Election 2024 and the Irrationality of Majoritarian Voting

When Kamala Harris ran for the Democratic Party’s Nomination for President in 2019, she did so poorly that she dropped out of the race before a single vote was cast in any of the Party’s primary elections. She had a bright moment after embarrassing Joe Biden in a debate about his 1970s position on busing public-school students, but her star faded quickly after she flip-flopped on socialized medicine and generally demonstrated that she was a poor candidate. Biden nevertheless chose her as his running mate, and she performed rather poorly as a vice-president, something which is hard to do. Even friendly partisan media aired criticism of her performance as vice-president. Then, after Biden was set aside by pressure from Party leaders in and out of government and big donors who threatened to withhold campaign and superPAC money, Harris became the Party’s presumptive nominee for President without a single primary vote. Last week, Party faithful in Chicago formally anointed her as their candidate, and she leads in national polls over Republican Donald Trump. In political terms, it is a long time until November 5, but right now it looks like she could possibly win the race and be elected President of the United States. Against the Left: A Ro... Rockwell Jr, Llewellyn H Best Price: $3.98 Buy New $8.00 (as of 01:59 UTC - Details)

How could a candidate go from being a clear loser in 2020 to being a possible winner in 2024 without accomplishing anything noteworthy in the meantime? Economists studying voter behavior have demonstrated that one of the features of majoritarian processes is that votes between pairs of choices can yield irrational cycles. That is, when people are given choices in pairs, a rational person who prefers A to B and B to C should also prefer A to C, but sometimes collective choices violate this principle of transitivity and are thus irrational. When Democrats had choices between Harris and other Democratic candidates for their Party’s nomination in 2020, they made clear that they did not want her as their Party’s nominee. Now, when the choice has essentially been made for them by Party elites, big donors, and their corporate media organs, they are all excitedly supportive of her, and she is currently leading in national polls over Trump.

One of the early proofs in social choice theory was that majority voting can result in collectively irrational cycles. Let’s say there are three voters. Voter 1 prefers Trump to Biden and Harris. This is a Republican voter. Voter 2 prefers Trump to Biden and prefers Harris to both Biden and Trump. Polls now suggest there were many such voters. Voter 3 prefers Biden to Harris and Harris to Trump. This was the typical Democratic primary voter. There is nothing necessarily irrational about any of these individuals’ preferences, but they yield the majoritarian social choice of Trump over Biden, Biden over Harris, and Harris over Trump. This is because Trump has two votes out of three over Biden, Biden has two votes out of three over Harris, and Harris has two votes out of three over Trump. This is an intransitive social choice and therefore irrational, because it is like someone saying they prefer apples to oranges, oranges to pears, and pears to apples. What is irrational for one person is dubbed “democracy” when a whole society does it, and it reflects what just might happen. Trump was defeating Biden in the polls, and Democratic primary voters preferred Biden to Harris. When elites and big donors effectively replaced Biden with Harris, she (at least for now) leads Trump in the national polls. If you ever thought “our democracy” might produce irrational results, you were right.