wants to offload their shares onto the other person. The goods can be anything, e.g. the last brownie, but they’re more often “bads” like who will get up in the middle of the night with a vomiting child, or who will book plane tickets for a trip.We find this an elegant means of assigning loathed tasks. The person who minded least winds up doing the chore, but gets compensated for it at a price that by their own estimation was fair.
Joint purchase auctionThe decision auction and variants are about allocating shared or partially shared resources to one person or the other, or picking one person to do something. Once in a while you have the opposite problem: deciding on a joint purchase.Suppose Danny thinks we need a new sofa (this is very hypothetical). I think the one we have is just fine thank you. After some discussion I concede that it would be nice to have a sofa that was less doggy. Danny, being terribly excited about getting a new sofa does a bunch of research and finds his ideal sofa. I think it is a bit overpriced considering it is going to be a piece of gymnastics equipment for the kids for the next 6 years. Conflict ensues! I could bluff that I’m not interested in a new sofa at all and that he can buy it himself if he wants it that badly. But he probably doesn’t want it that bad, and I do want it a little. If only we could buy the sofa conditional on our combined utility for it exceeding the cost, and pay in proportion to our utilities to boot. Well, thanks to separate finances and the magic of mechanism design, we can! We submit sealed bids for the sofa and buy it if the sum of our bids is enough. (And, importantly, commit to not buying it for at least a year otherwise.) Any surplus is redistributed in proportion to our bids. For example, if Danny bid $80 and I bid $40 to buy a hundred dollar sofa, then we’d buy it, with Danny chipping in twice as much as me, namely $67 to my $33.
Generosity without sacrificing social efficiency“The payments are simply what keep us honest in assessing that.”If you’re thinking “how mercenary all this is!” then, well, I’m unclear how you made it this far into this post. But it’s not nearly as cold as it may sound. We do nice things for each other all the time, and frequently use yootling to make sure it’s socially efficient to do so. Suppose I invite Danny to a sing-along showing of Once More With Feeling (this may or may not be hypothetical) and Danny doesn’t exactly want to go but can see that I have value for his company. He might (quite non-hypothetically) say “I’ll half-accompany you!” by which he means that he’ll yootle me for whether he goes or not. In other words, he magnanimously decides to treat his joining me as a 50⁄50 joint decision. If I have greater value for him coming than he has for not coming, then I’ll pay him to come. But if it’s the other way around, he will pay me to let him off the hook. We don’t actually care much about the payments, though those are necessary for the auction to work. We care about making sure that he comes to the Buffy sing-along if and only if my value for his company exceeds his value for staying home. The payments are simply what keep us honest in assessing that. The increased fairness — the winner sharing their utility with the loser — is icing.
I’m curious about how this works with very differing levels of income. My first thought was that that’d break it, since the system ceases to be fair if the absolute upper limit that I can afford to bid on anything is $50 whereas my roommate can easily blow $150 on something in the category of “I don’t mind too much, though I do have other things to do now”. On the other hand, that would also cause me to very quickly obtain lots of extra money that I couldn’t have had otherwise, so that’s definitely a bonus. But it still seems like the balance of power would be quite strongly tilted in favor of the wealthier person.
Bethany and I philosophically bite the bullet on this, which is basically to just agree with your second point: the wealthy person gets their way all the time and the poor person gets what’s to them a lot of money and everyone is happy.
If that’s unpalatable or feels unfair then I think the principled solution is for the wealthy person to simply redress the unfairness with a lump sum payment to redistribute the wealth.
I don’t think it’s reasonable—ignoring all the psychology and social intricacies, as I’m wont to do [1] -- to object both to auctions with disparate wealth and to lump sum redistribution to achieve fairness.
Now that I’m introspecting, I suppose it’s the case that Bethany and I tend to seize excuses to redistribute wealth, but they have to be plausible ones.
You can’t accept the money either from an auction or a lump-sum redistribution without losing status, and a roommate relationship is one where you particularly want to maintain similar status levels. If I wanted to be a live-in servant instead of a friend, I could probably find a better deal on Craigslist without sacrificing an existing friendship.
If you’ll excuse the critique of your syntax, it should be “to object both to … ” As it stands, it’s a garden path sentence, with the initial parsing being that there are two auctions with disparate wealth, and you don’t think it’s reasonable to object to both of them.
Also, if an annotation consists of a link, you can put it like this [1]
Fixed and fixed. Thank you!
Taking the word “afford” literally, if you can only afford $50 on the first auction, and you lose the auction, then you’ll have an extra $50 on the next auction, and will be able to afford $100. If you lose that auction, you’ll be able to afford $200 on the auction after that. I think that the concept you’re thinking of is not so much afford, as marginal utility cost. For someone with a yearly income of $200,000, a marginal util is going to cost a lot more than for someone with a yearly income of $40,000. Thus, the richer person may be willing to bid more, because the utils are worth more to that person. It is therefore more efficient (that is, it is a Pareto improvement) for the richer person to win the auction, and give money to the poorer person that the poorer person can use to buy utils elsewhere. And I really wonder at who’s deciding what goes in the Google Chrome spell checker dictionary, because apparently “util” is in it, but “externality” is not.
Could you elaborate your interpretation to the extreme, i.e. a classical marriage, with one person earning money and the other caring for home and children?
One person earns money through work, and the other one stays home and earns money for all of the chores. The stay-at-home partner needs to bid high enough on e.g. childcare to pay half the rent, but not so high that other options become better.
The balance of power is strongly tilted in favor of the wealthier person to the extent they’re willing to throw money at the poorer person. Which is to say, that’s as it is normally. With the cash in hand, the cost of chores will rise. It shouldn’t be as steeply as ThisSpaceAvailable says, so that the poorer person doesn’t get wiped out by the richer doing something once a week, but it will still rise. The poorer person is not an indentured servant any way they choose to play it.
Whether this is conducive to long-term happiness or would warp a friendship I don’t know, but I have a hard time seeing it as worse than the rich and poor roommates splitting the chores equally for free.
You can bid time instead of money. And internally we count convert time to money in a fixed rate but only in one direction time->money.
Time isn’t fungible though. 5min cleaning the toilets should count for more than 5min unloading the dishwasher.
As the poorer person, all the money you get from yootling should go into a budget account which you use only for yootling. That way you are guaranteed both that you won’t pay more than you can afford, and that in the long run you will win as much as you lose yootle auctions.
I bet this would be a big sticking point for many couples, “What do you mean you’d rather stay home than come with me? We are a couple! You would pay me how much to leave you alone?! What am I, a whore? Worse than a whore, even, you would pay me as much JUST TO LEAVE YOU ALONE!” (Door slam)
One has to have a very special relationship to not feel either rejected or coerced in situations like that.
Of course, there are situations that raise the prostitution issue even more directly.
“So, honey, just how much of a headache do you have?”
Upvoted for the delightfully flattering implication for my and Bethany’s relationship. :)
But, yes, a prerequisite is that everyone think like an economist, where everything you care about can be assigned a dollar value.
See also the core assumptions at the top of Bethany’s article [http://messymatters.com/autonomy].
I always enjoy your contributions and it makes me sad that you use the site less than you would because of a/the downvote stalker.* I’m interested in applying microeconomics to these sorts of domestic or between-friends situations in which it might conventionally be taboo to do so, and this type of bidding in particular is something I’ve wondered about, so thanks for posting this!
*(I am not sure how easy it would be for an admin to look at the database and figure out what to do once someone’s been identified as a downvote stalker, but I’m skeptical it would not be worthwhile at least trying to sort it out given how destructive it is, and at the very least I’d like to know why it seems nothing’s been done. (Not to assign blame, but to try to figure out how we can get faster response on such issues in future.) If there really is one or a small number of people behind most of the downvote stalking, then checking the downvotes against victims should take (<)<15 minutes. I’d put >80% probability on this turning up one or more stalkers even just doing a naive database query using the set of victims in this thread.)
The first person who ran some detection programs on the whole database didn’t discover useful hits. I recently wrote them again and asked them to check daenerys as target specifically.
Thank you for clarifying what had already been attempted (and that something had been), and making further attempts!
Hmm, if Dan or Bethany happen to be reading this, why split the surplus proportional to the bids when making a joint purchase rather than split it equally? An equal split seems fairer at first glance, and that mechanism definitely hits the Myerson-Satterthewaite bound in equilibrium if both people act non-cooperatively. The proportional split mechanism is messy enough I can’t see the equilibrium immediately, so I’m curious if there is some advantage to it I’m not seeing.
Great question, and upon reflection (I actually looked this up in my PhD dissertation just now!) I agree. I actually can’t remember the last time Bethany and I used a joint purchase auction. For some reason it never comes up—we just each buy things and don’t worry about joint ownership. If we did disagree about whether to buy a household item we’d probably just straight up yootle for whether to buy it (with the cost split 50⁄50 if we did).
If this is something that can be looked up in your PhD dissertation, where can I get a copy?
Edit: here (pdf)
This mechanism seems like a Vickrey auction (Wikipedia).
Steven Landsburg mentioned using such a method (albeit simpler) in The Armchair Economist, where the example concerned choosing which movie to watch.
Looks more like a normal first-price auction to me. “B bids $100, D bids $15, so D ‘wins’ the bid, and B pays them $15 to go get the kids from their grandma’s.” The low bidder wins, and receives the amount they bid. In a Vickrey/second-price auction B would pay D $100.
You’re right that it’s similar to a Vickrey auction in that the 2nd highest bid (in the 2-player case) is used as the price, but it’s different in that there’s no 3rd-party seller. The good is jointly owned and the payment will go from one player to the other. In particular, yootling is not strictly incentive compatible like Vickrey is (though in practice it seems to be close enough).
Thanks for the pointer to Landsburg! Looks like he worked out a way (by enlisting another economist couple) to have meaningful auctions despite having joint money with his spouse. I predict that system didn’t hold together though. I should email him!
It’s very much a first-price auction; here, you’re minimizing loss instead of maximizing gain. If you add a third person who bids $10 to pick up the kids, that person does it (because they’re the lowest-cost option).
Actually, wouldn’t it make sense to only pay the winner 1/n of their bid (from each other participant)? In the case of picking up the kids, the union has received a negative windfall, and is attempting to price it. The cheapest solution is $15, so the cost is $15- which is then borne entirely by one party!
Now, this is assuming that people are pricing their bids at indifference ($15 completely compensates for having to pick up the kids), which may not be the case. You could try to equate B’s regret at paying D’s price and D’s dissatisfaction with having to perform the task, but this seems silly compared to pricing indifference.
Alternatively, rather than trying to allocate the windfall equitably (which leaves both parties worse off by the same amount, but with different levels of surplus), you could try to equalize surplus- which would be B paying D $42.50. I think this makes the incentives inside the bidding stronger, but makes the incentives on when to bid more troublesome, because this encourages you to yootle when the other person has a lot at stake.
I’m impressed! That’s kind of the conclusion we gradually came to as well, after a lot of trial and error. Better to not have people feel like their desperation is being capitalized on.
Another way to put it: when you’re really desperate to win a particular auction it’s really nice to be able to just say so honestly, with a crazy high bid. Trying to allocate the surplus equitably means that I have to carefully strategize on understating my desperation. (And worst of all, a mistake means a highly inefficient outcome!)
PS: To be clear about first-price vs second-price, it’s technically neither since there’s no distinct seller.
Here’s the n-player, arbitrary shares version:
Each participant starts with some share of the decision. Everyone submits a sealed bid, the second-highest of which is taken to be the Fair Market Price (FMP). The high bidder wins, and buys out everyone else’s shares, ie, pays them the appropriate fraction of the FMP.
“Even yootling”, or just “yootling”, refers to the special case of two players and 50⁄50 shares. In that case, instead of bidding a fair market price (FMP), you say how much you’re willing to pay if you win. True FMP is twice that, since you only have to pay half of FMP with even yootling. So instead of deciding what you’d pay, doubling it to get FMP, then halving FMP to get the actual payment, we short circuit that and you just say the payment as your bid. For yootling with uneven shares it’s easier to bid FMP and then pay the appropriate fraction of that.
An interesting system. How would this be modified to work for couples who actually have joint finances?
In the article I linked to, Bethany argues that separate finances are a requirement to this, and I tend to agree.
A workaround might be having a joint account, AND separate accounts that are used for whatever fun/luxury you each want. You each get $x/month in your fun/luxury accounts, and that is the money you use to yootle with (and pay for dance class, and buy a new sewing machine with, and whatever other luxury, etc)
Julia and I organize our finances this way, and I would recommend it for couples whether or not they plan to yootle.
My partner and I use a single joint account, but if I had to do it over again, I’d probably do it this way too.
Technically we also use a single joint account. We keep track of our three accounts (joint, Julia’s, Jeff’s) on a spreadsheet.
Use a zero sum point system (MMO model) with an interest system to suit. A cooperative relationship will aim to keep things close to even. Downside is of course this is just a counting method with no real payout, reward, or penalty.
And in the prescript of the link it was mentioned that this was tried didn’t work.
This sounds efficient and a good way to get around the bad feelings that can often build up when people live together and disagree during decision making.
I imagine if I were to implement this there might still be disagreement in deciding when to use yootling for making a decision (Please no meta-humor on this). Using it for every decision sounds annoying.
Are you concerned that the next people who you live with may be less receptive to this method of decision making? Using this system could cause you to miss out on learning the subtle social skill of coming to a group consensus.
We have a protocol for deciding when to yootle: if the possibility of yootling is so much as mentioned then we must yootle. The only fair way to object to yootling is to dispute that it’s a 50⁄50 decision. If it is a fundamentally joint decision then how would you object? “I want to get my way but not pay anything”? Not so nice. You could say “I don’t want to yootle, I’ll just do it your way”. But that’s equivalent to bidding 0, so might as well go through with the yootling. And after 9 years we do have quite efficient ways to conduct these auctions, with fingers or our phones or out loud.
I’ve lived with other people (either spouses or roommates) pretty much my entire life (30 years), so I feel like I’ve already acquired the social skills to do without it. Other people’s situations may be different. I am generally in support of people learning social skills, so yootling might not be the best answer if it is a replacement for that.
Once you have a bot to run it, can’t you drop the 10% chance of 10x bit and just transfer money every time?
Or just have one piece of paper, and write the transactions there.
The bot doesn’t run the money transfer. It runs the auction (collects bids from everybody, displays bids when all have been collected), and runs a random number generator.
We have also used the same bot to play a Schelling Point Game, where someone names a category (eg “a book”) instead of a thing to auction, and we all make a guess (e.g “Strategy of Conflict” or “The Bible”) instead of a bid. You get a point if your guess is the same as someone else’s.
The bot could keep track of who owes what, and then you could settle monthly or something. Easier than adding money transfer.
Agreed, we just haven’t gotten to that yet. The auctioneer chatroom bot is pretty new.
I’d love to hear more about the bot. How does it work? Where is it run? Can others access it too?
I don’t speak Computer, but this is the bot: http://aaronparecki.com/articles/2011/02/12/1/loqi-the-friendly-irc-bot
We use him in a company hipchat room, and I don’t know if he has been altered/reprogrammed in any way to run auctions.
Specifically, here’s the little add-on for Loqi that conducts auctions: https://github.com/aaronpk/zenircbot-bid
The chance of paying 10x also seems like it constrains the bids to less than a tenth of where people start to lose risk neutrality- in order to bid $100, you need to be willing to pay up to $1000!
Alternatively it trains you to be more risk neutral.
I’m assuming that the individuals have divided their funds into “risk neutral” and “risk averse” in a discrete way, rather than with a continuous utility function. This makes sense when there’s a clear discretionary / non-discretionary split; I can easily adjust my entertainment budget this month to compensate for losing $100, but I might not be able to easily adjust my rent budget to compensate for losing $1000.
If people don’t have any funds they consider risk-neutral, then I think that doing some sort of gambling to develop the psychological skill of risk neutrality is important, but I doubt this is the optimal way to do that training.
Am I mistaken, or is this a case of Coasian bargaining?
Yes, we’re super keen to make sure the efficient thing happens regardless of the initial distribution of resources/responsibilities/property-rights/etc. And we use yootling as a bargaining mechanism to make that happen. In general we’re always willing to shove work to each other or redistribute resources as efficiency dictates, using payments to make that always be fair.
;-)
If you both want it, or bought too many cookies if neither of you wants it.
In the comments you mentioned that you have been doing this for 9 years. Have you had to resolve attempts to game yootling, gone through phases where yootle was played to win, or ended finding stable price equilibriums? I like the idea and am trying to predict the problems I would encounter.
The example that comes to mind is: I don’t mind doing dishes, my roommate despises the task. Under the introduction of yoodling a task will start at $5 : $55, then supply/demand, icecream stands on a beach, and all those other key words I did pay enough attention to will kick in, next thing you know we are sitting at 30:30 price equilibrium and playing the game of ‘what do I think this is worth to them’, ‘how much can I milk them for’ and the unmentionable ‘dammit, I won. I was only trying to force their price down’. All meta-games I’d rather avoid.
As an aside, similar systems have developed in some of my more open/honest friendships: Join me at my social event and I’ll buy the drinks, If I go to your social event you are buying the drinks. Those same systems have also blown up in my face with less established friendships:
In practice the sealed-bid version seems to be ungameable, at least for us! None of the problems you mentioned have arisen. My parents have tried this and had more problems but as far as I could tell it always involved contention about what to consider to be joint 50⁄50 decisions. Bethany and I seem to have no problem with that, using the heuristic of “when in doubt, just call it a 50⁄50 decision and yootle for it”.
In a second price auction the optimal strategy is to bid your true valuation.
When it comes to literally taking the last cookie, I will very often tell the rest of the group “I will do you all a favor, and save you the guilt of taking the last cookie.”
Possibly more selfish people feel affronted by this, but at the level of courtesy at which I used to operate, anyone who saved me the distress of deciding whether taking the last one was acceptable would really have been doing me a favor. Eventually, I decided that if anyone was going to provide that service, it might as well be someone conscious of the social role, so now I take the last cookie and don’t feel guilty about it.
This can be easily combined with this advice:
http://lesswrong.com/lw/j0f/link_bet_your_friends_to_be_more_right/
We do this quite some times. You can bet e.g. for household chores or treats. It is also helpful for my older sons to calibrate their confidence—esp. when betting for pocket money.
The currency being shared with someone outside the group seems irrelevant. What’s the advantage to using dollars as the currency?
“Yootles” would still have to be scarce, and preferably be exchangeable at known rates for something else.
If we yootle for repainting the spare room and I bid $1.2k to your $1.5k, we should probably just hire a painter.
Shouldn’t it be more something like 15+(100-15)/2$? So both win (about) the same amount of utility? Otherwise, the one who was ready to pay 100$ saved (“won”) 85$ and the other won nothing (s/he was indifferent to pay or do it for 15$).
Nice post by the way. Such techniques seem useful if you trust the other will make a bid that really represents the amount s/he’s ready to pay.
Thank you! See above (“Better to not have people feel like their desperation is being capitalized on.”) for my response to your first question. And we actually believe that our system is, in practice if not in theory, strategy-proof. It’s explicitly ok to game the system to our hearts’ delight. It seems to be quite robust to that. Our utilities tend to either be uncannily well-matched, in which case it’s kind of a coin flip who wins, or they’re wildly different, but we never seem to have enough certainty about how different they’ll be for it to be fruitful to distort our bids much.
The strategy of “just say a number such that you’re torn about whether you’d rather win or lose” seems to be close enough to optimal.