# Maths website stops you being ripped off by your flatmates

Aleksandr Kichigin/Alamy Stock Photo By Timothy Revell Jealous that your flatmate has a better room than you? Time to use Spliddit – a website that works out the mathematically fairest way to decide who sleeps where and for what price in shared accommodation. Every renter knows that not all rooms are created equally. One bedroom might have an en-suite bathroom and a view of the seaside, whereas another is half the size and overlooks a dump. It’s only fair that the person who gets the better room pays a larger share of the rent. The question Spliddit tries to answer is: how much? Mathematicians have known for over 40 years that an envy-free method of dividing up rooms exists in every possible situation, resulting in everyone feeling that their room and rent contribution is at least as good as anyone else’s. All that’s required is to know the highest portion of the total rent each person would be willing to pay for each room, and an algorithm can then do the rest. But although there are many envy-free solutions in each situation, some of them can be a little odd. For example, it’s theoretically possible that a solution is given in which one person in the building doesn’t pay any rent at all. This outcome would still fit with the mathematical definition of fairness, but would probably not sit well with most people. Mathematics and reality don’t always align. “We’re looking at what is the fairest solution of them all. This is what I care about,” says Ariel Procaccia, one of the creators of Spliddit. So in 2015, Procaccia and his colleagues made a big change to their rent-splitting algorithm. Instead of just picking any old envy-free solution, they started choosing those that minimised the difference in rent payments between residents. When asked on a scale of 1 to 5 how happy people were with their own allocation and how fair they perceived everyone else’s to be, the average scores under the new method were 4.3 and 4.2, versus 3.2 and 2.9 for the old one. “That’s a really significant difference, showing how fair our solutions are,” says Procaccia. The results will be presented at the International Joint Conference on Artificial Intelligence in Melbourne, Australia, in August. Testing whether people think mathematically fair algorithms are actually fair is pretty tricky. If this is done in the lab, the situation is nearly always hypothetical or of low value. So what people consider fair is skewed by the fact that they don’t really care about the outcome. In comparison, tens of thousands of people have used Spliddit to work out how best to divide their rent – something of high value that people really care about. The results indicate that the service’s tweaked version of mathematically fair aligns well with what people think is fair too. The firm claims that its algorithms can also find fair ways to divide up taxi fares when multiple passengers are picked up from different locations, assign credit in a group project, divide up assets from an estate, or assign tasks such as household chores or work shifts. Each situation comes with various mathematical guarantees on the fairness of the outcome. Without Spliddit, dividing rent would often leave someone unhappy or in an unfair situation, says Jérôme Lang at Paris-Dauphine University in France. “It’s simple, beautiful, and one may wonder why no one had thought of it before,” he says. More on these topics: