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The economist Harold Hotelling has already inspired one Diff piece, on the optimal extraction rate for finite resources ($), but Hotelling has another rule that explains political non-polarization, fast-followers in tech, and the ubiquity of fried chicken sandwiches. Companies, parties, subcultures tend to converge over time, and a simple model can illustrate how.

Consider a stretch of beach 100 feet long, running east to west. Beachgoers are positioned randomly on the beach. There are two hot dog vendors who are both selling to beachgoers. Where should they position their hot dog stands?

One option is for one vendor to be a quarter of the way from one side, and the other to be a quarter of the way from the other side. This means that everyone is, at most, 25 feet away from a snack. That's socially optimal. But let's suppose the vendor on the eastern side moves a bit to the west. Everyone east of them will still patronize them, because they're still closer, if not the closest. But some customers in the middle will switch! So the other hot dog seller responds by moving east, and the same result ensues. Eventually, you end up with two vendors in the middle of the beach, and now the median distance customers travel, 25 feet, is the former maximum distance anyone used to travel.

You can substitute any other cost or one-dimensional positioning feature for this. If there are two snack food manufacturers, the socially-optimal setup might be for one of them to sell something sweet and the other to offer something salty, but the same convergent force will eventually lead both of them to sell a salty-sweet combo; customers with specific preferences will be worse-off, but they'll still have a favorite, while any convergence captures some of the customers who were close to indifferent before.

Making the model more reflective of the real world illustrates some of the assumptions it depends on. For example, we were always assuming exactly two competitors, but now let’s add in new entrants and departures. The model gets simpler if one of the initial two hot dog vendors quits—ironically, in this case the monopolist's profit-maximizing position is also the social welfare-maximizing position (though they'll probably respond to their new monopoly power with higher prices). In snack foods, if the formerly diverse market is now just a choice between salty-sweet and sweet-and-salty, a new entrant might introduce some product for the flavor purists and capture the market that way.

The model does describe cases where there are limits to new entrants. For example:

• In a voting system that tends to disproportionately reward winners, you'll expect some convergence between parties. They want enough differentiation for voters to feel like they're making a choice, but beyond that it makes sense for both sides to compete on similarity rather than difference.¹

• Businesses that are dependent on continuously delivering products with low value density will tend to have a few national brands and lots of regional ones, as with Coke and Pepsi. Both beverages are pretty similar, and retain just enough differentiation for customers to feel like they're making a choice. The amount is small, but nonzero: in the 1980s, when Coke was losing to the sweeter Pepsi in blind taste tests, they introduced a new, sweeter formula, a decision they reversed after a consumer backlash.

• Software products with high switching costs tend to get more complex over time, as standalone products get subsumed as features of a larger suite. As long as the pace of increased complexity is controlled, this doesn't hurt user experience too much. It does eventually lead to a sprawling mess, but by then a new kind of switching cost kicks in—the sunk cost of learning to use the system is so high that it feels wasteful to switch.

• This model also describes regulated industries that lack extraordinary returns on capital. It's hard for a bank to become a monopoly because it takes so much capital to grow, and while even the largest banks have some regional skew to their branch networks, they tend to settle on a similar model. They also diversify in similar ways: issuing credit cards, getting into investment banking, having a capital markets business of some sort, etc. (As Matt Levine pointed out, big banks' trading businesses act as a hedge for lending: when loans are suddenly defaulting, markets are high-volatility and high-volume, and intermediaries make a killing.)

• Online platforms tend to start with a very simple value proposition—find out which classes you have with someone you met at a party last night! Send a message that won't stick around on someone's phone forever! Upload a goofy lip-sync video!—and then start duplicating one another's features. The existence of competing apps indicates demand for a different interaction model, and the presence of users means that that model will be able to scale.

Hotelling's simplified model describes an iron law: under the right set of assumptions, sellers end up homogenizing their products, and niche interests end up under-served. In the real world, there are countervailing forces, and in practice the dimensions on which companies compete are messy enough that "adjacent" doesn't really work. But Hotelling's Law also illustrates why there's relentless pressure for homogeneity: if some people like product A and some people prefer product B, something halfway between the two will capture part of that audience. And the producer of A or B is probably in a better position to make this new compromise product C.

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Read More in The Diff

Hotelling’s Law shows up as background information in a few Diff pieces, including:

• Why Duopolies? ($)

• Hotelling’s Law also explains why the slippery slope is not a fallacy for contentious political issues.

• A General Theory of Product Convergence ($) wraps up several different instances of this in consumer Internet.

• Why Legacy Media Wins in Podcasts ($) shows that it happens in other kinds of media, too.

1. This is more visible in local politics; there really isn't an especially Republican or Democratic approach to filling in potholes, making sure the garbage gets picked up on time, etc.

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