Civic-minded observers of the presidential race in the United States often express consternation that one of the leading contenders is a celebrity best known for “reality television”—real estate mogul Donald Trump achieved new levels of recognition by appearing for a decade on The Apprentice.

Some argue that reality TV doesn’t help us understand complicated political and economic issues. But some reality TV actually does offer useful lessons.

Exhibit A: American Idol. (Actually, not just Idol, but any of the shows that feature voting such as Dancing with the Stars, will also suffice for this lesson.) Let’s say there are four singers left: Amanda, Bob, Carla and Daryl. Most people think that Bob, who has weirdly anachronistic punk stylings, is the weakest singer. Amanda fans see Carla as the greatest obstacle to Amanda’s success, and vice-versa, because both Amanda and Carla are sweet-voiced country singers. Most viewers find Daryl’s R&B-lite sound inoffensive but generally uninteresting, although he does have some devoted fans.

Believe it or not, it’s entirely possible that Bob could win.

Although in this example, country music is the preferred style of the majority of viewers, the “country vote” is split between Amanda and Carla, with the result that Amanda is eliminated by a narrow margin, leaving Bob, Carla and Daryl. Again, while most people find Bob the weakest, Amanda’s voters may throw their support behind Carla, because she’s in the same genre, but they may defect to Daryl or abstain—possibly out of a lingering anti-Carla loyalty to Amanda, possibly because they prefer Daryl to Bob and think Daryl could use their help, possibly thinking that Carla is popular enough to be “safe”—and the voting comes out 32 per cent for Bob, 30 per cent for Carla, and 38 per cent for Daryl. Carla is eliminated, and in the final round, the alienated country bloc largely abstains from voting, leaving Daryl well short and Bob victorious.

Stranger things have happened.

When the basic framework is majority rule, but there are more than two options, one possible (and indeed not at all unlikely) outcome is that the winner has a plurality—more votes than any other one option—but actually represents a minority, not a majority. More people dislike the plurality holder than like it, but no other single option has more support.

As this blog goes to press, we’re seeing a similar phenomenon in the U.S. primary elections, as the Republican Party tries to go about selecting its nominee for the general election in November. As of this writing, Donald Trump has won 646 delegates, quite a bit more than any other candidate. But the non-Trump voting comes to 707 delegates. More Republican voters oppose him than support him, yet he’s in fact in the lead. The other candidates are like Amanda and Carla—if their fans could somehow coordinate their efforts, Bob wouldn’t win. When the weakest singer wins, there’s something weird about the singing contest.

One possible response is to note that it’s not necessarily the best singer, just the most popular. But this objection misses the point: Bob wasn’t the most popular either. More people disliked Bob than liked him. Similarly with candidates; it’s not even a matter of whether Trump is better or worse than the others by some objective standard, as long as he’s the most popular. But the voting results show that while he’s more popular than any particular alternative, he’s not preferred by the majority.

This and other related paradoxes of voting are well-known enough that one would expect to encounter them in an introductory course in political theory. We also learn in such courses that even when the majority does prevail, the result is not always what you wanted to happen, or what should have happened according to some objective standard.

Sadly, most people don’t study political theory. But they do watch reality television. The great disappointments we experience regularly on such shows have a lot to tell us about the disappointments we face in politics.