What is Fair?
Merriam­Webster:
fair (adjective)
a : marked by impartiality and honesty;
free from self­interest, prejudice, or favoritism b : conforming with the established rules
c : free of obstacles (archaic)
Fairness is often associated with equality.
Another interpretation of fairness is when all recipients
believe that they have received a fair amount.
Examples
fair game – each player is equally
likely to win the game
fair die – each side has an equal chance of being rolled
fair trade – related to equity in international trade
fair ball – a batted ball that conforms to given rules
What is a Fair Election?
What You Said
• everyone has the option to vote (perhaps age restriction)
• all candidates have equal chance of running
• multiple political parties allowed
• every vote is counted (count is accurate)
• equal campaign funding
• winner determined by a majority vote
• no electoral college
• everyone who votes has equal voting power
• diversity of choices
• election laws are followed
What is a Fair Election?
What You Said
• people are free to vote as they choose
• election result is directly related to the counted votes
• unbiased people count the votes
• equal access to voting information
• equal access to polling places
• voting is based on educated decisions
• every eligible voter votes
• candidates/issues have equal access to media
• candidates/issues worth voting for
• written/spoken campaign
What is a Fair Election?
U.S. Department of State
Principles of Democracy
http://infousa.state.gov/government/overview/election_dem.html
Inter­Parliamentary Union
Declaration on Criteria for Free and Fair Elections
http://www.ipu.org/cnl­e/154­free.htm
United Nations
Universal Declaration of Human Rights
http://www.un.org/en/documents/udhr/
Common Borders
http://www.commonborders.org/free_and_fair.htm
Fairness Criteria – Who Should Win?
So far we have the following:
The Majority Criterion If candidate X has a majority of the first­place votes,
Then candidate X should be the winner of the election.
Not every election has a majority candidate.
The Condorcet Criterion If candidate X is preferred by the voters over each of
the other candidates in a head­to­head comparison,
then candidate X should be the winner of the election.
Not every election has a Condorcet candidate.
Election Results
Number of Voters
14
10
8
4
1
1st choice
2nd choice
A
C
D
B
C
B
B
C
D
D
3rd choice
4th choice
C
D
B
C
B
D
A
A
A
A
Who is the Condorcet candidate?
Condorcet candidate – the candidate preferred by a
majority of voters over every other candidate when they are compared in head­to­head comparisons.
Election Results
Number of Voters
14
10
8
4
1
1st choice
2nd choice
A
C
D
B
C
B
B
C
D
D
3rd choice
4th choice
C
D
B
C
B
D
A
A
A
A
Let's start by comparing A to everyone else:
A > B 14 A > C 14 A > D 14 14 is not a majority.
Election Results
Number of Voters
14
10
8
4
1
1st choice
2nd choice
A
C
D
B
C
B
B
C
D
D
C
D
B
C
B
D
A
A
A
A
3rd choice
4th choice
Now compare B to everyone else:
B > A 23
B > C 18
B > D 28 18 is not a majority.
Election Results
Number of Voters
14
10
8
4
1
1st choice
2nd choice
A
C
D
B
C
B
B
C
D
D
3rd choice
4th choice
C
D
B
C
B
D
A
A
A
A
Now compare C to everyone else:
C > A 23 C > B 19 C > D 25
Each is a majority.
Election Results
Number of Voters
14
10
8
4
1
1st choice
2nd choice
A
C
D
B
C
B
B
C
D
D
3rd choice
4th choice
C
D
B
C
B
D
A
A
A
A
Now compare D to everyone else:
D > A 23 D > B 9 D > C 12 Not all are a majority.
Election Results
Number of Voters
14
10
8
4
1
1st choice
2nd choice
A
C
D
B
C
B
B
C
D
D
3rd choice
4th choice
C
D
B
C
B
D
A
A
A
A
Therefore, C is the Condorcet candidate.
The Borda Count Method
Number of Voters
14
10
8
4
1
1st (4 points)
A: 56 C: 40 D: 32 B: 16
C: 4
2nd (3 points)
B: 42 B: 30 C: 24 D: 12
D: 3
3rd (2 points)
C: 28 D: 20 B: 16
C: 8
B: 2
4th (1 point)
D: 14 A: 10
A: 4
A: 1
A – 79 points
B – 106 points
C – 104 points
D – 81 points
A: 8
Candidate B is the Borda winner.
Why is this not good?
School Principal Election
Number of Voters
6
2
3
1st choice
2nd choice
A
B
C
B
C
D
3rd choice
4th choice
C
D
B
D
A
A
Who is the majority candidate? A
Who is the Condorcet candidate? A
Who is the Borda winner? B
The Borda Count Method
The Good:
Takes into account all the information on
preferences. The winner is the candidate
with the best average ranking. The Bad:
It does not satisfy the Condorcet criterion or
the majority criterion.
The Not­So­Bad:
Violations of these two criterion don't happen very
often, especially when there are many candidates. Despite it's flaws, the Borda count method is considered by voting theory experts as one of the best for deciding elections with many candidates.
In fact, this method (or some variation of it) is used to determine the Heisman Trophy winner, the NBA Rookie of the Year, the NFL MVP, etc.
It is also used to pick the winners of music industry awards and to help in hiring processes.