Your methodology is fair from the objective vantage point of the rooms, but not necessarily from the subjective vantage point of the people.
Consider the following strawman scenario: Roommate A is earning a million dollars a year, and the other three are student artists, surviving on odd jobs. Would it be "fair" for roommate A to to pay no more than $215 - $135 = $80/month more than the others, when their ability to pay is so much greater?
That's obviously a contrived example, but not too different from my own situation. I'm a consultant / business owner whose income is not extravagant, but is reasonably above the UK mean. I have a flatmate -- who is fact a student artist -- who contributes roughly 20% of the total costs to the household, including utility & council taxes and whatnot. An 80/20 split may sound terribly inequitable, but we're both paying a similar percentage of our earnings for rent, so it's quite equitable from that perspective.
Absent this arrangement, I could still afford to live on my own, but I'd be left with less cash at the end of the month, and my place would seem a bit empty. My flatmate, in turn, could probably only afford to live in some tiny squalid place far from the city centre. If we were to insist on a 50/50 split which is "fair" from the perspective of the space & utilities (rather than from the perspective our respective pocketbooks), then no accommodation could be found: my flatmate could never afford to pay half the rent. But by optimising around a subjectively fair allocation of our personal resources and preferences, I get an excellent flatmate and more spending money, and they get a much nicer place in London than they could otherwise afford. This is a far better outcome for both of us than we could achieve by insisting on an "objectively fair" split.
As for your chores dilemma: just have a basic rule about not leaving one's personal crap in the common areas. Then for the routine tasks (vacuuming, mopping, etc.), collect an extra $5/week from everybody, and use that money to hire a professional cleaner (or if one of the flatmates is short of cash and particularly good at / enthusiastic about cleaning, pay them to do it). Seriously, it's worth it. People have vastly different capabilities and preferences when it comes to cleaning, and trying to make everybody equal in this respect is an un-winnable game. Don't even try.
tl;dr: the less you strive for egalitarianism through uniformity, and the more you accommodate the divergent abilities and subjective viewpoints of your flatmates, the better you'll be able to find win/win scenarios in shared-living situations.
I'm not following... We are paying roughly market rates divided by the space we actually use. While it could be looked at as only being fair if each pays a percentage of their income, this (as you mentioned) reduces the benefit living with people to get cheaper rent.
I actually do make a decent bit more than my roommates, but I choose to live an extremely simple life for other benefits. If my rent was higher than it is now (to match my income), living there would not be worth it and I would get my own apartment without roommates, etc. It would also create trouble between us as I don't always find the benefit in just having them around for how great they are.
I can very well see how your situation works for you, but I do not agree that my setup is at all unfair.
As far as cleaning goes, none of my roommates have the income to constantly pay professionals... So that is why they can take a pick off the list as opposed to being assigned tasks.
I don't think your method is necessarily unfair. I just don't think it necessarily is fair, either. If all of your roommates have roughly equal views on the value of money, square footage, and various intangibles (such as, say, the quality of light in a room), then your method is probably entirely fair -- no arguments there. If, on the other hand, they each assign very different values to space or money or those various intangibles, then it's possible that -- despite paying similar amounts of money for similar amounts of space -- they are actually experiencing very unequal levels of economic utility in exchange for their rent. Which would be where something like the NYT algorithm begins to make sense, since this attempts to maximise the utility function for all parties, regardless of how they themselves define utility.
As for the cleaner: yours is a very common reaction that I get whenever I give this advice to my friends. But professional cleaners are surprisingly affordable. In multi-person households -- unless you're living close to the poverty line -- they should be entirely affordable (much less than the proverbial cup of coffee per day), and go SUCH a long ways towards reducing household drama! Have you tried actually crunching the per-person numbers? You might be surprised at the results.
Is it fair that just because someone has the ability to pay, they ought to pay? If a millionaire was planning to move in, and you said "for you, you pay 100% of rent," then the millionaire would probably just go somewhere else. Afterall, they're probably looking for cheap, since they could surely afford a place to themselves or perhaps even a house (depending on location). Likewise, the students may be "poor," in monetary expense, but one could argue that they are simply spending their money on other things that are important to them, and so why should they get a free ride because of that?
In the situations I've been with, I'm fine with (rent/number of renters). the lease holder gets her choice of room, the rest is first come/first serve.
I think you're missing the point. This is a value-optimisation problem, and 1.) not all value is monetary, and 2.) the perception of value is inherently subjective. That's why optimisations cannot be created via static externally objective criteria, and must be the process of a negotiation, as the NY Times calculator proposes.
If the millionaire readily agreed to pay 100% of the rent, then that would be "fair" because clearly in order to make that agreement, they'd have to be receiving some kind of non-monetary benefit from the arrangement. On the other hand, if they walked away from that proposition, then obviously no optimisation has been achieved, which is why a static "the millionaire pays for everything" policy is not a good idea. Instead, the millionaire should return with a counter-offer, and this should continue until parity is achieved. When all the subjective qualitative factors are included, there's no guarantee that it will be at 50/50 (which may not even be a possible solution, as in my example with my flatmate). That's the beauty of the Times' calculator: it allows people to apply whatever personal subjective criteria they like when making their own valuations, and then finds the dynamic equilibrium between these.
Your situation assumes that you could not find a great roommate who would split the cost 50/50, or at least split the cost based solely on the objectives (room-size).
That said, your arrange works really well for you, and the utility value of the "fully optimial rent" amount clearly isn't important to you, so there isn't much incentive for you to address it.
As a minor aside, tl;dr should be posted at the top :)
Consider the following strawman scenario: Roommate A is earning a million dollars a year, and the other three are student artists, surviving on odd jobs. Would it be "fair" for roommate A to to pay no more than $215 - $135 = $80/month more than the others, when their ability to pay is so much greater?
That's obviously a contrived example, but not too different from my own situation. I'm a consultant / business owner whose income is not extravagant, but is reasonably above the UK mean. I have a flatmate -- who is fact a student artist -- who contributes roughly 20% of the total costs to the household, including utility & council taxes and whatnot. An 80/20 split may sound terribly inequitable, but we're both paying a similar percentage of our earnings for rent, so it's quite equitable from that perspective.
Absent this arrangement, I could still afford to live on my own, but I'd be left with less cash at the end of the month, and my place would seem a bit empty. My flatmate, in turn, could probably only afford to live in some tiny squalid place far from the city centre. If we were to insist on a 50/50 split which is "fair" from the perspective of the space & utilities (rather than from the perspective our respective pocketbooks), then no accommodation could be found: my flatmate could never afford to pay half the rent. But by optimising around a subjectively fair allocation of our personal resources and preferences, I get an excellent flatmate and more spending money, and they get a much nicer place in London than they could otherwise afford. This is a far better outcome for both of us than we could achieve by insisting on an "objectively fair" split.
As for your chores dilemma: just have a basic rule about not leaving one's personal crap in the common areas. Then for the routine tasks (vacuuming, mopping, etc.), collect an extra $5/week from everybody, and use that money to hire a professional cleaner (or if one of the flatmates is short of cash and particularly good at / enthusiastic about cleaning, pay them to do it). Seriously, it's worth it. People have vastly different capabilities and preferences when it comes to cleaning, and trying to make everybody equal in this respect is an un-winnable game. Don't even try.
tl;dr: the less you strive for egalitarianism through uniformity, and the more you accommodate the divergent abilities and subjective viewpoints of your flatmates, the better you'll be able to find win/win scenarios in shared-living situations.