For something like sweeping, or dusting, though, where it’s a true public good, the market system would work pretty well. The traveling roommate would contribute less to the mess, but because they aren’t there as often, they’d also likely set a lower value to having the place clean. Granted, nobody wants to come back to a shitty apartment, but in dollar terms, whats that worth to you? Under the above system, you set that price, and either pay it to the other roommate, or to a third party who will do the cleaning.

Clearly there’s still some kinks that need to be worked out in the idea before anyone tries to implement it, and I wouldn’t suggest using it with a live-in girlfriend. The economic logic might hold, but a “pareto optimal” living situation isn’t the same thing as a happy one (that’s why you have to put the toilet seat down).