Reverse Hotelling's Theory

Hotelling’s Theory is named after the man’s name and has nothing to do with hotels. It is an interesting economic theory explaining why free actors will provide consumers with the minimum possible amount of variety. The free actors are the businesses involved and all they want is money and the more the better. If their product is too different it will not appeal to the largest group and they will make less money. But if it is identical to other competing products they will only receive a share of the market that is interested in that product. The ideal money making situation is make their product just barely different enough from existing products that they do not have to compete for the same market while still appealing to the largest possible number of consumers. This leads to free actors providing only the minimum amount of variety possible. It’s an interesting theory, even if somewhat sad in its outcome. But its even sadder in my opinion when applied to politics, but let me first explain Hotelling’s original idea.

In your mind imagine the horizontal line is a public beach. Bob places his hot dog cart as shown, it is the only hot dog cart at the beach. All the beachgoers walk to his cart and buy his hot dogs and he has the entire market to himself. Bob is doing well. Joe sees how well he is doing and decides to move his hot dog cart to the same public beach. For the beachgoers the ideal location for Joe’s hot dog cart would be like this:

Bob and Joe’s hot dog carts are each one third the distance from the ends thus minimizing the amount of walking beachgoers have to do. This is the ideal placement of just two hot dog carts from the perspective of the beachgoers. But Bob and Joe are free actors and serve their interests first. Joe will really place his hot dog cart as shown here:

Joe’s cart is barely any distance from Bob’s. Almost no walking time is being saved. The beachgoers are barely benefiting at all from the addition of a second hot dog cart. But Joe is benefiting, he is now closer in walking distance to the majority of the beachgoers and does the most business. Bob recognizes the problem. He can see that Joe is doing the majority of the business because there is less walking distance between Joe and the majority of beachgoers. So he moves his hot dog cart a few feet over, now his hot dog cart is closest to the majority and he does the most business.

Joe recognizes the impact of this move on his business and counters by moving his hot dog stand. This continues until the system reaches a resting point with both hot dog stands nearly side by side at the center of the beach as shown:

This is the inevitable end as long as Bob and Joe are free actors. They are trying to maximize the money they make and the beachgoers are trying to minimize the distance they walk. As long as all are free actors the inevitable result is Bob and Joe minimizing the difference between themselves and the addition of a second hot dog cart adds very little to the beachgoers experience. The inevitable result as free actors is different from the ideal result of each hot dog stand being one third the distance from the end. This sad result is what Hotelling’s Theory is about. I will argue that it is even sadder applied to politics but first the obvious objection to this example is it restricts the beach to only having two hot dog stands. This is the weakness of the example as applied to economics. Yet this restriction does apply to American politics as all countries with winner take all district voting end up being dominated by just two political parties. What makes this example unrealistic as applied to business makes it realistic as applied to American politics. As every reader knows, in American politics there are only two hot dog stands.

Instead of a public beach we are now moving along a political spectrum from left to right. The cost to the beachgoers was walking distance. The beachgoers wanted to minimize this cost, they want to walk the minimum distance. Ideally they want the hot dog stand to be right behind them on the beach so they can walk the shortest distance. But with only two hot dog stands the majority of beachgoers will have to do some walking.

The cost to the voter is the distance between his political positions and the position of the party he votes for. Ideally the voter will agree with everything the party says. But with only two parties most voters will have to vote for a party they have disagreements with. They will choose the party they disagree with the least, the one closest to their position on the political spectrum. This describes a system identical to the previous economic example and it should reach the same equilibrium. Given the desire to make the most money possible we end up with the two hot dog stands straddling the center line to appeal to the most possible consumers. If parties desired the most votes possible they would obey Hotelling’s theory and straddle the center line to appeal to the most voters possible. Money is the goal of the hot dog seller and the hot dog business obeys Hotelling’s theory. American politics does not obey Hotelling’s theory.

Consider the above a recent change in politics. Previously both the Republicans and Democrats were at the center and the Democrats veered to the extreme left. If this was hot dogs the Democrats would have just committed suicide. If this was hot dogs the Republicans could just stay in place and be closer to the majority of the voter’s preferences and win the majority of the votes. The Republicans could even move further to the left themselves and as long as they stayed to the right of the Democrats they would still appeal to the most voters and get the most votes and win all the elections. If American politics was like hot dogs this sudden move to the extreme left by the Democrats would be suicidal and the Republicans would win everything until the Democrats decided to return to the center. But anyone experienced with American politics knows what really happens. What really happens is what is shown here:

The Republican response to the Democrats veering to the left is to veer to the right. I refer to this as Reverse Hotelling’s theory. In politics parties try to maximize differences while in economics businesses try to minimize differences. Politics conforms to Reverse Hotelling Theory.

If politicians viewed votes the way businesses viewed money they operate according to normal Hotelling’s theory. When the Democrats veer to the left the Republicans make a second move to gain the majority of voters as shown here:

After many moves and counter moves the system would reach equilibrium as shown here:

This would be the sensible result and the best for all involved, especially the people of the country. As an American I wish this was the result. I wish our politics was run like our hot dog stands. I wish our parties were aiming for getting the most votes and straddling the center for that purpose. It would be a better world for everyone. Instead we end up with the situation as shown here:

Both parties stake out positions to the left and right of the majority of voters. The positions are carefully selected to allow for the greatest possible amount of extremism while still just barely winning an election. American politicians consciously aim for 51% solutions. They consciously choose the positions which are the most extreme possible that still allow for winning 51% of the vote. This is Reverse Hotelling’s theory.

The key to understanding this is to understand parties view appealing to voters as a cost not a benefit. The hot dog seller wants as many customers as possible, he wants to sell as many hot dogs as possible. This is different from wanting to buy as many hot dogs as possible. The hot dogs cost money and he only wants to buy the minimum necessary, it is sales he wants to maximize and not purchases. This is how the political parties think. They view voter support as a necessary cost to be minimized. What they want maximized is political extremism. American parties will only exhibit moderation to the minimum necessary to get to 51% of the votes.

This is because the real goal of the politician is not winning votes. Votes are a practical tool for what he really wants to do, which is change history. The hot dog seller buys hot dogs as a necessary tool for making sales and getting what he wants. The politician gets votes as a necessary tool for the goal of changing history. To go down in the history books is what the politician wants. You can’t do this by keeping things the same, you have to change things. History is the record of changes and to go down in history you have to make one of these changes.

What the majority wants the majority gets. What the majority wants is what we already have, to continue this is not something new, it is not change. It is not making history. The power comes from the majority but this source of power is inherently opposed to change. So the politician looks for the 51% solution. He looks for the smallest possible coalition, not the largest. He looks for the political positions which will allow him to make the largest possible historical change which means the most extreme position that still gets 51% of the vote. This is the tragedy of American politics. A tragedy is something which didn’t have to happen but was still inevitable. Things don’t have to be this way, but it is all inevitable.

At least at the national level American politics will be dominated by extremists until there is some sort of fundamental change in how this country operates. Our country will continue to be tortured by both parties as they try to write their names into the history books with their 51% coalitions. The real answer is to close the history books. If they can’t be written in the politicians will give up. We need a fundamental change which makes our country immune from the historical ambitions of our politicians. Until this change comes American politics will always be run by Reverse Hotelling’s theory and we will all suffer for it.