Why I Hate Potlucks

I hate potlucks. I hate potlucks so much I call them potyucks. You expect a dinner but end up with a plate full of rice, rolls, and cookies. Someone always brings a bucket of KFC original recipe, but the bucket only has fifteen pieces, and they are gone by the time you get to them. I know some of you are already typing your comments: "My ward has the best potlucks..." or "My mom always makes this amazing dish..." Hold off for a second, because there is a much deeper reason for my communal dining hatred. There are exceptions to general rule of potluck crappiness, and I will get to those eventually. 

A potluck is a game theorist's worst nightmare because there is a logical, gaping flaw in the incentive system that the potlucker relies upon to create a good meal. The flaw is the same one found in the insinuated explanation of the Nash Equilibrium from the movie "A Beautiful Mind." We need a quick review of the movie before we dive headfirst into the three rice dishes, unlimited rolls, and cookie fest that is a typical potluck dinner, about which even John Nash himself would have turned to his imaginary friends and said, "Screw this, guys. I'm going to Taco Bell."

The explanation I refer to is when Nash and his friends are hanging out in a bar. A beautiful blond woman walks in with her less-attractive brunette friends behind her. Nash has his "aha" moment. The friends begin to joke about how they will fight, "shall we say swords, gentlemen, pistols at dawn" to be with her.

Friend:  Have you remembered nothing? Recall the lessons of Adam Smith, the father of modern economics.

All together: In competition, individual ambition serves the common good. 

Friend: Every man for himself, gentlemen. And those who strike out are stuck with her friends. 

Now the scene is set; the blond looks over, and Nash sees her face flash. Here comes the breakthrough. Cue the mystical music.  

Nash: Adam Smith needs revision. 

Friend: What are you talking about?

Nash: If we all go for the blond, we'd block eachother. Not a single one of us is going to get her. So then we go for her friends, but they would all give us the cold shoulder because nobody likes to be second choice. But what if no one goes for the blond? We don't get in eachother's way, and we don't insult the other girls. It's the only way we'd win. That's the only way we'd all get laid. 

And...scene. 

However, there's a problem with this scenario, and this same problem creeps up when you examine a potluck mathematically. Let's assume I am one of Nash's two other friends. Nash is right: I would go for the blond just like all the other guys. 

But let's say we follow Nash's advice, gather around a pool table and hash out a game plan. Here are the strategies I have to choose from:

A. Hit on the blond. 

B. Hit on friend #1.

C. Hit on friend #2.

D. Hit on friend #3. 

We decide to listen to Nash and agree that strategy A is not an option. So I choose strategy B, Nash chooses strategy C, and our other friend chooses strategy D. This is the agreement we make when we put our hands together, yell "break!" and start the execution of our plan to get laid by non-blondes. After we leave the pool table, what do you think will happen?

We will all go for the blond.  Why?

If I, as an individual in the group, know everyone else has chosen a strategy that does not involve the blond, I have a voluptious incentive to deviate from my present strategy and hit on her. However, every other man leaving the table thinks the same thing. So we end up crowding the blond, even after we've created a strategy for exactly the opposite.

A Nash Equilibrium is a list of strategies, one for each person, such that if each player knows the strategies of the rest of the group, he has no incentive to deviate. The payoff for deviating must be less than the payoff for sticking with the plan. That is why all this "What if no one goes for the blond?" business is not a Nash equilibrium, because I am going for the blond if I know nobody else is. So what would be a Nash equilibrium in this scenario? 

Let's say I am stronger than both Nash and our other friend combined. If I said, "Listen, I'm going for the blond. If you guys go for the blond, I will take you out to the alley behind this bar and smash your face in with a crowbar." 

Now I get the blond, and my friends (if I can call them that after this exchange) have no incentive to deviate from their strategies of going for her friends, because they know there's no way they will get laid with a smashed face. We all follow the plan because the plan is the best thing for each individual. 

Now let's transfer this knowledge to the scenario of a potluck dinner. A potluck is an agreement between a group of people to each bring a dish from one of usually four or five categories: Main Dishes, Bread/Rolls, Desserts, Drinks, etc. But let's assume, to start, that we only have one category: Main Dishes. Usually everyone assumes this will be a great meal because everyone will bring their "favorite" dish. I will also assume that a big bowl of rice or pasta does not count as a main dish. What would you say if you asked your mom what she was cooking for dinner and she said "We are having just plain white rice!" or "Cooked pasta!" Exactly. Not a main dish.  

The blond, the holy grail in this scenario, is to make something as cheap and quick as possible. Her brunette friend is the strategy to make something delicious and dinner-worthy. Granted this is an oversimplification, but I'm not going to list every strategy in the potluck strategy set. 

Everyone agrees to the unwritten potluck law: to bring your favorite dish (by the way, this scenario works whether or not there is a sign up sheet).  That is the brunette: we all agree to bring something dinner-worthy. But, with little accountability mechanisms or potluck regulations, as soon as we leave the pool table incentives such as cooking-time and the value of a dollar cause nearly all of us to deviate from our agreed strategy, and for the same reason Nash and his friends would deviate: if everyone assumes everyone else will stick to the agreement to bring something dinner-worthy, I can get a great dinner for ten minutes and fifty cents worth of rice. I'm going for the blond.   

This is even more evident in a multiple-category potluck. Ever wonder why the Breads and Dessert categories fill up quicker than the Main Course on a sign up sheet? It's cheap and easy to make cookies or buy a cake and essentially trade that for a full hot meal. Ever wonder why more desserts and less main courses seem to show up, even though your sign up sheet has them equal? People don't bring what they sign up for, because it's not rational to do so. If I see all the slots for desserts and bread filled up, I'm forced  to bring a main dish. Therefore, I will either make a crappy, cheap main dish, or I will just bring a dessert and not tell anyone. The incentives to deviate are stronger than the incentives to keep my agreement. 

I know some of you think this is not true, because you've been to a few amazing potlucks in the past. Guess what: it is true, and the potlucks you're thinking of inadvertently created a Nash equilibrium to solve it! There are two ways to achieve Nash equilibrium: make the blond uglier, or the brunette prettier. 

This best example of this I can think of is in my ward back in Washington DC. At their monthly potluck, they had thick Middle Eastern meatballs, juicy BBQ chicken, and taco salads. And they always had leftovers. Why does this potluck work, where others fail?

The answer is this: the meatballs were called "Brother Ahmad's Middle Eastern meatballs," the BBQ chicken was referred to as "Sister Johnson's Amazing Chicken," and the taco salad was known as "Elder Wayne's Southwest Taco Salad." Every month, the members of this potluck knew their names would be attached to the dishes they presented. There was a good pride incentive to make the best dish possible, and to make enough so that everyone could try it. The better yoru dish is, the more you want to make. 

If the potluck is a one-time thing, you could require each dish to have the name of the person who made it. The public reason could be because you want everyone to know whom they should thank for this dish. But the private, real reason is to create a barrier to deviation, because nobody wants their name associated with a crappy dish. The blond just got a little more homely, thereby forcing a Nash equilibrium on the potluck. 

Another way is to make the brunette eclipse the blond. This can be done with a positive incentive structure like a main course contest, where each member of the potluck votes for their favorite dish, and the winner receives a prize. Also, if you have a sign up sheet, no one will try to sneak in a dessert instead of a main course, because everyone will know they didn't keep their word. Now there is both a desire to win and a a reason to put your name on your dish; a double Nash whammy! 

Potlucks are like negotiations. Successful ones have incentives and barriers that force each party to perform his part of the agreement, because that is the best course of action. The Middle East peace negotiations suffer from a broken incentive structure. Maybe it's time a mathematician got in on those negotiations and opened up a can of whoopnash. But please don't bring that to the next potluck, unless you're bringing a bucket of KFC to go with it.