Marie Jean is a man’s name. This is not he, but his wife, Sophie de Condorcet. Marie Jean was executed for being a Republican in Revolutionary France.

During the French Revolution, Marie Jean de Condorcet proposed a paradox with significant consequence for all elective democracies: It was far from clear, de Condorcet noted, that an election would choose the desired individual — the people’s choice — once three or more people could run. I’m sorry to say, this has played out often over the last century, usually to the detriment of the GOP, the US Republican party presidential choices.

The classic example of Condorcet’s paradox occurred in 1914. Two Republican candidates, William H. Taft and Theodore Roosevelt, faced off against a less-popular Democrat, Woodrow Wilson. Despite the electorate preferring either Republican to Wilson, the two Republicans split the GOP vote, and Wilson became president. It’s a tragedy, not because Wilson was a bad president, he wasn’t, but because the result was against the will of the people and entirely predictable given who was running (see my essay on tragedy and comedy).

The paradox appeared next fifty years later, in 1964. President, Democrat Lyndon B. Johnson (LBJ) was highly unpopular. The war in Vietnam was going poorly and our cities were in turmoil. Polls showed that Americans preferred any of several moderate Republicans over LBJ: Henry Cabot Lodge, Jr., George Romney, and Nelson Rockefeller. But no moderate could beat the others, and the GOP nominated its hard liner, Barry Goldwater. Barry was handily defeated by LBJ.

Then, in 1976; as before the incumbent, Gerald Ford, was disliked. Polls showed that Americans preferred Democrat Jimmy Carter over Ford, but preferred Ronald Regan over either. But Ford beat Reagan in the Republican primary, and the November election was as predictable as it was undesirable.

Voters prefer Bush to Clinton, and Clinton to Trump, but Republicans prefer Trump to Bush.

And now, in 2015, the GOP has Donald Trump as its leading candidate. Polls show that Trump would lose to Democrat Hillary Clinton in a 2 person election, but that America would elect any of several Republicans over Trump or Clinton. As before,  unless someone blinks, the GOP will pick Trump as their champion, and Trump will lose to Clinton in November.

At this point you might suppose that Condorcet’s paradox is only a problem when there are primaries. Sorry to say, this is not so. The problem shows up in all versions of elections, and in all versions of decision-making. Kenneth Arrow demonstrated that these unwelcome, undemocratic outcomes are unavoidable as long as there are more than two choices and you can’t pick “all of the above.” It’s one of the first great applications of high-level math to economics, and Arrow got the Nobel prize for it in 1972. A mathematical truth: elective democracy can never be structured to deliver the will of the people.

This problem also shows up in business situations, e.g. when a board of directors must choose a new location and there are 3 or more options, or when a board must choose to fund a few research projects out of many. As with presidential elections, the outcome always depends on the structure of the choice. It seems to me that some voting systems must be better than others — more immune to these problems, but I don’t know which is best, nor which are better than which. A thought I’ve had (that might be wrong) is that reelections and term limits help remove de Condorcet’s paradox by opening up the possibility of choosing “all of the above” over time. As a result, many applications of de Condorcet’s are wrong, I suspect. Terms and term-limits create a sort of rotating presidency, and that, within limits, seems to be a good thing.

Robert Buxbaum, September 20, 2015. I’ve analyzed the Iran deal, marriage vs a PhD, and (most importantly) mustaches in politics; Taft was the last of the mustached presidents. Roosevelt, the second to last.