Hotelling's Law suggests that in many markets it’s rational for producers to make their products as similar as possible and their stores as close together as possible. Hotelling’s law can help us understand political party convergence.
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On Northland Road there are three pizza shops next to one another.
All the major brands are represented: Pizza Hut, Domino’s, Hell’s. How did they all end up in the same spot? Hotelling's Law is an observation that in many markets it is rational for producers to make their products as similar as possible and their stores as close together as possible.
From Wikipedia:
“Suppose there are two competing shops located along the length of a street, with customers spread equally along the street. Both shop owners want their shops to be where they will get the most market share of customers. If both shops sell the same range of goods at the same prices then the locations of the shops are themselves the 'products'. Each customer will always choose the nearer shop as it is disadvantageous to travel to the farther.”
For a single shop, the shop owner is indifferent about the location of the shop since it will draw all customers to it by default. Interestingly, though, Hotelling's law predicts that a street with two shops will also find both shops right next to each other at the same halfway point. Why?
Imagine there are two ice-cream carts, one at each end of a beach. If there is an equal distribution of rational consumers along the beach, each ice-cream cart will get half the customers, divided by an invisible line equidistant from the carts. But, each ice-cream cart owner will be tempted to push their cart slightly towards the other, moving the invisible line so that the owner is on the side with more than half the beach. Eventually, the ice-cream carts will end up next to each other in the centre of the beach.
The same thing played out with the three pizza shops on Northland Road. The strip of shops on Northland Road lies on the intersection of three suburbs: Northland, Karori, and Kelburn. This makes it an optimal mid-point for a single vendor to put their pizza shop. When there are three vendors, they end up next to each other because to deviate from the midpoint would mean conceding market share to their competitors. It would be more socially beneficial if the pizza shops separated themselves—each could still draw one third of the customers but customers would, on average, make a shorter journey. However, no shop would be willing to do this independently as it would then allow the others to capture more than their fair share of the market.
Hotelling's Law is connected to an idea from political science: policy convergence.
Politics is a marketplace. To achieve a critical size and to command the parliamentary majority, parties must bid for support from a diverse electorate. They adjust their appeal to changes in the public sentiments or priorities which seem likely to influence voting patterns. The whole object is to produce a slate of policies which, perhaps, only a minority would have chosen as their preferred options but which the broadest possible range of people can live with.
In more technical language, spatial models of political competition predict that parties are vote-seeking, positioning themselves to capture the interests of the median voter. The median voter may be the median voter politically, in terms of left-right, or it may be the median-income voter. Parties are not necessarily vote-seeking though. They may be office-seeking, vying to become a coalition partner. Or they may be policy-seeking, advancing particular policy objectives that are linked to underlying ideological positions. Rather than appealing to the median voter, policy-seeking parties seek to move the median voter towards their policy positions. Yet even if vote-seeking does not constitute the end goal in itself, maximising the vote share remains an efficient strategy for office- and policy-seeking parties. Consequently, we expect parties to naturally converge around the median voter, and the evidence shows that this is often the case.