Current Affairs

How Centrism Loses, Even When It Wins: A Mathematical Model

Relentlessly chasing the elusive political center isn’t just shortsighted—it’s downright disastrous.

Since at least Bill Clinton’s 1992 presidential victory, it has been Democratic Party dogma that centrists win elections. Gore and Kerry both ran toward the middle, as did Hillary and, most recently, Biden. In fact, the only exception to that rule is also the only president to win a legislative supermajority in recent memory—Barack Obama (though he governed as a centrist, he ran as an anti-war dynamo for change​).

Running from the center is a sound strategy in theory. After all, if most people vote for the candidate closest to them ideologically, then triangulating correctly should ​always​ result in an election victory. This argument is made consistently by journalists like Matt Yglesias and moderate politicians alike.

However, with a 20 to 40 percent win rate in presidential elections since 1999 (depending on whether you count Obama’s re-election as a centrist campaign), and with recent data​ showing that progressive Democrats did better than centrists in swing districts during the 2020 elections, the doctrine that running as a centrist is the most reliable way to win elections has not borne itself out in reality. The obvious question, then, is:


The reasons are numerous and complicated. For starters, the assertion that voters choose the closest candidate ideologically (or that voters behave ideologically at all) is ​difficult to prove​. Surveys done by political scientists like Lee Drutman have demonstrated that voters regularly vote against their stated social and economic political beliefs—and with U.S. voter turnout rarely reaching even 50 percent, elections are as much about driving turnout as they are about finding the ideologies of the average voter.

However, as the model below shows, even if the “Triangulation Strategy” (i.e., attempting to find and run from the center) were correct about voter behavior, it will still tend to shift the electorate away from the original center, and eventually, hand power to the more “extreme” party. After I walk you through how my model works, we’ll look at the math and explore one possible reason for why centrists tend to lose over time.

This model was written in Python and was intentionally built to be readable. You can find it here,and be sure you send me any interesting results you come up with!

To test different election strategies, I coded a very simplified Python model of U.S. elections. The model begins by generating a group of 10,000 voters with random ideologies (measured by an “ideology score”) centered around 0. Each party is assigned an ideological position, and each voter votes for the party closest to that ideology.

To be clear: this model will not and cannot predict real electoral outcomes. It relies on assumptions (like ideological voting) which I frankly find dubious. Instead, this should be read more as a thought experiment using math as a tool to cast doubt on a commonly-held electoral doctrine.

For the purposes of this article, I will be asserting that the Democratic Party (not necessarily its voters) is center left, while the GOP is far right. Given the widespread opposition to popular left-wing policies like single-payer healthcare and total sudent loan forgiveness among Democrats who ran in the 2020 presidential primary, and considering the Republican Party’s ties to white nationalism and its overwhelming pro-Trump attitudes, that seems to me a fair assertion. 

That said, given a center left party running against a far right party, and assuming (for now) that only election victories shift the public’s ideology, a few decades of elections in my model looks like the image below. 

As you can see, in this completely static model, the triangulation strategy works wonderfully—the party which is closest to the average voter ideology (zero, in this case), wins every election, and sways public opinion in their favor over time.

The red line is the right party’s ideological position, the blue line is the left’s, and the gray line shows the average ideology of the voters over time. An upward trending line (shown above) demonstrates that the public has moved left of where they started; a downward trending line would show the opposite. The blue background indicates that the left party remains in power through this entire test.

Of course, no voter base is static. Let’s add in a few variables.

Win gravity​ – when a party wins an election, they stack the odds in their favor and thereby shift the ideology of the electorate every time they win. Traditionally, this has taken the form of voter suppression and gerrymandering on one side, and voter enfranchisement on the other (each party can have a different score, showing how effectively they stack the odds).

Election gravity​ – every election, each party tries to convince the population to move toward their position. More extreme positions have a greater “pull” on voter ideologies, in an attempt to model the ​Overton Window. Take Trump’s famous “build the wall!” credo for example—a position which was on the edge of Republican (and public) politics in 2015 has now become a mainstay of American political discourse, with Democrats repeatedly voting to spend billions of dollars on building Trump’s wall. 

Ideological shift​ – sometimes the electorate is naturally drifting in one direction. Every election, this variable shifts every voter in some direction by the same amount. In Obama’s first term, for example, a U.S. blue shift was observed by some and attributed to a demographic shift away from traditionally Republican voters. (It’s debatable whether this shift was real or lasting—the 2020 election cast some significant doubts—but that is a topic for a different day.)

Randomness ​- of course, not every voter votes by ideology, and not every election is clean. This variable randomly shifts a voter’s election day ideology by some amount, changing how they vote in the moment, but not their ideology long term. Think of a breaking news event or call from a friend that convinces you to take a leap you otherwise wouldn’t have.

Each of these variables can be changed to reflect different scenarios, as can the mean ideology of the population and the position of each party.

Though this model relies on a number of over-simplifying assumptions, it does introduce two important factors that are underappreciated by U.S. pundits—that ​elections change voter ideologies​, and that victories do too.​ And to be extra clear, this model relies on the same assumptions that the “triangulation strategy” does: namely that voters vote ideologically and that most voters hug the center. ​This is not to say those assumptions are correct, only to explore why centrism can fail even if they are.

With that out of the way, let’s jump into the pretty pictures.

First, let’s try to understand the landscape. Given two centrist parties (ideology scores of 1 and -1), and equal win gravities, the voters shift ideologically toward the party that wins the first election (and scores the first win bonus, perhaps by passing a popular stimulus that endears them to voters, or managing to suppress a group of voters which traditionally opposes the party). Tried 100 times in the chart below, you can see a predictable divergence based on the coin flip that is the first election:

Each white dot here represents the “average ideology” of the voter base in several elections. Because only the “win gravity” is impacting ideology at this point, the party who wins the first election pushes the electorate left and causes an unchanging trend.​

This shows us two things. First, in this static model where neither party changes their position over time, and where the electorate is never shifting right or left, the first party to win naturally accumulates an advantage. Second, it shows us that if both parties pursue the same strategy, the first election is the most consequential.

Now let’s move the parties. In the examples below, we are assuming that campaigning is roughly twice as impactful on a voter’s ideology as governing is. This is ultimately an arbitrary choice, but considering elections are the contexts for most national policy discussions, it is an arbitrary choice I feel comfortable making.

Here, we have a center left party and a far right party. As you can see, even though the left party wins initially, the right party’s more extreme position means they have a larger ideological pull than the center left. After a handful of elections, the far right party eventually wins, and even more concerningly, they pull the electorate right with them.

Next, let’s add in some triangulation. In this model, the left party looks for the average voter’s ideology and shifts slowly towards that position.

As you can see, this strategy is disastrous. It not only loses more elections than a static center left party, but drives that party rightward in the process. As the left party gets closer to the center every cycle, it stops pulling the electorate left and, in fact, aids the right party ideologically. Eventually the voters move so far right that the triangulating left party cannot meet their ideology, and government control flips to the far right.

This might be a decent reflection of the Clinton presidency. Though the triangulation strategy won Democrats the White House, Clinton’s support for the crime bill, NAFTA, ​soft-opposition to abortion,​ and conservative foreign policy brought the electorate closer to the Republicans’ position—a mistake that would lead to two terms of far right George W. Bush.

To make matters worse for the advocates of triangulation, the tilt toward extremes that it causes can even overcome “natural” shifts in the opposite direction. Below is a model of a triangulating center left party running against a far right party in a country experiencing an ideological shift to the left for any number of reasons (every voter moves .01 ideology points left per cycle).

Although the left party puts up a better fight, the gravitational pull of the far right party, in combination with meager ideological resistance from the left party and an unwillingness to use their early wins to stack the odds, causes an inevitable shift to the right.

If we are looking for historical analogies, the Obama years are what come to mind. ​Obama’s Democratic Party enjoyed an apparent demographic shift left that pundits attributed to an increasingly nonwhite population in combination with a decidedly left-leaning youth​. In spite of those advantages, however, between 2008 and 2016 Democrats lost the Senate, the House, dozens of governorships, state legislatures, and courts.

Had Obama used his initial majority (not unlike the early left wins in the model above) to improve the odds for Democrats (for example, by expanding the House, stopping gerrymandering, changing campaign finance laws, and/or stacking courts), Democrats could well have maintained power and even triangulated themselves to the left—a possibility modeled below.

So (if you believe this model) the question ultimately becomes whether you think Democrats will use this most recent victory (or their victories in general) to shift the public left. If they do, triangulating to win will have been a worthwhile strategy in spite of its short term consequences. If they do not (or worse, if they ​cannot​), then the “centrists win” dogma is little more than a bludgeon—a weapon recklessly used against the left while the far right only grows stronger.

And, in a world where Biden is already ​praising Republicans​ and Pelosi is openly and repeatedly wishing for a “​strong Republican Party​”—even after the vast majority of Republican voters and politicians supported (tacitly or explicitly) an attempted coup—I must confess I am not optimistic that Democrats will make their triangulation gambit worthwhile.

In the absence of a leftward shift, and assuming extra-electoral activism like Black Lives Matter and attempts to replace centrist Democratic leaders fail, it seems likely that Democrats will continue to run to the middle, continue refusing to capitalize on their victories with popular policies (e.g., the $2,000 stimulus promise that won them the Senate before they pulled a bait-and-switch), and ultimately, continue to drive the country further right. Keep in mind, this model was built assuming that elections are fair, voters are more likely to vote for centrists, and that the country really is shifting left.

I am sorry to say that reality might be much more grim.

This piece is dedicated to Russ (Boopop) Simpkins”Great minds like a think!”

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