On the economics of leftovers: it's probably better not to

At the end of dinner last night in a Chinese restaurant, there was the inevitable discussion about who will take home the leftovers.

As with other elements of bistromathics, this can be awkward, indeterminate, and occasionally testy. If not handled sensitively, everyone--including the person who takes the leftovers--can end up feeling worse off.

So for the question, "who takes home the leftovers," we are presented with a prisoner's-dilemma matrix of outcomes. Except the central assumption of the prisoner's dilemma is that everyone has the same goal: that a smaller prison sentence is better than a longer one. With leftovers, it isn't a given that each person will consider it to be a benefit to bring home more leftovers than fewer. For example, a vegetarian will not be interested if the leftovers contain meat. Or a monster.

At least the nature of Chinese restaurants simplifies the options by separating each dish into its own leftover container, so taking home a vegetarian dish doesn't necessitate taking home all the other dishes, including the meat ones. But it does add complications. With containerized leftovers, the question now must be broken down from "who takes the leftovers" to "who takes which leftovers?". In effect, the question gets multiplied by the number of dishes: "Who takes the chop suey," "who takes the fried rice," "who takes the fried tofu," "who takes the bird's nest?"

The other complicating factor is that some people would prefer not to take any leftovers home. So the question of "who takes home which leftovers" is further broken down into "who wants to take home which leftovers?"

The problem we encountered last night, despite being a small group with only one vegetarian, was that the vegetarian was interested in taking home the vegetarian dish, but nobody was particularly keen on taking home any of the rest. It eventually got narrowed down to whether I or another person was going to take home the non-vegetarian dishes. The other person had a regular lunch on Fridays, so they wouldn't be taking it in for lunch today. My fridge is generally where leftovers go to die.

So for both of us, the desire factor was low. We've already asked for it to be packaged, so somebody's got to take it. The question has at this point devolved again from "who wants to take home the remaining leftovers" (answer: nobody) to "to whom will the remaining leftovers be assigned for the purpose of being taken home?" In other words, who doesn't want them least?

Probability to the rescue!

I tend not to like labels, or categorizing things into black and white. Everything is probabilistic. Will I die tomorrow? I can't say no, but the probability is very, very low.

And one last assumption that had been hovering over the conversation was that whoever took the food home would eat it. So I offered up the fact that there's about a 50% chance of the leftovers being eaten if I took them home. I knew this and this was factoring it into my decision, but it was not known to the remainder of the group.

All of a sudden, this cemented the decision. My competitor for the leftovers didn't particularly want them, but if they brought them home the leftovers would get eaten (convenient, since this happened to also be the person who paid for the meal).

The central goal of leftovers is to not let the already-prepared food go to waste. A 100% chance that they will be eaten versus a 50% chance that they will be eaten makes the decision much easier.

Were it not for that, we might still be at the table wringing our wrists about who would take them home. At least we'd have something to eat.

- RG>