Voting Theory

Voting Theory studies how to take individual rankings of voters and aggregate them to form the global ranking.


  • Votes for a president of a company/country, etc. All voters communicate their results and based on that the president is chosen
  • Search engines: there are many results, how to show them?

Notation and Relations

  • let $A = \{a, b, c, ...\}$ be the set of candidates
  • there are $N$ voters
  • each voter can express his preference on the basis of a total order
    • i.e. he has to rank all the candidates

For this notation we define the following relations (Voting Theory Relations)

  • Weak and Strong Preference
  • Indifference

Voting Mechanisms and Principles

A voting mechanism (or voting procedure or voting method) takes a collection of votes (individual preferences of the candidates from set $A$) and forms the global ranking. Usually it choses a single candidate from the set $A$.


There are several voting procedures:


How to characterize "good" voting methods?

There are several criteria

PV 2PV Borda Cond.
Solution Existence
Condorcet Fairness

Other principles:


Examples and Exercises



  • Mathematics of Voting - slides [1]
  • Criteria [2]
  • EC228 Voting Theory Lecture Notes [3]
  • Social Choice Theory and Multicriteria Decision Aiding [4]
  • Book: Voting, Arbitration, and Fair Division [5]
  • Methods vs Voting Criteria [6]


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