While a game-theoretic school of political science has existed since Riker’s innovation of the 1950s (see Riker 1992), nineteenth-century English writers on methods of election employed arguments which indicated a recognition of the strategic interdependence of voters—and, even more so, parties. Spurred by parliamentary reforms of suffrage and such abuses as rotten boroughs and redistricting, they contemplated substantial changes in geographic representation, seats per district, votes per elector and criteria for winning. The most interesting of this literature is that written by proponents of various forms of proportional representation (PR).
The PR literature is quite different from the better-known and pioneering work of Condorcet and Borda in the eighteenth century, which focused on properties of voting rules by drawing attention to such anomalies of the majority voting rule as vote cycling and tended towards the mathematical and axiomatic. Most of the PR literature is in prose and addresses issues from a perspective of coalition and side payment which has since been codified in cooperative game theory. 2 Although Droop, Baily and J.G. Marshall made relatively systematic observations, Hare, the most famous exponent of proportional representation and founder of the Proportional Representation Society (PRS), was among the least analytic of these writers. In itself, such literature, which is discussed in the first section below, would not merit more than a brief discussion in this book. This literature is important as furnishing the environment from which a most important analysis of strategic interdependence in electoral rules emerged. 3
The Oxford mathematician Dodgson (better known as Lewis Carroll) published a pamphlet, The Principles of Parliamentary Representation (1884g: henceforth PPR), which is still a stunning accomplishment. Although the perspective of other advocates of PR resembles that of cooperative game theory, Dodgson’s model in which players are two political parties and a rule-maker is non-cooperative. It is in fact very close to being a full-blown mechanism design model. Black has called Dodgson’s work ‘the most distinguished contribution that has been made to Political Science since the seventeenth century’ (Black 1970, 28), and it was Black (1967, 1969) who brought PPR and its game-