When looking at the popular vote for 2016, about 49% to 51%, and the current numbers for 2020, it's astonishing how close it is — how evenly the country is divided.

Surely this is unexpected and anomalous? Have US elections typically been so close on such a scale, or is this as mathematically surprising as it seems?

Does political science predict something like this in long-term two-party systems?

  • Several hundred million people have a choice between a hot dog and a hamburger. On average, about half will choose one and half the other. It's just plain stats. – bishop Nov 7 '20 at 5:38
  • @bishop That assumes the two options are equally appealing. You can't just slot any two nouns in there and expect it to come out even; some menu items are just more popular than others. Actually, I'm not even sure it holds true for hot dogs and hamburgers at the average barbecue I've been at ;) I suppose that means the underlying question is how the two parties ended up equally appealing to so many people, which is why I like Rohit's answer. – Luke Sawczak Nov 7 '20 at 13:43
  • And I assert they are equally appealing. See also this paper on choice, particularly the idea of preference Completeness. – bishop Nov 7 '20 at 15:43

(Note: I don't have a background in political science.)

Imagine playing a "vote-getting" game. It's a two-player game, and you get votes by stating your positions on various policy matters.

You and your opponent play a round, and let's say you lose with only 20% of the vote.

Your goal is to win. You're not wedded to any particular policies; everything is negotiable. Because if you don't win then none of your policies can be implemented.

So you start tweaking. Make adjustments with the goal of moving that 20% up to 50%. It's tricky, because these adjustments aren't monotone functions, and the levers you pull don't all move independently. But move them you can, and the results can be observed.

Now imagine you and your opponent do this repeatedly. Each of you is trying to get to 50%, each of you feels free to adjust your policies to move the vote.

Eventually you will both hover around 50%.

In real life, political parties do have policy positions which are sacrosanct, but many can be adjusted. The media disseminates their messaging and debates it in the public forum, and polling organisations continuously check how voters feel. In the United States this information feedback loop is very well developed.

  • Although unsourced (I am not a political scientist or historian either), this is a very good explanation. – Damila Nov 6 '20 at 3:40
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    Interesting take. Reminds me of the game theory question about why two competing coffee shops invariably end up sharing the same intersection... – Luke Sawczak Nov 6 '20 at 4:36
  • This logic goes both ways. A party with an especially strong lead can give less weight to public opinion and more weight to the party line. – Brian Nov 6 '20 at 16:40
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    If you want a source, try Duverger's law. While the intent is to explain why first-past-the-post voting systems typically generate two parties, the actual details within that argument also indirectly explain why voting systems typically generate two evenly split parties. – Brian Nov 6 '20 at 16:46

Ever since 1828, it is quite common for the popular vote to swing in the 40-60% range. In some years, the margin by which one party won has been in the double digits.

I found a good illustration of this on Wikipedia. It has the following description:

Presidents of the U.S. listed in a timeline graph of elections with results of the popular vote color coded for political parties. A gray arrow points to the name of a person who became president without having been elected as president (9 total). The double arrow indicates becoming president without having been elected as vice president as well (Ford). 5 other former vice presidents are underlined (14 total). The top line indicates the Presidency number (e.g. Reagan: 40th) with Roman numerals indicating election (and term) number.

Here's the figure (click to enlarge):

enter image description here

By ChrisnHouston on Wikipedia CC0

As you can see, the last few elections (since Clinton's second term) have been closer to the 50% line than some of the previous ones. Looking at the full timeline, however, I wouldn't say it's an anomaly.

Does political science predict something like this in long-term two-party systems?

No, not that I'm aware of. Based on the figure, I would say that at least in the US it's not uncommon for the popular vote to swing around some equilibrium. As you look at consecutive elections, there seem to be plateaus where Democrats or Republicans were in power for quite a while. I think that's attributable to two things:

  • Strong candidates that remained popular: Cleveland, F.D. Roosevelt, Eisenhower, Raegan, Obama.

  • Demographics: if you're a Republican now, you're probably still one at the next election. There's only a small group of swing voters, so if the equilibrium is at 50-50, it's unlikely to change a lot in a short period of time.

  • Apart from the early Demcratic-Republican/Democratic dominance (when the popular vote didn't matter as much, since many electors were appointed rather than elected), there have actually only been two plateaus: 1864-1908 when the Democrats were discredited as a party in the aftermath of the Civil War, and 1932-1948 with the personal dominance of FDR. – Mark Nov 6 '20 at 2:25
  • @Mark I'd say the Democrats have quite a stable popular vote turnout percentage as well over the past 6 elections. The first Obama vote was a bit of a peak, but after that it returned mostly to the same plateau. – JJJ Nov 6 '20 at 2:28

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