Chris Dicken needs Revision: Dividing the Check

On everyday game theory and "Dividing the Indivisible:"

This blog references another blog called Mind Your Decisions, something I stumbled upon while researching some SDA class concepts. Presh Talwaker does an excellent job, and in fact conducts a quite thorough analysis of discussing the topic of Dividing the Restaurant Bill among a group of people.

I love to look at the faces of my friends or coworkers and at their "confused, yet insistent on finding a solution quickly" expression when the server asks "are you guys ready for the check?" Often we are dining in a time-limited manner and need to get back to work, or to the Georgia Tech - Miami Thursday night football game where the 'canes got whipped 41-23, and we need to get outta Dodge.

We learned that divisions can only ever meet two out of the three E's: Equitable, Efficient, and Envy-Free. Toward the middle of the blog post, Talwaker makes a similar comparison when "thinking about an ideal outcome." He reasons that the following are best at exactly one trait, but with my Goizueta-induced interpretation we find two:

• Splitting the bill is efficient and equitable, but not envy-free. Who really want's to pay for someone else's prime rib when all he got was some fried mushrooms. Mmmm, fried mushrooms.
• Paying for what you ordered is efficient and envy-free, but not equitable. There's alway some sorry sop who ends up getting stuck with the tip or moree due to someone else's dishonesty,
• Separate checks is envy-free and equitable, but not efficient. The server always has to spend time tallying up everyone's meals, often inaccurately and needing correction.

In his blogging fury, Talwaker suggests a solution which is frankly a buzz kill--limiting people's options and assigning multiple clerical and leadership jobs to, if they're my friends, lazy bums who want to trudge through life the easiest way possible. (No offense ya big lugs.)

A reader proposes the "Chris Dicken" method which covers a lot of the issues but which leaves out the crucial detail of how exactly the check is divided other than by specifying a general "unit." Without blogging redundantly on the method, the "unit" rule of thumb should be:

• Score your meal on a scale of 1-10 with regard to how much you enjoyed your meal, adding a point for each "exotic" beverage. The tally becomes the dividing unit, and the total plus tip is distributed to each group member according to his score.

Equity arrives in the form of each person paying an equal "dollars per enjoyment" portion of the meal; Efficiency is achieved by anyone with a cell-phone calculator (usually me,) and here's the final rub: Envy-Free-ness comes from the satisfaction that you got what you paid for, plus a free review of the other guys' meals. Cheating is discouraged by having to publicly state how much you valued your selection. (Really, the prime rib was a little rare for your liking? Poor baby...) It works even better if everyone knows the rules before they order.

I know that I appear to claim to overcome the impossibility of achieving all three E's. But I don't quite get there either. There is efficiency to be lost in the process if everyone hates each other and just wants to eat, pay and get out of the restaurant as quickly as possible. But as social creatures, surely we can find a way to have fun with this method. After all, why are you there in the first place?

Caltech Physicists--amateurs.