Ice Cream Wars

Imagine a beach on a hot steamy day. People are scattered uniformly along the beach, and on this hot sunny day they could really use a chilling and soothing treat. Luckily two ice cream vendors show up, loaded with goodies. We can call the vendors Ben and Jerry, or Haagen and Dazs, but let's call them Donkey and Elephant; no harm in that.

Donkey and Elephant establish positions on the beach, and customers start flowing. It quickly turns out that both carry the exact same merchandise and sport identical prices. With quality and price being equal, customers choose the closest ice cream vendor.

Let's examine our vendors' business opportunity. Elephant has positioned himself towards the right end of the beach. Donkey is to the left of Elephant, but still right of center. All the customers to the right of Elephant will spend their hard earned dollars at Elephant's, and those to the left of Donkey will do so at Donkey's. the customers positioned in between the two vendors will be split half and half. Hmm... Perhaps a picture can help. Let's depict Donkey's customers in blue and Elephant's customers in red; no harm in that.

Elephant soon realizes that he holds the short end of the beach. After a deep session of meditation he shifts closer to Donkey:

Sweet! Elephant starts dreaming about retirement as more coins pour into his pocket. But then, after the initial indulgence, he realizes that Donkey is still making more money than him. Unacceptable!!! He dips again into intense meditation and comes up with a daring strategy: he will venture farther left, past Donkey!

Life is good for Elephant! He is clearly the king of the beach. But what's that??? Donkey has just moved to his left, towards the center of the beach!

Donkey has regained the lead. Elphant ignores some customers and rushes left, closer to mid-beach, passing Donkey yet again...

At the end of the day our exhausted ice cream vendors have reached the only stable equilibrium: they stand back to back at the exact mid-point of the beach. The customers are split equally between the two.

The American political system is a two body problem, and is therefore rather simple from a statistical standpoint. While people are excited about one candidate or another, in the long term the democrats will win about half the elections and the republicans will win the other half. Any other solution is unstable.

Zzzzz...

(Thanks to David Meiri for the ice cream analogy)