New Website Offers Provably Fair Solutions To Everyday Problems

An anonymous reader writes Carnegie Mellon researchers have just launched Spliddit, a website that offers methods for helping people split rent, divide goods, and share credit. The novelty is that these methods are all "provably fair": there are mathematical proofs showing that each algorithm on the site provides rigorous fairness guarantees. For example, the method for splitting rent is guaranteed to be envy free: the assignment of rooms and division of rent is such that a housemate would never want to swap places with another housemate. All it takes is a pair of siblings to prove that there's no such thing as "provably fair," non-mathematically.

Comments

Re:sibling fairness

[Kvasio]

the algorith is old one, I remember it from Hugo Steinhaus's math book.
It works for any number of parties and goods.

Say we have 4 brothers who have to divide the heritage: home, car and bicycle

Step 1: each brother provides his valuation, e.g.
Adam home $200,000 car $10,000 bike $100 - total value $210,100 thus his "fair part" is $52,525
Brad home $150,000 car $3,000 bike $120 - total value $153,120 thus his "fair part" is $38,280
Caleb home $180,000 car $11,000 bike $80 - total value $191,080 thus his "fair part" is $47,770
Damon home $50,000 car $3,000 bike $60 - total value $53,060 thus his "fair part" is $13,265

Step 2
whoever "bid" the highest for given good, gets it, at his own valuation.
Adam gets home (valued by him $200,000), which is $147,475 more, than his "fair part", so has to pay $147,475 to the pool
Brad gets bike (valued by him at $120), which is $38,160 less, than he believes he should get
Caleb gets cat (valued by him at $11,000) which is $36,770 less than his definition of a fair part.
Damon gets no item, which is $13,265 lower, than he had hoped to get

Step 3
Adam should pay $147,475 to the pool.
Brad gets $38,160 from the pool
Caleb gets $36,770 from the pool
Damon gets $13,265 from the pool

Now every brother got exactly what he valued as a 1/4th of total items value.

And we've still got $59,280 in pool to share. Which may:
- be split equally - each brother gets $14,820 "bonus"
- be split proportionaly - each brother gets part of that $59k split by weights of their total valuation sum (in our example - each would bet 39.04% more than he expected)
- be stolen by the court/the man splitting goods ;-)

Hugo Steinhaus also mentioned that this procedure may be altered to minimise cash flows (items go to person with lowerst valuation, but results in everyone getting less than expected) or to consider not equal shares in total goods.