Voting theory  -- how to play democracy.

Assumption -- all the people are of equal value.


Preference ballot  -- Each voter provides a ranking of all the candidates

                             -- No information lost from "pick only one"

Preference schedule -- Tally of all ballots







If we're talking about a majority from a set, we mean that greater that 50% that have a specific characteristic. 


If we're talking about a plurality, it means the largest group with that characteristic.








A voting method is how we pick a winner (or ranking) of an election from the preference schedule.  Should include tiebreakers.


A voting criterion  (plural is criteria) is a statement about how a voting method should behave.  We say that "a voting method satisfies the <X> criterion" only if it conforms to the criteria no matter how many voters, how many candidates, and how everyone does their ranking.








Our first method  -- The method we use at the state level in the US for presidential elections is the plurality method. The candidate with most 1st place votes wins.


Our first criterion -- The majority criterion.  If a candidate receives a majority of 1st place votes, that candidate should win the election.






Issue  --  Insincere voting.  People shouldn't game their votes.  Leads to Duverger's law.  Plurality leads to two party systems.


2000 Florida election results






French system  -- (This is oversimplified)  If no majority then runoff of the top 2.


New method -- Plurality with elimination also known a instant run-off.