The Roommate’s Dilemma

Well hello!

Lobby and Fobby

Creepy hallway

Kitchen

Living room

Slave Bedroom

Slave Bedroom

Master Bedroom

All rooms lead to balcony

All rooms lead to balcony

Another view of the living room. Also, an idiot.

Kitchen again

The reason this place is affordable

It will be totally possible to dive from here

The Roommate’s Dilemma is an instantiation of the Cake Cutting Problem. Basically, n=2 (dashing, handsome, etc.) roommates need to be assigned to n rooms, which are not identical. Since they are not identical, the rent should not be split equally. Each room presents different utility to the roommates, so the assignment and rent split should reflect this and try to maximize everyone’s utility. How to do it “fairly”?

The solution to the cake problem is to let one person cut the cake and let the other choose. Thus, the person has an incentive to cut the cake as equally as possible, lest the other take the bigger. Neglecting physicalities, such as the impossibility of splitting something exactly equal, this algorithm ought to leave both parties satisfied that the outcome is fair. If the chooser is not satisfied, it is his own fault for being a dumbass and picking the inferior cut; if the cutter is not satisfied, he has only himself to blame for not cutting it fairly.

The direct analogue of this solution is to let one person split the rent and let the other choose which room to live in. I started thinking about this, though, and I think this is actually not fair. It is not possible for the cutter to live in a room and pay less than what he thinks it is worth, but it is possible for the chooser.

For example, suppose that roommate 1’s utility is at 1200/800, and 2 is at 1500/500, for rooms A and B, respectively. If 1 is cutting, then he has no choice but to place the rent at 1200/800 (assuming he doesn’t know 2’s utility split). For were he to do otherwise–for example, at 1300/700, then 2 may choose room B, leaving 1 with room A, and having to pay higher than what he thinks room A is worth. Only at 1200/800 would he be neutral about the outcome of 2’s choice–it’s an equilibrium of sorts. Then, 2 will choose room A, and pay 300 less than what he thinks it’s worth. Thus, basically, 2 has benefited $300, while 1 has benefited $0 from this mechanism.

Of course, in real life, 1 can try to guess 2’s utility. If he knew what his utility was, he could place the split at 1499/501. 2 will then pick A (assuming he knows the value of an honest dollar), leaving 1 with a $299 discount.

The system we’ve agreed on is to each write down our utilities by secret ballot, then average the utilities, and assign the rooms “down”. For example, in the example above, the averages are 1350/650. Then, 1 would take B and pay 650, and 2 would take A and pay 1350. Then each has mutually benefited $150 (essentially, wealth is created from the utility differential).

Now to decide what my utilities are and see if I will actually be happy with the outcome of this experiment… Today I measured the sizes of the rooms, using my armspan, which ought to be the same as my height. The smaller room is 2×2.4 Siwei’s, and the larger is about 2×3.5. However, the balcony door to the smaller room is bigger, so it’s brighter. Hmmm…

我也要吃粽子55555555 T____T

L’autre journée, mes enfants ont pris leurs examens finaux. Pendant ceci, un etudiant m’a demandé une question au sujet d’un des problèmes. Sur ce problème, on roule un dé quelque fois, et on doit trouver les probabilités d’obtenir des nombres identiques ou distincts. L’etudiant m’a dit, “que veut dire ‘distinct’?” Je lui ai donne un look(?), comme “are you fucking kidding me?” (How do you say this in French???) Mais il était complètement sérieux. J’ai dit “‘distint’ signifie ‘tous différents’”. Il m’a répondu avec “n’est-ce pas le même que ‘identique’?” Je lui ai donne un autre look de “are you fucking kidding me?” J’ai dit “non… c’est le contraire… ‘Identique’ veut dire ‘tous le même’…”

Mes enfants sont retardés.

生活等於烦恼

这几天忙碌着。六月底要搬家，我现在才开始找房子。。。如果可以的话，我宁愿一直住在现在的房子里，即使每月多付几百块钱也可以，因为它又离学校近，又新。我跑到BRENTWOOD看了几间一千六到一千八的(比现在便宜一点)，都比较旧。而且需要乘BUS。沮丧。。。