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.
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.