Bistromathics was Douglas Adams' term for the crazy difficulty of dividing up l'addition at a restaurant properly. The very rules of math seem to go wrong, which is why they were able to make a stardrive as long as the ship had a bistro in it.

When groups go out to dinner, many people feel that "Div N" is the safest way to go. Namely divide the total bill with tip by the number of folks and everybody pays that. It has the advantage of great simplicity, avoiding the bistromathics. And it is close to a must with shared dishes and the norm for Chinese/Indian.

For many people, Div-N balances out over time, but many people resent Div-N for various reasons:

• For non-drinkers, they are bothered at paying a bar tab that often is as big as the food tab. Sometimes two totals are given because of this.
• For vegetarians, not only are their dishes usually cheaper, but many have an ethical problem with paying for other's meat.
• Dieters are as they are due to lack of self-control. Many have a compulsion that bothers them if they pay for food but don't eat it. (Larger restaurant portions are blamed by some for the obesity epidemic.)
• Women tend to eat less than men, causing a sex-bias.
• Some are just plain poor, and can't handle the high Div-N bill. Because Div-N encourages liberal ordering of expensive dishes and apetizers, it tends to raise the overall price.

Often there will be somebody (frequently of low income) who wants to break the Div-N rule and pay just for what they ordered. My rule for this now is to hand them the bill and say they are responsible for calculating and collecting the bill for everybody. I do this because there have been times when I have been the banker that people have announced they will only put in for what they ordered after much of the div-N payment has been done. While one can sympathise if they only ordered $10 of food and div-N is $25, what they are asking is that the banker now take the loss. This is why they should become the banker.

I was told last year of a new system which is gaining popularity in Europe. It works as follows. One diner is indeed the banker. The bill is passed around and each is told to put in "what they think they owe." The banker takes the pile of money and does not count it. It is made very clear that the banker will not be counting, at least not at the table. The banker then pays the bill out of their own wallet, usually by credit card, though sometimes with cash. To avoid counting, paying with cash should typically be done by just taking out a modest number of the large bills from the stack if the banker is short. If there is a shortfall, the banker loses out. However, those who described this system to me say that, based on experiences of bankers counting after they leave the restaurant (declasse as this may be,) the banker typically comes out of it a winner, often getting their meal for free, sometimes even making money on top of that. This, it is presumed, is because the people in the dining party tend to overcompensate, knowing that paying in low means cheating somebody they know, and not a faceless pile of money. This more than makes up for people who are bad estimators or misers.

The real beauty of this system is that everybody goes away happy. Nobody has put in more money than they felt was fair. Bankers may lose out a few times but on balance, it is reported, come out fine. The restaurant only gets the tip the banker announced. In other systems sometimes they get a windfall. The main downside is it does require people to have a sense of the cost of what they ordered, or they have to look through the bill which takes time.

I have yet to have the guts to try this, though. Some doubt it would work with people in the USA. Some suspect it will only work among those of reasonable means, or among good friends. Hard to say.

Of course, restaurants could also just not be so resistant to separate cheques. So many of them look at you like you've popped a 3rd head if you ask for it. Sure, it's more work but it's not like it's rocket science, especially since so many places have computers to handle the bill. One could even design paper billing systems that make it easy to do the individual accounting. Many groups of diners would also happily volunteer to tip (or plain old pay) an extra 50 cents/person for separate cheques. Even if it takes 1 minute extra per person to do the accounting, which I doubt, that's $30/hour for the work.

Updated note:

Now there is one reason for this. When a meal is done Div-N, people are encouraged to order more food, and more expensive dishes, since it makes very little difference in what they will pay. That's very good for the restaurant, and so they want to encourage both Div-N and expense accounts which cause the same thing. If this European system caught on, they might find it becomes worthwhile to do separate cheques. Separate cheques are important for things like group meetings, where there is no central sponsor, and the people gathering don't know one another very well (or at all.) Some groups I know that meet at restaurants end up either getting a deal for separate cheques, or limit themselves to cafeteria style restaurants where each person orders for themselves at the counter. That's a shame.