Condorcet's Social Mathematics
Condorcet argued that quantitative study of society should help guide government. Ellenberg presents this commitment to social science as an enduring part of Condorcet’s political thought, despite the limits of his voting-system aspirations.
THE IDEA
Condorcet’s Vision of Progress
Condorcet’s Sketch for a Historical Picture of the Progress of the Human Mind lays out his vision of the future. It is an astonishingly optimistic document, describing a world from which the errors of royalism, sex prejudice, hunger, and old age would be eliminated in turn by the force of science. This passage is typical:
May it not be expected that the human race will be meliorated by new discoveries in the sciences and the arts, and, as an unavoidable consequence, in the means of individual and general prosperity; by farther progress in the principles of conduct, and in moral practice; and lastly, by the real improvement of our faculties, moral, intellectual and physical, which may be the result either of the improvement of the instruments which increase the power and direct the exercise of those faculties, or of the improvement of our natural organization itself?
Nowadays, the Sketch is best known indirectly; it inspired Thomas Malthus, who considered Condorcet's predictions hopelessly sunny, to write his much more famous, and much bleaker, account of humanity's future.
Shortly after the above passage was written, in March 1794 (or, in the rationalized revolutionary calendar, in Germinal of Year 2), Condorcet was captured and arrested. Two days later he was found dead—some say it was suicide, others that he was murdered.
Just as Hilbert's style of mathematics persisted despite the destruction of his formal program by Gödel, Condorcet's approach to politics survived his demise. We no longer hope to find voting systems that satisfy his axiom. But we have committed ourselves to Condorcet's more fundamental belief, that a quantitative 'social mathematics'—what we now call 'social science'—ought to have a part in determining the proper conduct of government. These were 'the instruments which increase the power and direct the exercise of [our] faculties' that Condorcet wrote about with such vigor in the Sketch.
Condorcet's idea is so thoroughly intertwined with the modern way of doing political business that we hardly see it as a choice. But it is a choice. I think it's the right one.
When to use it
Evaluating alternative voting systems for organizational elections.
Data-driven policy design in public health, education, or economics.
Assessing the ethical implications of using quantitative measures in life-or-death decisions.
Designing experiments to test social interventions before scaling.
FROM THEORY TO EVERYDAY LIFE
In practice
Voting System Design
Condorcet’s work on voting systems illustrates his belief that mathematics can clarify political decisions. A Condorcet method elects a candidate who beats every other candidate in head-to-head comparisons, if such a candidate exists. Cyclic majority preferences show why that condition need not identify a winner.
Modern Policy Analysis
A government evaluating an education policy with statistical models or a controlled trial illustrates the quantitative approach Ellenberg associates with Condorcet’s social mathematics. The analysis supplies evidence for a policy decision, while questions about goals and acceptable tradeoffs remain.
A MOMENT TO REFLECT
Put it to work.
How does Condorcet's social mathematics differ from purely theoretical or ideological approaches to governance?
In what areas of modern life might we be over-relying on quantitative social science, and where might we underutilize it?
Can you think of a decision (personal or societal) that would have been helped by explicit application of 'social mathematics'?
References
- Sketch for a Historical Picture of the Progress of the Human Mind — Marquis de Condorcet (1795)
- An Essay on the Principle of Population — Thomas Malthus (1798)
CONTINUE THE CONVERSATION
Source texts
- How Not to Be Wrong The Power of Mathematical Thinking (Ellenberg, Jordan)