A new topological model connects a centuries-old voting paradox to a surface with no distinct inside or outside.

Mathematically speaking, democracy is next to impossible.

That may sound like the premise of a Silicon Valley billionaire’s six-hour podcast, but it’s actually a statement about a remarkably stubborn problem: How do you translate a group of individual preferences into a single choice?

In 1785, the French mathematician and philosopher Nicolas de Condorcet discovered that a majority can sometimes vote itself into a logical loop. In elections with three or more candidates, each voter might rank the candidates in a perfectly clear and consistent way — yet when all the votes are tallied, every candidate loses in a head-to-head contest against one of their rivals.…