Algorithms are a staple of modern life. People rely on algorithmic recommendations to wade through deep catalogs and find the best movies, routes, information, products, people and investments.

The original version of this story appeared in Quanta Magazine. Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price.

Digital quantification determines Americans’ quality of life. Algorithms select job applicants for interviews and employees for performance bonuses. They aggregate stories and products as we shop for ...

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