The Age of Enlightenment promoted knowledge through science and the organization of the state on rational grounds, having paved the way for the French, American and Polish Revolutions. At the same time, the Enlightenment left a historical puzzle. Although both of its leading political thinkers, Montesquieu and Rousseau, explicitly linked selection of magistrates by lot to democracy and election by vote to aristocracy, the post- Enlightenment democracies adopted ‘aristocratic’ elections as their only instrument of appointment to public offices. This re-identification of the distinctive features of democracy and aristocracy marks the end of the way democracy had been understood for over two millennia. From this turning point on, ‘democracy’ means something different than the classical democracy of Athenian type. This chapter describes the political theories of Montesquieu and Rousseau and their influence on the electoral studies of French mathematicians Borda, Condorcet and Laplace, who attempted to adapt elections to democracy, which, unlike aristocracy, assumes no commonality of values among voters. Extending the voting problem to a heterogeneous electorate resulted in intuitive and logical inconsistencies. Although some new approaches were developed, the principal difficulties remained unsolved.
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