Splitting the bill revisited

My late mother-in-law's highly numerate son comments:

Where I had doubts about your argument was with your suggestion that numeracy or innumeracy is the primary factor leading people to choose between splitting the bill evenly and totalling each individual's meal. In my experience the main reason for not making each person pay for himself is the difficulty of identifying securely what each person has eaten or (even harder) drunk, especially at a large table. It can be done, but only by one person spending the whole meal keeping an eye on everyone else and/or being prepared to engage in painful arguments, and I suspect that mathematicians are no readier for this than the rest of us.

My own solution, as I may have told you, [no, and left to my own devices I grossly underestimated the degree of complexity involved in achieving a fair solution] is to divide the final bill up by categories - hors d'oeuvres, main course, dessert, wine, coffee and so on (adding an appropriate percentage in each case for tips). I then divide each category by the number of people who had something under that heading. So if 8 of the 10 had hors d'oeuvres, I divide the hors d'oeuvres on the bill by 8 and share it between them; if 6 had drunk wine I divide the cost of the wine by 6 and share it, and so on. I then arrrive at a final reckoning for each individual on that basis. This means that a high measure of fairness is maintained, with everyone paying in rough proportion to what they ate and drank, without my having to remember who exactly had had the sole and who confined themselves to the pasta or whatever.

Of course, this did require me to be numerate (perhaps more so than totting up individual bills would have done?) ...

[a pity the economists responsible for the original article did not consult a numerate restaurant-going classicist before embarking on research, one may feel -- and all the more scope for an unscrupulous NRGC to impose on his less numerate colleagues, one may also feel]