The Median Voter Theorem is a Clarity Trap

What the Democratic party needs; what it demands; is bold, persistent experimentation

There is a reason I don’t accept paying subscribers for this newsletter (although I am grateful to those who offer to pay). I want to be free to use terrible headlines like the one I’ve used for this post, without feeling even slightly conflicted about it.

I spent three years as the managing editor of a political science blog that was hosted at the Washington Post. We spent a lot of time thinking about how to write catchy and seductive headlines that would get people to read posts about social science.* The common wisdom about how best to do this shifted, as different social media platforms grew or fell (we were pretty well out of the game by the time that social media stopped driving traffic entirely). Preferred headlines got shorter as the metrics started suggesting that they worked better: the newspaper imposed a character cap for headlines that we all tried to adhere to.

One thing remained constant. You did not want to have any academic jargon whatsoever in your headline if you wanted to attract eyeballs. And you absolutely did not want to have a headline that juxtaposed two unfamiliar pieces of academic jargon, so that they could duke it out over which was better suited to drive punters away.

We knew how many readers each post got, and struggled to make the numbers as good as we could get them, while trying somehow to hold onto the truth that we weren’t, in the end of the day, primarily interested in the numbers game. It was what we had to do to justify our existence as a small ideas shop hitchhiking a ride on a much bigger publishing enterprise. Hence, when I started writing a newsletter, I decided from the beginning that it was going to be my newsletter. It would talk about the things I wanted to talk about in the ways I wanted to talk about them, without any profit model tugging me to juke the numbers by writing about the topic of the day or sanding away the weirdnesses of my writing style. I’m somewhat startled that so many people read it. My writing for it is deliberately idiosyncratic, discursive, even meandering.

Hence too, my unashamed love of C. Thi Nguyen’s new book, The Score. It is a book that is about metrics (like viewer numbers, though I don’t recall him citing those in particular) and how they define not simply our lives but our very selves, if we carelessly let them. It is a book about pizza. Also: weird yo-yo tricks and the zen-like states that accompany them. Also also: climbing, on which there is lots. Also also also: drunken cooking competitions. And that is just for starters. It is a book that absolutely ought not work, for the same structural reasons that bumblebees ought not be able to fly. The aerodynamics are all wrong. But good god, does it fly. The achieve of, the mastery of the thing! I would not have believed that a book about metrics could be a joyful and delightful book. The Score not only manages that extraordinarily difficult trick, but makes it look easy.

The Score, then, is about very many things, but it is not about electoral politics. This post explains why I think that its lessons travel to politics, in much the same way that Brian Eno’s ideas about music have nothing to do with democracy, except that they absolutely do.

In particular - and finally we begin to get to the meat of the post - electoral political strategy has increasingly driven by metrics and related simplifications. This has many advantages. It forces people to put their pet theories of what will work and what will not to the test, and makes it easier for everyone to coordinate around the same approach and message. But it has substantial drawbacks too, along the lines that Nguyen suggests. If everything gets reorganized around the metric, then all the important things that the metric hides are likely to rear their heads and devour you. Metrics are lossy abstractions of complex wholes. As Maxim Raginsky puts it, “abstraction hides a great deal of complexity from view, and this is both its main virtue and its primary peril.”

So first, I want to talk about a fight that is happening right now within the Democratic Party that conceals a more fundamental conflict about metrics and abstractions. Then, I’ll explain how the median voter theorem fits into this fight, and how it has become what Nguyen calls a “clarity trap.” Then, finally, I will talk about ways to maybe escape that trap and find something better.

*****

The electoral strategy of the US Democratic party mainstream is all about the main virtues of simple metrics. The perils that this ignores are the root cause of much unhappiness right now. Some of that spilled out into a forum in the Boston Review last week. Two prominent political scientists, Adam Bonica and Jake Grumbach, argued that the Democratic Party’s focus on milquetoast moderation was leading it astray. There were lively responses from those on the other side, including Matt Yglesias, who has argued that the Democrats need to moderate, and that left wing excesses explain Kamala Harris’s defeat.

This is one episode in an ongoing dispute with many rejoinders and counter-rejoinders about methodological particulars, “wins-above-replacement” metrics and the like. And it is not just an arid statistical squabble. Matt has written occasional spicy social media posts about how he is finally coming to understand the basic dishonesty of academic political science, while those on the other side, broadly considered, make their own mordant comments about the idiocy of pundits, and the economic incentives of pollsters who work regularly with the party.

While this fight seems superficially to be a back-and-forth over which are the best statistical instruments and abstractions to capture public opinion, it is bitterly fought because it maps onto a more directly political dispute over whether the Democratic party should turn to the left or to the center.

What I would like to see people paying real attention to is a third disagreement, which lurks beneath both the statistics and the politics. Should the Democratic party be sticking to tried-and-tested techniques (based on the standard metrics and assumptions) for attracting voters, or should it be trying new stuff out? At the moment, this fight very loosely maps onto the other two, because moderates are (a) the faction that would most visibly lose if the party starts experimenting with new ideas, and (b) are intellectually tied to a broader metric-driven approach that is shared across much of the business world, technology, and, perhaps weirdly depending on how you think about them, sports.** After Bezos gutted the Washington Post last week, he issued a statement defending the cuts that had been made on the theory that “the data tells us what is valuable and where to focus." That theory of what we ought pay attention to guides a lot of competitive activity these days.

But as Nguyen points out in the book, data often conceals as much as it tells us. As he describes the problem elsewhere, .

The basic methodology of data—as collected by real-world institutions obeying real-world forces of economy and scale—systematically leaves out certain kinds of information. Big datasets are not neutral and they are not all-encompassing. There are profound limitations on what large datasets can capture. … Data collection techniques must be repeatable across vast scales. They require standardized categories. Repeatability and standardization make data-based methods powerful, but that power has a price. It limits the kinds of information we can collect. … an overemphasis on data may mislead even the most well-intentioned of policymakers, who don’t realize that the demand to be “objective”—in this very specific and institutional sense—leads them to systematically ignore a crucial chunk of the world.

If you are already convinced that you understand how the world works based on a combination of the data and a few simplifying intuitions, you are going to be disinclined to experiment to find things out that you don’t already know. If you are the kind of cook who sticks mechanically to a particular recipe, you may produce good meals, but you are going to miss out on other, perhaps great meals that you could discover by messing around. If you live in a static world and don’t mess around, you are going to remain stuck at a possibly inferior local optimum, when there are much better possibilities out there that could be discovered by doing things that deviate from the ordinary (as Nguyen’s stories about the strange discoveries of drunken cooking illustrate; you can think about throwing ingredients together when you are half loaded as a kind of simulated annealing if you really have to).

And if you are in a rapidly changing environment, then things might be much, much worse. Your insistence on looking at the world through fixed metrics may make you incapable of seeing the transformations that are happening around you, but that get filtered out by the metrics that you think are important.

That, plausibly, is what is happening now with a largish chunk of the moderate wing of the Democratic party. I, myself, am a lefty, but from a broader political perspective, the problem with Democratic moderates right now is not that they are moderate. It is that they are defining their moderation in ways that depend on metrics and simplifying notions that (a) are increasingly out of sync with the environment, and (b) tend to preclude experimentation.

I think that the Democratic party would be in a significantly better place if the moderates became experimentalists. That is, it would be great if moderates moved decisively away from the position that the metrics tell us what we need to know, and treated them as valuable but limited tools of inquiry for grappling with a world that is vastly more complex than any metrics can plausibly capture, and started trying to explore those complexities in different ways. That is not least true because there are likely things that moderates can discover, if they are so inclined, that lefties (and conservatives cannot).

I don’t think that the debates between the left and moderates would necessarily be any friendlier if they were disagreeing over the best ways to experiment to attract voters and create compelling policies, but I do think that they would be more likely to result in interesting and unexpected discoveries than what we have now: interminable disagreements over whether the statistically maybe-sort-of-measurable-if-you-squint-in-a-charitable-way rewards of moderation are a .5%, 1% or 2% greater share of the vote.

One way to get moderates moving in this direction might be to get them to move away from the “median voter theorem,” a particularly beautiful mathematical abstraction that has become what Nguyen calls a “clarity trap” for moderates: hence my incomprehensible seeming headline. But what is the median voter theorem, and why is it so weirdly politically important?

*****

The median voter theorem is, as the box says, a theorem. That is, it is a proof that if you start from certain mathematical assumptions, then certain conclusions follow. It is, furthermore, a really neat theorem. Its mathematical virtues do not explain why it has become politically important, but it is helpful to have at least a summarized version and simplified version of what the theorem actually says.

The median voter theorem starts in economics rather than politics, and its most broadly influential version is the one in Antony Downs’ book An Economic Theory of Democracy. It is in broad form a particular application of Harold Hotelling’s ideas about market convergence.

The bowdlerized version of Hotelling’s account goes as follows. Imagine two shopkeepers that want to maximize sales, but both have to locate their store on the same street. They know that customers are likely to frequent the shop that is closest to them. That means that the shop that is located just a little bit closer to the middle part of the street will get slightly more customers than the one that is further away. Like many influential economic models, this one has an equilibrium, a final state that rational economic actors will converge on. The rival shop owner will have an incentive to relocate their own store a little closer to the center, to grab back some customers. This then plausibly leads the first shop to move too. Eventually, the two shops will end up side by side, bang in the middle of the street. That is the equilibrium where there is no possible better move that an actor can make.

For the Median Voter Theorem, imagine a version of this model, where instead of shops you have political parties, instead of customers you have voters, and instead of a street, you have a single ideological dimension on which the parties and voters locate themselves. Again, you assume that voters vote for the party whose position on this one-dimensional continuum is closest to them. And much the same thing happens. Over time, parties too are likely to converge towards the central point, so that each is in its best possible position to maximize vote share. The Median Voter Theorem then makes a simple prediction. Rational parties, if they want to win elections, will necessarily pursue the median voter right at the center (according to one measure) of the political spectrum. Whoever attracts the median voter will win a majority. Hence, parties that want to win ought become centrists.

If you treat this as a mathematical theorem, you might want to think carefully about the many mathematical assumptions that lie behind this rather lovely result. Voters’ preferences need to be well behaved in certain ways (“single peaked”). More pertinently, it has to be possible to collapse the entire space of political issues into a single dimension of political contention. If there are two dimensions of political contention, things get a lot messier (although there are still some regularities). If there are three or more dimensions, then anything goes (social choice theory has various `chaos theorems’ that say that outcomes will be unpredictable). Finally, voters’ political preferences need to be fixed in advance. Parties cannot persuade voters under this model. They can only adapt themselves towards what the voters want. This is a static universe - the only dynamics are the ones that conduct voters and parties to the single predictable equilibrium.

If you forget the assumptions and treat the median voter theorem instead as a guide to party strategy, it is incredibly attractive to moderates. The median voter theorem entails that there is one weird trick to winning elections: always move towards the center. If you are a rational politician, you always need to asking yourself (and the polls), what the voter right at the center is looking for. If you give the median voter what they want, you will win. You don’t have to worry about voters on the left (if you are a Democrat) or the right (if you are a Republican). They will vote for you, because you are the party that is closest to them, even if they think that you are a centrist sellout. You should absolutely ignore what various identity groups are telling you about what to do - their advice is at best misleading and at worst treacherous and dangerous.

If you take this idea to its logical conclusion, you don’t even need a political party. All you need are accurate measures of public opinion, built on survey data that captures voters’ fixed preferences, and politicians who are willing to respond to it in the ways that their rational desire to win office dictates.

Of course, nobody - or nearly nobody - actually takes these ideas to their logical conclusion. But some moderates come a lot closer than you might imagine. I’ve seen one well-known Democratic ‘strategist’ (a term that covers a multitude of sins) describe the median voter theorem in terms that seem better suited to a recent, urgent personal religious revelation about the true nature of the world. They are young, so I am not naming them. And it is not hard to see why they feel so strongly. When you are inclined towards centrism, and find a simple, clarifying theory that tells you why your understanding of politics is not only right but inevitably right, it is difficult to resist. Add a panoply of surveys, and some other useful simplifications as auxiliary hypotheses and you are set up in business for life.

Furthermore, as per Raginsky’s dictum, the median voter theorem is a useful abstraction under many circumstances. It allows politicians to focus on strategic issues that are plausibly quite important. Pushing towards the center is indeed, quite often, an electorally useful strategy. The theorem, in its pop-culture form, furthermore serves as a valuable disciplining mechanism, to help prevent politicians from wishcasting the public that they would like to have into existence, instead of dealing with the public that they actually have. Finally, it helps build party discipline, getting a variety of disparate actors to concentrate on the same thing, rather than heading off in a million different and mutually contradictory directions.

Equally, as Raginsky suggests, these virtues can become perils. They can conceal a lot of dangerous complexity that you really ought be paying close attention to. Or as Nguyen might describe it, using a different but related vocabulary, they can make it far harder for you to see the world around you in all its glorious weirdness.

That is what Nguyen is getting at when he talks about “clarity traps.” When an idea - whether it be a weird conspiracy theory, a seductive social science result, or a beautiful graph - seems to simplify an altogether-too-complex world, it may give you the sensation of sudden understanding, of having the scales fall away from your eyes so that you suddenly arrive true understanding of the world. That sense of epiphany (a word descending from the Greek word ‘to show’) is not always altogether a bad thing. Beautiful ideas are often beautiful because they do carve the world at its joints, or at least closer to the joints than we have hitherto been able to achieve. But this loveliness can betray you if you mistake the apparent clarity for the undoubtedly messier truth. As Nguyen puts it;

So here is a recipe for a seductive clarity trap:

First, build a belief system that offers a satisfyingly clear, coherent explanation of the world.

Second, make sure the belief system conceals any evidence of its own error.

The median voter theorem, and a set of closely associated ideas have become a clarity trap for Democratic moderates. They offer a simple, clear explanation of what the Democratic party always ought do. Moderate! Move to the center! Figure out what the median voter wants, and do just that! And they also offer a means of concealing errors. Whenever Democrats fail to win elections, it is definitionally due to their failure to observe this universally sound advice. Very obviously, they have been listening closely to the groups and failing to pay attention to rigorously conducted opinion surveys, which are the true and proper barometer of what the public wants.

There are other diagnoses that seem to me more plausible. Public opinion is not, actually fixed in the ways that the median voter theorem suggests, even if they are not nearly as protean as people on the left might want them to be. The more that political parties rely on metrics and other simplifications, the more they are likely to be blindsided by voters whose wants and ideas are not readily captured by simple measures.

Most radically (and this has implications for left-leaning political scientists too), we are living through times of upheaval in the underlying structures of democratic politics. In such times, all our instruments for identifying causal relationships will become less helpful, because some of the causal relationships we are most interested in are likely to be undergoing rapid ferment. Even the most accurate photographs of unpredictably moving targets may not be that useful for very long.

The deep problem of clarity traps such as the popularized version of the median voter theorem is a side effect of their attractiveness. Exactly because they are so attractive - they tell you that you are right goddamit, and there is objective proof of it - they are extremely difficult to escape.

*****

One way to conclude this essay might be to claim that moderates are wrong and that people to their left have the right of it. And there is a particular and temporary way in which this is true. In their essay, Bonica and Grumbach not only wallop the Median Voter Theorem, but say the below:

The reality is that electoral politics has entered an era of profound volatility, one when yesterday’s certainties become today’s mistakes. We are not making a general case for running to the left instead of to the center but for dispensing with outdated conventional wisdom. Instead, we favor experimentation and exploration. Embracing these requires expanding our sense of possibility and the range of our explorations, partly by paying close attention to what has worked in other countries that have faced democratic backsliding.

That seems to me to be absolutely on the money. But the lesson I personally take from it is not that moderates should abandon their values and priors. Those priors are likely to very often be quite useful. Many members of the public are likely more comfortable with moderate views than lefty ones. Some parts of the country are likely much more moderate than others. Perhaps (and on some issues probably) there are much easier national majorities to find based on moderate appeals than immoderate ones.

Instead, I think that moderates should put far less trust in their preferred simplifications and metrics. The median voter theorem is politically attractive to them because it reflects their political priors so perfectly, making it very hard to give up. Again: this also explains why it is liable to be a particularly vicious clarity trap. Who would not prefer to have the world clarified in ways that suggest that everyone who does not converge on their own preferred political philosophy is stupid, wicked or dishonest? It is in the nature of clarity traps that they continue to seem compelling even as they draw you ever closer to the brink of the abyss. It is really hard to escape this kind of trap, especially if you have built your identity around it. But it can be done, and doing it opens up new possibilities.

I think that there is a lot of room for moderates to start engaging in experimentation with different political approaches that are less reliant on opinion polls and median voter assumptions. Here, I particularly like a recent Daniel Schlozman essay that argues (as I read it - maybe wrongly) that it is the left that ought to start paying more attention to the kinds of institutionalization and partisan hardball that normie Democrats built up before, and ought start trying to build again under different conditions. A program to build up a normie Democratic party that was actually a real political party, connecting politicians to voters, would be a great start.

A second approach might be to look to the lessons of the evangelical movement. Ezra Klein got a lot of grief from people on the left for saying that there was something right about what Charlie Kirk was doing. My interpretation (again maybe wrong) of Ezra’s core intuition is that the Democrats too need to start evangelizing as Kirk did, by getting out and talking to people who they don’t agree with and don’t usually talk to. Again, there are a lot of ways in which some moderates are better positioned to experiment with doing that than people to the left (although left economics also maybe provides some useful starting points).

A third is that moderates should be stealing in quite different ways from the left than the ways that they are doing now. This gets back, in a weird, backhanded and not necessarily very intellectually coherent way, to something that my brief account of Nguyen’s book mostly misses out on. The Score a genuinely joyful book, about the delights and surprises of everyday life. It is striking that few people would deploy “joyful” as an adjective to describe the Democratic party’s way of thinking and communication. That of course reflects the real grief, anguish, anger and frustration of the world around us. But it also reflects bad habits of carping, begrudgery and misdirected anger that plague all of us.

It would be great to try to break these habits, and I think that it is still, occasionally possible to find weird and surprising joy amidst it all. The most valuable transferrable lesson of Zohran Mamdani’s victory and early governing style may not be the talking points about “affordability.” Instead, it’s the capacity to discover delight in being outstaged by kids at press conferences, to admit fallibility, to experiment while admitting that things don’t always work, to build connections and to try to draw new constituencies in. I don’t see any fundamental reason why moderates shouldn’t be able to work with some version of that style of discovery and communication just as well as lefties, and I suspect that it would get them much further, and to more interesting and unexpected places, than doubling down on technocracy.

* Or at least, start reading them. If you ever want to get depressed about the reading public, ask a newspaper executive how many people actually finish reading an article after clicking it.

** There is a great essay to be written about how Nguyen’s ideas about games intersect with “Moneyball.” This is not that essay.