4 ms·

This reminds me of how I used to split rents with my roommates: Identify surplus value, and split that value evenly. 0. Given a prospective rental house. (And

This reminds me of how I used to split rents with my roommates: Identify surplus value, and split that value evenly. 0. Given a prospective rental house. (And therefore a known set of rooms and a known total rent) 1. Each person "bids" by pricing every room in the house. Goal: each person should be looking for "break-even" pricing. Try to price such that all the rooms feel "equally good" at your given prices. 2. Just one restriction on the pricing: each bidder's room-prices must sum to the house's monthly rent. 3. Reveal all bids. 4. Choose the room-assignment that yields the highest total price. Because of the restriction in [2], we're guaranteed a surplus over the true total rent. (Unless everyone somehow put in identical bids) 5. Split the surplus evenly. Everyone gets a room at the price they bid for that room, minus 1/nth of the surplus. Effectively, everyone gets an identical surprise discount. We lived together for over 10 years, through 5 different rentals. We split up when it came time to start families and buy houses.

exo-pla-net 5y ago
0: Total rent is $10, for ten rooms, to be split among ten people. 1: One person who really wants a certain room bids $10 on it, and he assigns $0 to the nine other rooms. His roommates bid a neutral $1 on all rooms. ... 4: The person gaming the system gets his special room. 5: The surplus is $10 + 9*$1 - $10 = $9. Split evenly, $0.90. Thus, the gamer pays $9.10 for his special room, and everyone else pays $0.10 for their rooms. He has clearly made a terrible mistake. He's covering the cost of the entire rental nearly by himself. Next time, he bids $1 + one gummy bear on his special room, and he bids $1 on the other rooms. He imagines that now he'll merely have to buy one gummy bear every month, split it in ten, and give everyone a slice. He's outwitted his roommates, he thinks. However, much to his dismay, he overlooked that one of the rooms in this next rental was underground. Furthermore, the room was next to a leaky sceptic tank. Everyone else bid $0 on it. The gamer handily wins the sewage room, instead of his special room, and he hardly gets any discount for putting up with it. Oops, foiled again. All of this is to say, your system seems robust. There's danger in over and underbidding on your assessment of a room's value. You want to be very careful in deciding how much a room is worth to you. I think I'll use this system for renting Airbnb's with friends in the future. Thanks!
- mjevans 5y ago
  Much like with underutilized amusement park rides, the system must accept 'negative' value on some queues (lost guest displacement time in that case) to correctly price the value of the desired outcomes. As far as the 'sewer room' option goes, I think it would have to be priced at the cost of renting somewhere else; so a negative value. For the split on the surplus rent there are a couple solutions to this. IIRC it might be a dutch auction rule? The one where if N of a thing are available a there are N winning bidders all the winning bidders pay the lowest price? Take that rule except apply it to the lowest choice total among the set that yields a full rent. There's also an argument about how to split the savings. In the 10 + 9 * 1 scenario the portion of the total rent the distribution of savings might be better split up as: 'refund' = SURPLUS * nROOM / (RENT + SURPLUS) nRENT = nROOM - SURPLUS * nROOM / (RENT + SURPLUS) If A = 10 and B..J are all 1 5.263... = aRENT = 10 - 9 * 10 / 19 0.526... = xRENT = 1 - 9 * 1 / 19 Rent (10) == A (5.26315789474) + Everyone else (4.73684210526) Even in the pathological case offered this works well enough.
SamBam 5y ago
This sounds like a really great system, although I feel like it doesn't deal with edge-cases. For example: suppose the total rent is $100 for 4 rooms of varying qualities. I have very little money, so I'm willing to take the terrible cupboard-under-the-stairs room for $15. I have no way to arrange my bids to say that I can't afford more than $15, since the average of all my bids needs to be $25.
- exo-pla-net 5y ago
  I think a modification to the rules would fix this: you don't have to make all your bids sum to $100. You bid what a room is worth to you, in your case capped at $15. If, after rooms are assigned, the grand total is less than total rent, the lot of you are too broke to afford the place, and you'll have to look for a cheaper alternative.
  - dsr_ 5y ago
    Whereas a conversation with your prospective roommates might have resulted in them agreeing that nobody wanted the cupboard under the stairs, so they could precommit to allowing your $15 rent and making their bids sum to $85 for three rooms. The problem with game-theorist economists is that they always neglect long-term externalities because they're messy. Having a reputation as a decent human being is a long-term externality that's very messy.

exo-pla-net 5y ago

0: Total rent is $10, for ten rooms, to be split among ten people. 1: One person who really wants a certain room bids $10 on it, and he assigns $0 to the nine other rooms. His roommates bid a neutral $1 on all rooms. ... 4: The person gaming the system gets his special room. 5: The surplus is $10 + 9*$1 - $10 = $9. Split evenly, $0.90. Thus, the gamer pays $9.10 for his special room, and everyone else pays $0.10 for their rooms. He has clearly made a terrible mistake. He's covering the cost of the entire rental nearly by himself. Next time, he bids $1 + one gummy bear on his special room, and he bids $1 on the other rooms. He imagines that now he'll merely have to buy one gummy bear every month, split it in ten, and give everyone a slice. He's outwitted his roommates, he thinks. However, much to his dismay, he overlooked that one of the rooms in this next rental was underground. Furthermore, the room was next to a leaky sceptic tank. Everyone else bid $0 on it. The gamer handily wins the sewage room, instead of his special room, and he hardly gets any discount for putting up with it. Oops, foiled again. All of this is to say, your system seems robust. There's danger in over and underbidding on your assessment of a room's value. You want to be very careful in deciding how much a room is worth to you. I think I'll use this system for renting Airbnb's with friends in the future. Thanks!

mjevans 5y ago
Much like with underutilized amusement park rides, the system must accept 'negative' value on some queues (lost guest displacement time in that case) to correctly price the value of the desired outcomes. As far as the 'sewer room' option goes, I think it would have to be priced at the cost of renting somewhere else; so a negative value. For the split on the surplus rent there are a couple solutions to this. IIRC it might be a dutch auction rule? The one where if N of a thing are available a there are N winning bidders all the winning bidders pay the lowest price? Take that rule except apply it to the lowest choice total among the set that yields a full rent. There's also an argument about how to split the savings. In the 10 + 9 * 1 scenario the portion of the total rent the distribution of savings might be better split up as: 'refund' = SURPLUS * nROOM / (RENT + SURPLUS) nRENT = nROOM - SURPLUS * nROOM / (RENT + SURPLUS) If A = 10 and B..J are all 1 5.263... = aRENT = 10 - 9 * 10 / 19 0.526... = xRENT = 1 - 9 * 1 / 19 Rent (10) == A (5.26315789474) + Everyone else (4.73684210526) Even in the pathological case offered this works well enough.

SamBam 5y ago

This sounds like a really great system, although I feel like it doesn't deal with edge-cases. For example: suppose the total rent is $100 for 4 rooms of varying qualities. I have very little money, so I'm willing to take the terrible cupboard-under-the-stairs room for $15. I have no way to arrange my bids to say that I can't afford more than $15, since the average of all my bids needs to be $25.

exo-pla-net 5y ago
I think a modification to the rules would fix this: you don't have to make all your bids sum to $100. You bid what a room is worth to you, in your case capped at $15. If, after rooms are assigned, the grand total is less than total rent, the lot of you are too broke to afford the place, and you'll have to look for a cheaper alternative.
- dsr_ 5y ago
  Whereas a conversation with your prospective roommates might have resulted in them agreeing that nobody wanted the cupboard under the stairs, so they could precommit to allowing your $15 rent and making their bids sum to $85 for three rooms. The problem with game-theorist economists is that they always neglect long-term externalities because they're messy. Having a reputation as a decent human being is a long-term externality that's very messy.