Populism and the Median Voter Theorem
A Theoretical Sketch with an Application to the French Immigration Bill
Preliminary Note: This essay is significantly longer than usual. It is the product of several weeks of rumination over the vote by the French parliament of a law on immigration, as well as reflections based on joint work with a colleague on populism and democracy. It may also be a bit more “technical” than what I’m used to write here. For readers who want to go directly to the heart of the issue, start reading at the section “Two Kinds of Democratic Regimes.”
2024 (happy New Year by the way!) is apparently set to be the year with the most elections ever. While at the surface this is comforting news (there cannot be democracies without elections), there are also reasons to be concerned. Of the 76 states that will hold elections in 2024, many of them are not democratic in the “liberal democracy” sense. Many of those elections will be rigged and are artificially staged to reinforce the domination of the autocrat in power. In many of those countries that properly qualify as liberal democracies, the fear is that elections will ultimately deliver a result that undermines the very liberal foundations on which the whole democratic game has been built.
It could be answered that this last worry is, in a way, wrongheaded. After all, the point of elections and more generally of a democratic regime is to make sure that the way the state runs the country appeals to a majority of the population and corresponds to the beliefs and preferences that prevail among voters. As it happens, this may not be the best (or even a good) justification for a democratic regime, but let’s put this point aside. In political economy, the concept of the median voter is generally used to capture the democratic property of tracking the “general will” through an election. The median voter is one whose political preferences are exactly located at the “center” of the preference distribution in the population. In the simplest, one-dimensional case where voters’ preferences are arranged along a line from the left (“progressives”) to the right (“conservatives”), the median voter’s political preferences are such that there are exactly as many voters located “at her left” as voters located “at her right.”
The Median Voter Theorem in Political Economy
The relevance of the concept of the median voter is both normative and positive. The normative relevance is related to what I’ve just said in the preceding paragraph. If you consider that the justification of democracy is tied to its ability to ensure that what state officials are doing corresponds to what voters really want them to do, then there is a strong pro tanto reason to give the preferences of the median voter a special status. After all, by its “centrality,” the median voter has a distinctive character. Her preferences may not correspond to the “general will” properly speaking, but it is probably the best proxy we can realistically have. More pragmatically, by aligning with the median voter’s preferences, you seemingly minimize the probability that a large number of citizens will oppose your decisions.
The positive relevance of the concept is related to a famous theorem first demonstrated by Duncan Black.[1] The median voter theorem (MVT) states that under some conditions C, (i) a Condorcet winner always exists,[2] and (ii) the Condorcet winner is the closest candidate to the median voter. When it applies, the MVT singles out an interesting property of democratic elections, i.e., their ability to track the preferences of the median voter. The MVT therefore helps to predict the outcome of an election under specific circumstances and to explain the political strategies of candidates. Even more interestingly, once this positive result is combined with the normative postulate of the particular relevance of the median voter’s preferences, you have a powerful justification for the implementation of voting mechanisms that identify a Condorcet winner.[3]
A less formal statement of the MVT is to be found in the work of Harold Hotelling and Anthony Downs. Hotelling has famously argued that in a one-dimensional space, economic and political competition between two suppliers/candidates tends to converge “toward the center,” or more exactly toward the median consumer/voter. Anthony Downs will later use this result as a backbone for his economic theory of democracy, though he is clear that this convergence property holds only in very specific circumstances.[4]
What is interesting is that the MVT is still largely popular today among political economists. To cite only a couple of examples, it is at the core of Acemoglu and Robinson’s general theory of the transition from dictatorship to democracy.[5] Acemoglu, Egorov, and Sonin have more recently used it to explain the rise of South America's type of populist politics.[6] Their basic idea can be summarized as follows. In a two-party election where voters are uncertain about whether parties are corrupted by elites, it is rational for “honest” parties to signal their honesty by announcing and implementing (if elected) policies located “at the left” of the median voter. The assumption is that elite corruption pushes policies toward the right of the political spectrum and, since implementing leftist policies is less costly for a non-corrupted party than for a corrupted party, “populism” is a costly and credible signal of honesty. In other words, voters may rationally prefer to vote for a populist party even though strictly speaking it does not fully align with their preferences because they are relatively confident that this party is not corrupted. There is therefore a tradeoff between voting for one’s preferred policy and confidence in a party’s honesty that is at the roots of populist politics.
Acemoglu et al. demonstrate some interesting comparative static results but overall, there are significant doubts that their model captures anything substantive about the populist phenomenon. The general setup is quite artificial and at best only applies to the kind of leftist populism that is (or was) typical of South American democracies. The extension of the model to the case of “rightist populism,” though mathematically straightforward, leads to many interpretative issues. More fundamentally, I’ve serious doubts that the MVT is a good place to start to understand populism.
In Which Case the Median Voter Theorem Does Apply?
To understand why, we have to return to the conditions C under which the MVT applies and that I’ve not detailed above.[7] In substance, for the MVT to apply, you need to have a Condorcet winner. But of course, there may not be one – this is one of the implications of Arrow’s impossibility theorem.[8] A sufficient condition for the existence of Condorcet winner is that voters’ preferences are “single-peaked.” Roughly, that means that you can order all options (here, candidates or parties) along a single axis such that, for every voter, any option that is at the right (left) of her preferred option is preferred to any option that is even further on the right (left). As an illustration, you can see below two possible sets of political preferences for a voter, but only the one in orange is single-peaked. On top of that, to make sure that the Condorcet winner will be the closest candidate to the median voter, you have to assume (a) that the information is perfect and (b) that voters cannot abstain. Actually, even if (a) doesn’t hold, the MVT can still be relevant to derive useful predictions, as Acemoglu et al.’s paper indicates. Condition (b) is more significant here. Before explaining why, note that contrary to what is sometimes written, the MVT may apply when there are more than two candidates/parties and when the distribution of preferences is not unimodal (i.e., has more than one “peak”). Regarding the former point, what is true however is that the majority rule will not necessarily pick the Condorcet winner when there are three or more candidates; therefore, the MVT only applies to the majority rule with two candidates. Regarding the latter point, it is important because it indicates that the fact that political preferences may be polarized is not enough to reject the MVT.
Let’s suppose that the political case we are considering is such that the MVT applies. What kind of politics can we expect to observe? First, we would expect to have the kind of “politics of convergence” that Hotelling and Downs describe. Parties that aim at winning the election will tend to converge toward the median voter. If we allow for some degree of uncertainty and/or assume that parties cannot change their platform without cost, the convergence will not be absolute. Some political differentiation will still prevail. We should nonetheless see mainstream parties being “centered” around the median voter. Second, it is also possible to observe other parties located farther away from the median voter. These parties are not primarily motivated by the goal of winning elections but rather intend to push for the diffusion of ideas or to highlight political issues that have been largely ignored until now (e.g., animal welfare). These parties are irrelevant as far as the results of the election are concerned, though they can be politically relevant, especially over the long run. Third, we would expect a relatively high turnout. This is so because if voters are prone to abstain when candidates are too far away from their political preferences, then it may pay off for candidates to opt for a less “centered” strategy. Fourth, and finally, we would expect a relative consensus to prevail over the characterization of parties’ views and policies such that they could be meaningfully represented within a one- or multi-dimensional ideological space, thus increasing the probability that political preferences are single-peaked.
Even a casual glance at contemporary politics in Western countries is enough to realize that this is not what we are observing most of the time nowadays. In many countries (especially France), the turnout has been historically low at most elections over the last two decades. The political supply is also less and less convergent. Parties who have a decent shot at winning tend to be farther away from each other, at least under the usual typologies of political views. In the U.S., the ideological drift of the Conservative party has increased the distance with the Democrats (who, for some of them, have been leaning further on the left). In France, while the two-big-parties-with-similar-agenda situation has prevailed since the 1980s, the 2022 presidential elections have consecrated a new political equilibrium with three major actors, one of them located at the far right, the other (though this can be disputed) at the far left. This is partly due to the fact that political preferences may have polarized but this is only part of the explanation. This is also because parties that traditionally were at the fringe of the minimal democratic consensus and were not aiming at winning elections have successfully persuaded voters, especially those who were prone to abstain.
Two Kinds of Democratic Regimes
The bottom line is that populist politics is very different from the kind of politics we would expect to observe under the conditions where the MVT applies. Though the distribution of political preferences has undoubtedly changed over the past two or three decades, that does not imply that the localization of the median voter has been radically modified, at least over the short run. It may just be that the median voter is less politically relevant.
My point is that to understand the populist phenomenon, we should distinguish between two “regimes.” In what I would call the normal regime, the MVT mostly applies. Political preferences are relatively well-known (though not necessarily unimodally distributed) and dominant political parties defend largely consensual views and policies with which most voters minimally agree – or at least do not reject outright. In presidential systems like the U.S. or the French ones, the mainstream political supply is constituted by a small number of actors (2 or 3 parties). In parliamentary systems, more actors are at play, but coalitions are relatively stable and predictable. Finally, there is a general conventional agreement over the dividing lines between the parties and which issues are relevant to classify them, such that we may expect voters’ preferences to be single-peaked.
Then there is the transitory regime. In this regime, the MVT doesn’t apply. Traditional mainstream parties are not able to attract a large number of voters beyond their bases and, while the turnout is relatively low, parties that are farther away from the median voter are progressively succeeding in capturing a significant fraction of those who no longer vote for traditional parties. In the process, the political agenda of those parties becomes more visible, and, through information and persuasion mechanisms, this affects the distribution of political preferences. The dividing lines between parties are blurred and it becomes more difficult to characterize parties’ ideological stances. It becomes possible that a far-right (left) voter prefers a far-left (right) party to a center-right or left one, i.e., preferences may not be single-peaked. In this transitory period, “populism” consists in the paradoxical conjunction of a rhetoric relying on the appeal to “the general interest” and “what the People want” with strongly partisan politics not targeting the median voter but rather aiming to capture a specific but still large part of the electorate. In some circumstances, this may be enough to win the elections but otherwise, it is part of a more global strategy to “become mainstream.” When we return to the normal regime, the political equilibrium has changed. The structure of the political supply has evolved, as well as the distribution of political preferences. More fundamentally, the minimal consensus that defines the rules of individual and political behavior and that determines which public policies are perceived as acceptable has been deeply transformed.
The Case of the French Immigration Bill
Many Western countries are currently in the midst of what I call a transitory regime. In some cases, we already see the signs of a forthcoming normalization. This is the way I would interpret the recent vote by the French parliament on the immigration bill that considerably strengthens the conditions permitting immigrants to stay or to come to the French territory and to benefit from social programs. The bill, initially proposed by the (center-right) government, has been first amended by the parliament to introduce stricter dispositions. It has then been voted at the Assemblée nationale thanks to the votes of the traditional (and more and more leaning to the far-) right (Les républicains) and the far-right (Rassemblement national). More than 20 MPs of the governing coalition have however not voted for the bill, expressing their uneasiness with its xenophobic connotation. The minister of health has even resigned in protest.
Less than 10 years ago, such a bill would have never passed. Back in 2015, the then minister of the economy Emmanuel Macron was not shy about expressing his discomfort with a new law that restricting immigration conditions, though it was not even close to what has just been voted. So, what happened in the meantime? During this period, France entered into the transitory regime I characterized above.[9] The unprecedented weak scores of the two traditional parties (Les Républicains and the Parti Socialiste) at the 2022 Presidential elections and the corresponding emergence of three new dominant blocks (Rassemblement national on the right, La France insoumise on the left, Renaissance and its partners at the center) is more a symptom than a cause of the transition to a new political equilibrium. Dividing lines between political parties are considerably blurred. With respect to economic aspects, the program of the Rassemblement national is closer to the one of a typical left party (minus aspects related to immigration) than to a right one. On immigration and other “societal” issues, it is virtually impossible now to distinguish between the Rassemblement national and the traditional right party Les républicains. It is not uncommon to hear voters of La France insoumise (left/far-left) expressing their preferences for Le Pen over Macron – and many of them have indeed voted for Le Pen in the second round of the 2022 elections.
On the other hand, behind the smoke of the tumult caused by the immigration bill emerges a new normalized political landscape. Polls suggest that 70 to 80% of the French population support stricter conditions on immigration. While many politicians and intellectuals on the left have been attacking the bill and its vote, it might well correspond to what the majority of French are asking for. It’s unlikely that Macron’s views on immigration have radically changed since 2015 and it’s pretty sure that many of the MPs of the governing coalition who have voted for the bill don’t support all its content. But what we are seeing might be the political attraction power of the median voter at play. In the perspective of the 2024 European elections and even more of the 2027 French Presential elections, it is just impossible for the governing coalition to completely ignore the political preferences of the majority of the electorate. That this is ironically a self-defeating strategy cannot have escaped the great strategic minds that surround Macron. Unsurprisingly, Le Pen has indeed claimed credit and symbolic victory for the vote of the bill. By leaning toward the political views of the populist right, Macron and the government are only legitimizing even more its ideas and reinforcing their normalization within the new minimal consensus.
History is open-ended and there is no certainty regarding what will happen in 2027. What is sure however is that the rule of the democratic game has changed, at least in the French case. While in the transitory regime, there was still a contradiction between the populist appeal to the general will and populism’s very partisan politics, the time when populists will be able to claim that the general will is indeed aligned to the preferences of the median voter is coming.
[1] Duncan Black, “On the Rationale of Group Decision-Making,” Journal of Political Economy 56, no. 1 (1948): 23–34.
[2] To find the Condorcet winner among two or more candidates, organize head-to-head elections for all pairs of candidates. The Condorcet winner is the candidate who receives a majority of votes in all its head-to-head confrontations against other candidates.
[3] As argued for instance by Partha Dasgupta and Eric Maskin, “On the Robustness of Majority Rule,” Journal of the European Economic Association 6, no. 5 (2008): 949–73.
[4] Anthony Downs, An Economic Theory of Democracy (Boston: Pearson, 1997).
[5] Daron Acemoglu and James A. Robinson, Economic Origins of Dictatorship and Democracy (Cambridge ; New York: Cambridge University Press, 2005).
[6] Daron Acemoglu, Georgy Egorov, and Konstantin Sonin, “A Political Theory of Populism,” The Quarterly Journal of Economics 128, no. 2 (2013): 771–805.
[7] Let me make it clear that the fact that the conditions under which a theorem applies are not verified for a specific case doesn’t imply that the theorem is irrelevant to the case under consideration. The theorem can still have heuristic value and serves as a backbone for a refined and more general model. The question is precisely whether the MVT can have this heuristic value here.
[8] Kenneth Joseph Arrow, Social Choice & Individual Values (Yale University Press, 1963).
[9] Maybe we were already in the transitory regime, considering Le Pen’s (the father) participation in the second round of the 2002 Presidential election and Sarkozy’s very rightist politics during his 2007-2012 mandate.