Short Course: Mathematics and Democracy


Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures
Steven J. Brams and D. Marc Kilgour

9:00 am – 1:00 pm

Proposed Short Course Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures Steven J. Brams, Department of Politics, New York University D. Marc Kilgour, Department of Mathematics, Wilfrid Laurier University In this course, we show how mathematics can be used to address two essential challenges of democracy:

  • how to aggregate individual preferences to give a social choice or election outcome that reflects the interests of the electorate; and
  • how to divide public and private goods in a way that respects due process and the rule of law.

Whereas questions of aggregation are the focus of social choice theory, questions of division are the focus of fair division. Democracy, as we use the term, will generally mean representative democracy, in which citizens vote for representatives, from president on down. But we also analyze referendums, in which citizens vote directly on propositions, just as they did in assemblies in ancient Greece. We analyze procedures, or rules of play, that produce outcomes. By making precise the properties that one wishes a voting or fair-division procedure to satisfy and clarifying relationships among these properties, mathematical analysis can strengthen the intellectual foundations on which democratic institutions are built. But because there may be no procedure or institution that satisfies all the properties one might desire, we examine trade-offs among the properties. In the case of some procedures, we also consider practical problems of implementation and discuss experience with those that have been tried out. The voting and fair-division procedures we analyze foster democratic choices by giving voters better ways of expressing themselves, by electing officials who are more likely to be responsive to the electorate, and by allocating goods to citizens that ensure their shares are equitable or preclude envy. In some cases we criticize current procedures, but most of the analysis is constructive—we suggest how these procedures may be improved. Designing procedures that satisfy desirable properties, or showing the limits of doing so, is sometimes referred to as institutional design or mechanism design. We present empirical examples to illustrate this approach, but the bulk of the analysis will be theoretical. The product of such analysis is normative: The prescription of new procedures or institutions that are superior, in terms of the criteria set forth, to those we now have. Like engineering in the natural sciences, which translates theory (e.g., from physics) into practical design (e.g., a bridge), engineering in the social sciences translates theory into the design of political-economic-social institutions that better meet the criteria one deems important. Requirements We assume a familiarity with high-school mathematics; a stronger background in mathematics will be helpful but is not necessary. We will present formal results as well as the intuitions underlying them.

**All Short Courses will take place on Wednesday, August 31 at the APSA 2016 Annual Meeting in Philadelphia, PA.