Primarily about Primaries


  • Allan Borodin University of Toronto
  • Omer Lev Ben-Gurion University University
  • Nisarg Shah University of Toronto
  • Tyrone Strangway University of Toronto



Much of the social choice literature examines direct voting systems, in which voters submit their ranked preferences over candidates and a voting rule picks a winner. Real-world elections and decision-making processes are often more complex and involve multiple stages. For instance, one popular voting system filters candidates through primaries: first, voters affiliated with each political party vote over candidates of their own party and the voting rule picks a candidate from each party, which then compete in a general election.

We present a model to analyze such multi-stage elections, and conduct the first quantitative comparison (to the best of our knowledge) of the direct and primary voting systems with two political parties in terms of the quality of the elected candidate. Our main result is that every voting rule is guaranteed to perform almost as well (i.e., within a constant factor) under the primary system as under the direct system. Surprisingly, the converse does not hold: we show settings in which there exist voting rules that perform significantly better under the primary system than under the direct system.




How to Cite

Borodin, A., Lev, O., Shah, N., & Strangway, T. (2019). Primarily about Primaries. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01), 1804-1811.



AAAI Technical Track: Game Theory and Economic Paradigms