Professor H. L. Bray        
                Video Series
                        What is Democracy?

Special thanks to Devon Henry and Stephen Toback of Duke University's Academic Media Services in the Office of Information Technology for helping me create this video series.

Also, kudos to Nicolas de Condorcet (1743 - 1794), a visionary in the Enlightenment who died fighting for democratic ideals, Nicolaus Tideman (1943 - ), who discovered the Ranked Pairs method for determining the winner of a preferential ballot election, and everyone else who has done their best to figure out "What is Democracy?"

1.01 - Types of Ballots in Elections
1.02 - Who Wins a Preferential Ballot Election?
1.03 - Plurality and Instant Runoff Voting
1.04 - The Unit Interval Model
1.05 - Instant Runoff Voting Is Not Monotone
1.06 - The Margin Of Victory Matrix
1.07 - The Borda Count
1.08 - The Borda Count is NOT Clone Invariant
1.09 - The Borda Count and Nuclear War
1.10 - Instant Runoff Borda is Condorcet
1.11 - Instant Runoff Borda and The Unit Interval Model
1.12 - The Game Theory of Condorcet Methods
1.13 - Worst Defeat
1.14 - The Schulze Method
1.15 - Ranked Pairs
1.16 - Comparison of Vote Counting Methods that use the Margin of Victory Matrix
1.17 - What is Democracy?

The above video series surveys the pros and cons of various methods for determining the winners of preferential ballot elections from a game theoretic point of view. Analyzing the game theory of each vote counting method is critical since changing the rules of elections will change the strategies used by both candidates and voters. The goal is to find the vote counting method that incentivizes the behavior of candidates and voters which is most compatible with democratic ideals.

The seven vote counting methods studied are Plurality, Instant Runoff Voting, the Borda Count, Instant Runoff Borda, Worst Defeat, the Schulze Method, and Ranked Pairs. Of these, only Ranked Pairs is Condorcet, clone invariant, monotone, and last place loser independent.

A Condorcet method is any method that always picks the Condorcet candidate, when one exists. A Condorcet candidate, which exists in the vast majority of real world elections, is the candidate that beats every other candidate in a head-to-head election (among all the voters, where the other candidates are ignored). The game theory for candidates in Condorcet elections is therefore to be able to win every head-to-head election against every other candidate. In certain geometric models of politics, it follows that the most centrist candidate always wins.

Clone invariance is the desirable property that solves the "splitting the vote" problem among similar candidates. Clone invariant vote counting methods neither penalize nor reward candidates that are very similar to other candidates. A collection of clones are defined to be candidates that are all ranked next to each other on every ballot. A vote counting method is clone invariant if adding clones of candidates to an election never alters the outcome, in the sense that either the original winner or a clone of the original winner still wins. The game theoretic implication is that, from the point of view of the voters, similar candidates can participate in the election without significantly altering the outcome.

A vote counting method is monotone if ranking a candidate higher on a ballot never hurts that candidate. While this does not eliminate all possible cases of strategic voting (known to be impossible), it does mean that candidates will never be penalized for convincing voters to rank that candidate higher.

Last place loser independent vote counting methods do not change the winner of the election if the last place loser (the candidate who would win if every voter reversed the order of their preferential ballot) drops out of the election. While this does not eliminate all possible cases of losing candidates dropping out of elections to alter the outcome (known to be impossible for Condorcet methods), it does guarantee that at least some fringe candidates cannot alter the winner of the election by dropping out.

If you'd like to carry out a Ranked Pairs election with all these properties, visit