While working at the RAND Corporation during the Cold War, Arrow’s supervisor wanted him to think about how to characterize the preferences of the Soviet Union. So Arrow started to think about the problem of how to translate individual preferences into a collective decision. This led to his famous 1951 book, in which Arrow proved that there is no mechanism that can both satisfy a set of reasonable assumptions and translate the preferences of rational individuals into a coherent collective decision. In other words, any mechanism of “preference aggregation” is either incoherent or dictatorial.

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To put it concisely: in these two works, Arrow proved the existence of a solution to the problem of economics and the non-existence of a solution to the problem of politics.

Arrow had three intellectual successors: Anthony Downs (a student of Arrow at Stanford), Mancur Lloyd Olson, and William Harrison Riker. Within political science, there have not been subsequent theories as innovative as those of Arrow, Downs, Olson and Riker. These remain the foundational building blocks of the discipline. As argued in a recent book by Kevin Clarke and David Primo, science is essentially about models, and political science is no exception. It is precisely this set of models that informs our current understanding of politics.

Olson defied the assumption that given a common interest individuals would form groups to pursue it. In doing so, he rendered collective action a puzzle to be explained, not something to be assumed. Downs challenged the premise that political parties were agents of particular segments of society. Instead, he posited that they were the creatures of ambitious politicians seeking power.

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It was perhaps Riker who fully extracted the consequences of Arrow’s discovery. In “Liberalism Against Populism”, Riker contrasted these two strands of democratic theory. Derived from the writings of Rousseau, populism states that democratic choices — including election outcomes — are the reflection of a coherent collective will. Consequently, an elected government carries a mandate to enact it. Arrow’s theorem established that this conception is illusory. Electoral outcomes depend critically on electoral rules. Thus, they cannot be easily interpreted as mandates.

The most we can demand from democracy is the liberal, Madisonian version: a system of regular elections that provide opportunities to sanction governments that perform poorly. Or, as the philosopher Karl Popper put it, citizens can rid of governments without bloodshed. However pedestrian this conception of democratic government might look like, we can still can throw the rascals out.

Arrow teaches us that politics has no “solution” — only ongoing conflict that is channeled through political institutions that lend at least some stability to the process. But the outcomes of this conflict are simply the contingent product of the struggle for power. What we hope for is that politicians can devise strategies that produce compromises that, albeit temporary, can pave the way to civilized political life.