Have you noticed that restaurants (or pharmacies, bakeries, coffee shops and ice cream parlors) are often neighbors? Have you ever wondered why there are two gas stations in adjacent blocks? Or several nightclubs on a city street?
Wouldn’t it make more sense if they were distributed evenly throughout the city to be at the hand of more customers?
If there are going to be, say, 5 pharmacies selling their products at very similar prices in a place with 5 streets, it would be best if there was one on each street.
The closer to your house, the better.
Why then do we often have to go further afield to find 2 pharmacies within walking distance of each other?
That was what Harold Hotelling wondered.
The Ice creams
Hotelling (1895-1973) was an American mathematician who was involved in the early 20th century movement to mathematize economics, as well as an influential mathematical statistician and professor, affiliated with Stanford, Columbia, and North Carolina-Chapel Hill universities. .
His name is still familiar to a range of professionals that includes, in addition to economists and statisticians, pedagogues and psychologists.
He left, apart from the law and other things, the Hotelling Lemma, the Hotelling Rule and the Hotelling T² test.
The law that bears his name is derived from an article entitled “Stability in Competition”, which he published in 1929, with a model that showed why “buyers face everywhere with excessive similarity“.
He explained what was happening using game theory and, as examples, cider merchants and religious communities, but later the model began to be illustrated with ice cream vendors and beaches… so let’s go with the sweeter version.
Go figure…
A kilometer long beach.
One day it occurs to Maria that she can sell ice cream. The next day, it occurs to José that María’s idea is a good idea.
Initially, each one is positioned 250 meters from each end of the beach.
Since they sell the same flavors of ice cream at the same prices, bathers go to buy the place that is closest to them: some go to the cart on the right and others, to the one on the left, and no one has to walk more than 250 meters to enjoy.
Those who are in the center do not care if they go to one side or the other, however, on this hypothetical beach, María and José initially sell the same amount daily.
But one day, José realizes that if he moves to the center of the beach, he can take away clients from María because he will keep his own and win those from the center who go to her cart.
Or that the similarities between video games, toothbrushes or toothpaste outweigh the differences?
Companies need to have as many customers as possible, and unless they have a distinctive product that sets them apart and the budget to advertise it, the best bet is to create products that (more or less) everyone likes.
If they chose a combination of features that especially appeals to a small segment of consumers, they would leave the largest segment to the competition.
Politicians
The model has also been applied to political candidates, who often tend to embrace “centrist” viewpoints during debates in order to appear the best option for the majority of voters.
Imagine that our two ice cream vendors are two candidates for the presidency: Maria is a liberal and Jose is a conservative.
Voters are distributed across the political spectrum, although there tend to be fewer at the extremes and more in the middle.
And they choose the candidate closest to their views.
Candidates need to converge in the middle.
It is not surprising then that politicians are always following the “average vote”.
And, neither, that it is usually difficult to differentiate the candidates during the electoral campaigns.
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