It may seem surprising, but theories formulas derived from physics turn out to be useful tools for understanding the ways democratic elections work, including how these systems break down and how they could be improved.

A new physics-based study finds that in the U.S., elections went through a transition in 1970, from a condition in which election results captured reasonably well the greater electorate’s political preferences, to a period of increasing instability, in which very small changes in voter preferences led to significant swings toward more extreme political outcomes in both directions.

The analysis also shows this instability can be associated with an unexpected situation in which outcomes swing in the opposite direction of how people’s true preferences are shifting. That is, a small move in prevailing opinions toward the left can result in a more right-wing outcome, and vice versa — a situation the researchers refer to as “negative representation.”

The findings appear in the journal Nature Physics, in a paper by Alexander Siegenfeld, a doctoral student in physics at MIT, and Yaneer Bar-Yam, the president of the New England Complex Systems Institute.

“Our country seems more divided than ever, with election outcomes resembling a pendulum swinging with ever increasing force,” Siegenfeld says. In this regime of “unstable” elections, he says, “a small change in electorate opinion can dramatically swing the election outcome, just as the direction of a small push to a boulder perched on top of a hill can dramatically change its final location.”

That’s partly a result of an increasingly polarized electorate, he explains. The researchers drew from a previous analysis that went through the Republican and Democratic party platforms in every presidential election year since 1944 and counted the number of polarizing words using a combination of machine learning and human analysis. The numbers show a relatively stable situation before 1970 but a dramatic increase in polarization since then.[…]

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