algorithm for common goods cost sharing
In situations where the cost of common goods or utilities is shared, such as the roommate situation, usually several algorithms are used. Sometimes people take turns bearing the cost of new purchases or renewals. Sometimes people split the cost per head. These are more convenient and efficient than each person acquiring a copy of such goods for oneself. But it isn’t necessarily fair due to usage differentials, although people tend to live with it.
It just occurred to me that a perfectly fair and distributed algorithm is for the person who happens to exhaust a unit quantity of a common good to replace it with a new unit, at own cost. This shares cost proportional to actual use (probabilistically), but doesn’t require any coordination or accounting.
