Despite last fall’s defeat of Donald Trump, populism in the United States is not dead. Perhaps next up for America is left‐​wing populism, which is more like the right‐​wing variety than many people realize. Hence, reviewing political scientist William Riker’s classic Liberalism Against Populism is appropriate and urgent. Published in 1982, the book is noteworthy both for its overview of social choice theory — a framework for analyzing how collective choices relate to individual preferences — and for the lessons it draws from the clash between populism and political liberalism.

Riker (1920-1993) was a professor of political science and department chairman at the University of Rochester. He pioneered what he called "positive political theory," based on rational choice, formal economic modeling, and empirically falsifiable statements. He led political scientists to discover economist Kenneth Arrow's seminal 1951 book Social Choice and Individual Values, which launched the modern theory of social choice. Riker was also involved with the economic theory of public choice, an overlapping but different research area, and was president of the Public Choice Society in 1966. About the time he published Liberalism Against Populism, he was president of the American Political Science Association.

Riker defined populism as embracing two propositions: First, the "will of the people" ought to be government policy. Second, "the people are free when their wishes are law." As for liberalism, he conceived it as any democratic system that does not attach any sacrosanct character to the will of the people. Riker's approach to liberal democracy is close to what F.A. Hayek described in Law, Legislation, and Liberty, vol. 3: The Political Order of a Free People (University of Chicago Press, 1979):

The true value of democracy is to serve as a sanitary precaution protecting us against an abuse of power. It enables us to get rid of a government and try to replace it by a better one. Or, to put it differently, it is the only convention we have yet discovered to make peaceful change possible.

Social choice and the imperfection of voting/ Which system is better, liberalism or populism? The theory of social choice is relevant to this question, Riker explains, because it analyzes how "tastes, preferences, or values of individual persons are amalgamated and summarized into the choice of a collective group or society." Social choice refers to the choices made through government — that is, political choices. The problem of populism, Riker argues, is that voting (elections and referenda) — or, for that matter, any other political aggregation of individual preferences — cannot reveal the will of the people or the content of the public interest, assuming that such things even exist.

Systems of voting and counting votes include majority voting, plurality voting, different methods of ranking candidates, and list voting in proportional representation systems. In the United States, one method of ranking candidates ("ranked-choice voting") is now used in some local elections and, in Maine, in state and federal elections, including for president. Two other states are considering adopting ranked-choice voting.

Different voting methods often produce different results. In fact, if you want a certain result from a given electorate, you can often find some voting system that would produce it. For that reason, there is no "objective" way to democratically choose the best voting method.

In the presence of three or more alternatives (candidates or issues), all voting methods violate at least one of a few basic technical or democratic-fairness criteria. One is monotonicity, which means that if one voter changes his mind in favor of an alternative, other things being equal, the social choice (aggregation) function should produce a result that does not increase the chances of another alternative. Undifferentiatedness or anonymity means that votes cannot be distinguished from one another: all voters are equal and anonymous. Neutrality requires that the voting system not favor one alternative over others. It has been mathematically demonstrated that majority voting between two alternatives, where one alternative gets more than 50% of the vote, is "the only method that simultaneously satisfies the criteria of monotonicity, undifferentiatedness, and neutrality," Riker notes. For example, if a primary is held to winnow a larger field to two, that would violate the neutrality criterion.

We must also consider the fundamental Condorcet criterion (named after 18th century French mathematician and philosopher Nicolas de Condorcet), which requires that the winner among many alternatives (opponents or proposals) be the one that would also win a pair-wise election against each of the other candidates. Problem is, a "Condorcet winner" does not always — or even often — exist when more than two alternatives are being voted on. And when a Condorcet winner does exist, it may not actually be chosen because of the voting system. For instance, in the 1912 presidential election, Progressive Party candidate Theodore Roosevelt may have been a Condorcet winner against Democrat Woodrow Wilson and Republican William Taft, but Wilson won the election.

Social choice, Riker concludes, depends as much on aggregation methods and political institutions as it does on individual values and tastes. Since each voting method can be justified by one or more democratic criteria (methods that look fairer, for example, may ignore the Condorcet winner), we must face the fact that an election has no "true" winner.

The "paradox of voting," discovered by Condorcet in the 18th century, lies in the observation that a Condorcet winner may not exist, leaving unstable cycles between alternatives. Consider three voters, V1, V2, and V3, and three alternatives presented to those voters, X, Y, and Z. Table 1, reproduced from Riker, gives the ordinal preferences of each voter. V1 prefer X to Y and Y to Z, which we can express symbolically as "X Y Z." V2 and V3 have different preferences but, by hypothesis, every individual's preferences are transitive, that is, coherent or rational. V1, who prefers X to Y and Y to Z, prefers X to Z. V2, who prefers Y to Z and Z to X, prefers Y to X. And V3, who prefers Z to X and X to Y, prefers Z to Y. (Note that, like elsewhere in this review, we are considering ordinal preferences — that is, the ranks that each voter assigns to alternatives — without any assumption about the intensity of the preferences of each nor any common metric to compare the voters' preference scales.)

If the voters are asked to choose between X and Y, V1 and V3 would vote for X because it is higher in their respective preferences; the social choice would thus be X. If our three voters are asked instead (or later) to choose between Y and Z, the result of the vote would be Y because V1 and V2 would vote for Y; the social choice would be Y. Now, if our three voters are asked to choose between Z and X, the majority, V2 and V3, would vote for Z; the social choice would be Z. So, we have social choices indicating that, "for society" (if we may talk this way), X is preferred to Y, Y to Z, but Z to X. Despite all voters having transitive individual preferences, the social choice function reveals intransitive preferences.

The "social choice function" is the mechanism or procedure that translates individual preferences into social choices. This function is also called the "social welfare function" because, in welfare economics, a similar device was used to supposedly maximize social welfare. In a democracy, it is assumed that some method of voting constitutes the social choice function, either in elections, referenda, or plebiscites.

Arrow's Impossibility Theorem/ It is easy to modify the data of the simple example above in such a way that the paradox of voting disappears, although it gets difficult as the number of voters increases. Moreover, different mechanisms for making social choices and for voting exist. This is where Arrow's work becomes crucial. He mathematically demonstrated that something similar to the voting paradox affects all sorts of social choices with more than two alternatives. The original demonstration appears in his book Social Choice and Individual Values. In simplified terms, Arrow's Impossibility Theorem states that no method of aggregation (the social choice function) can satisfy all of the following conditions:

• Axiom of collective rationality: If society prefers alternative X to Y and alternative Y to Z, it will also prefer X to Z.
• Condition 1 (Pareto condition): If all members of a society prefer X to Y, the social choice function (the voting mechanism) will choose X.
• Condition 2 (unrestricted domain): The preferences of individuals are not restricted to certain preferences that would produce certain desired results.
• Condition 3 (independence of irrelevant alternatives): Irrelevant alternatives don't affect a social choice. If society prefers X to Y and to Z, the disappearance of Z is not going to change the expressed preference of X to Y. This condition can be thought of as another requirement of collective rationality.
• Condition 4 (non-dictatorship): Between any two alternatives X and Y, it cannot be that one of them, say X, will necessarily be the social choice simply because a certain individual (the dictator) prefers X to Y.

Assuming that Conditions 1-3 are realized, Arrow's theorem implies that any social choice will be either dictatorial (violating Condition 4) or incoherent (violating the axiom of collective rationality). Incoherence leads to cycles: X would win against Y, Y against Z, Z against X, X against Y again, and so forth. Social choices are either dictatorial or, as Riker puts it, "arbitrary nonsense." And this is true whatever the method of aggregating individual preferences.

One way to escape incoherence in social choice is to assume that the preferences of all individuals are "single-peaked" — a limitation of individual preferences that violates Condition 2. Single-peakedness means that if we place each individual's preferences for the different alternatives on an axis (imagine that these alternatives are different tax rates), each individual has only one utility peak: as he moves away from his ideal alternative, in one direction or another (more taxes or less), other alternatives become less and less attractive. (See "The Public Choice Revolution," Fall 2004.) To simplify (a bit too much): under single-peakedness, no individual prefers what others consider extremes: in the Vietnam War, for example, an individual's two most preferred alternatives cannot be to get out immediately or to carpet-bomb the country. Although voters have different opinions, they share a common attitude on what is reasonable.

Assuming single-peakedness saves the coherence of social choices, but at a cost. In an election, candidates will be motivated to move to the center of the political spectrum in order to gather the largest number of votes. As they move there, they gain more votes from the other side of the median than they lose from the side they are on. This "median voter theorem" means that only the median voter (or group of voters), who is exactly in the middle of the distribution of political preferences, will see his top-preferred alternative translated into a social choice. Political parties become difficult to distinguish because they all want to please the median voter. If there are no more incoherent cycles, that is because, in practice, all the alternatives have been arbitrarily reduced to a single one at the middle of the political spectrum.

In a large, diversified society, of course, single-peakedness is unrealistic. And as soon as many genuine alternatives are available to voters, incoherent social choices will raise their heads.

The dilemma between nonsense and dictatorship is not very attractive. Much of the research in social choice theory after Arrow's theorem has been to try to salvage a transitive social choice function, often by weakening Condition 3 on the independence of irrelevant alternatives. This and other solutions, however, end up violating Arrow's conditions.

As noted by Riker, another escape was proposed by James Buchanan, the 1986 Nobel economics laureate — an escape that negates the whole concept of a social choice function. Buchanan pointed out that it is anthropomorphism to expect that a group or a society, which is not an actual living and thinking creature, will show the same logical coherence as an individual. The search for a meaningful social choice function is thus necessarily a vain enterprise. For Buchanan, it is anyway preferable to have succeeding cycles of temporary domination by different majorities rather than a continuous exploitation of minorities by a stable majority. (See Buchanan's "Social Choice, Democracy, and Free Markets," Journal of Political Economy 62[2]: 114-123 [1954].)

The advantage of market choices is precisely that they are individual choices and do not aim at imposing a social — that is, political — choice on everybody. It makes no sense to say that the number of chocolate bars bought by individual consumers is incoherent with the quantity of beer they drink. On the market, every individual gets what he wants (within his budget constraint); not so in politics. From there ultimately comes the incoherence or dictatorship of social choices.

Manipulation/ What we have seen thus far does not factor in voting manipulation, which can further undermine any procedure of social choice. One sort of manipulation is strategic voting — that is, voting against one's preferences in order to avoid a still worse outcome. This is common in Congress through vote trading, which according to Riker is "the most extreme version of strategic voting": I will vote for your pet project, which I don't like much or am indifferent about, in exchange for you voting for my pet project, which I absolutely want. This sort of horse trading can even lead to a set of decisions that is detrimental to everybody.

In general elections, major political parties try to crush out third parties by telling the latters' potential voters to vote strategically in order not to "waste" their votes. Strategic voting can also happen under proportional representation because voters may give their votes to a party more likely to participate in a governing coalition. However, as Riker admits, strategic voting is unlikely (I would say very unlikely) in all but small groups. In large elections, an individual voter has no practical influence on the result, which must be obvious to him if he does not suffer from cognitive limitations or is not a victim of propaganda. If this individual does not vote, the winner is extremely unlikely to be different because winners are not elected by a single pivotal vote.

Another legal method of voting manipulation is the control of the agenda by politicians or bureaucrats — that is, the process whereby voters are presented with only some alternatives or in an order favorable to the manipulator. It has been shown that "manipulation can occur under any method of voting," except if preferences are nearly identical across individuals. Voter manipulation can also occur in legislative assemblies. Riker gives the example of the 1902 rejection of the 17th Amendment (on the popular election of senators) by a Senate committee. He argues that an agenda manipulation suggested that no majority was forthcoming, which prevented the amendment from coming to the floor. (The 17th Amendment was adopted a decade later by a stronger coalition.) A laboratory experiment devised by Charles Plott and Michael Levine ("A Model of Agenda Influence on Committee Decisions," American Economic Review 68[1]: 146-160 [1978]) and replicated by Riker suggests that the right partition of issues can lead voters to vote just like the agenda setter wants them to.

Instability and discontent/ Even if a Condorcet winner exists, that alternative is unlikely to be chosen in elections. In policy space, "anything can happen," Richard McKelvey and Norman Schofield argued (McKelvey, "Intransitivities in Multidimensional Voting and Some Implications for Agenda Control," Journal of Economic Theory 12: 472-482 [1976]; Schofield, "Instability of Simple Dynamic Games," Review of Economic Studies 45[3]: 575-594 [1978]). This instability explains the wide swings in political choices, such as Donald Trump's election in 2016 and his policies. Four years later, his defeat and his reaction repeated the demonstration. The stability we otherwise observe is due to institutions that limit the choices submitted to majority rule.

It is not surprising that discontent is the hallmark of democratic politics. Not only are overruled minorities dissatisfied but, because the system very seldom reaches an equilibrium on a Condorcet winner, the current majority itself will soon be unhappy too. For politicians, the art of politics consists in profiting from that disorder, which can only intensify discontent. The more people expect from democracy, the more dissatisfied they will be, as Anthony de Jasay argued in his 1985 book The State.

Furthermore, Riker observes, "losing in the market is a relatively mild kind of losing compared with losing in politics." He gives the example of the losers from the adoption or increase of the minimum wage: they lose their access to the labor market because their low productivity has become too expensive and they are legally prevented from improving their lot by underbidding the more productive. So, he adds, the "dismal science" is political science, not economics.

Disequilibrium sometimes leads to revolution and civil war. Abraham Lincoln, who won with a plurality of about 40% of the votes in 1860, would have lost to Stephen Douglas or perhaps John Bell if other election methods had been used, Riker argues.

Liberalism against populism/ We are now in a better position to understand why Riker believed that social choice theory destroyed the intellectual justifications of populism and reinforced liberal theory. Populism fails because there is no way to know what is the "will of the people" — if that term even makes sense — and what the results of an election mean. Riker writes, "We do not know and cannot know what the people want." For the same reasons, "when people have to vote on which interpretation [of the public interest] is correct, then clearly the true public interest will not be revealed, without substantial unanimity." No political alchemy or voting gadgetry (like, say, ranked-choice voting) can change that. "Populism fails, therefore, not because it is morally wrong, but because it is empty," he concludes. Trump thought he represented the will of the people, but any other politician can claim the same (as Biden did in his inaugural address) because the will of the people is unascertainable.

The American political tradition has always been marred by "a strong strand of populism." Riker wonders why, despite the "disasters with the 'imperial' presidencies of Johnson and Nixon," people continue to search for ways to increase the president's power.

Liberalism, on the contrary, is consistent with the theory of social choice because it "does not demand much from voting." Liberalism does not require the outcome of an election to make sense. Voting only provides the majority with "a way to get rid of rulers." It is "a wholly negative kind of control." Liberal democracy is humble: it is not popular rule "but an intermittent and sometimes random popular veto" that has some capability "to restrain official tyranny."

Populism, writes Riker, "reinforces the normal arrogance of rulers with a built-in justification for tyranny, the contemporary version of the divine right of rulers." Populism demands a rapid realization of the will of the people, which is constrained by liberal institutions. Riker found the main constraining institutions in elections, bicameralism, and decentralization — as well as, to a lesser extent, an independent judiciary. I would suggest that he underestimated the importance of the latter and neglected what De Jasay called "private force," which is the presence of powerful private organizations that Leviathan does not dare to confront, although it is not clear if such organizations still exist.

Social choice theory persuaded Riker to abandon his populist intuitions. "It took me a score of years of reflection on [economist Duncan] Black's and Arrow's discoveries to reject the populism I had initially espoused," he explains. Many scholars probably say, "Me too!"

Riker's conclusions still stand, four decades after the publication of Liberalism Against Populism. But how and when can we expect the general public to understand the economic and mathematical underpinnings of social choice theory? Even the intelligent layman will struggle to follow the arguments, let alone the mathematical theorems. "The dissemination of a rather arcane theory is a task for generations," Riker noted, in an Enlightenment sort of optimism. If this task is achievable, Liberalism Against Populism will have mightily contributed to it by educating many students of politics.