Brittany Vacchiano
» Voting procedure in which voters can vote for as many
candidate as they wish
» Each candidate approved of receives one vote
» Single candidate with the most votes wins
» Not limited to a single vote like Plurality  more expressive
»
»
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»
»
»
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Ballot 1
x Pepsi
x
Sprite
Ballot 2
x Pepsi
Sprite
Ballot 3
Pepsi
x
Sprite
Ballot 4
Pepsi
x
Sprite
Winner – Sprite (3 votes)
Coke
x
Coke
Coke
x
Coke
» Gives voters flexible options
» Helps elect the strongest candidate
» Gives minority candidates their proper due (they receive
votes alongside majority candidates)
» It reduces negative campaigning
» Results are easy to understand
» Best method for choosing a beat-all-winner, stronger
and better system than Plurality
» Is a Condorcet method of voting winner will
always be ranked as the most popular choice
» Uses preferential ballots on which voters rank
candidates according to their order of
preference
» Voter can rank more than one choice at the
same preference level
» A matrix is created that counts the pairwise
voter preferences and their rankings
» Basically….
˃ Compares every possible sequence of preferential
choices and then associates those sequences with a
Kemeny Score
˃ Judges which candidate is preferred over others
» Suppose you had a ballot with 4 candidates:
Sprite, Coke, Pepsi and Dr. Pepper
» Those preferences can be expressed in a
popularity matrix
…over Sprite
Prefer
Sprite…
…over Pepsi
….over Coke
…over Dr. Pepper
68
68
58
83
58
Prefer Pepsi… 32
Prefer Coke…
32
17
Prefer
Dr.Pepper…
42
42
58
42
» Popularity Matrix- Pairwise counts are arranged
in a table in which choices appear in sequence
from most popular (top left) to least popular
(bottom right)
» Best overall ranking score (AKA Kemney Score)
= sum of all counts in the upper-right triangle
…over Sprite
Prefer
Sprite…
…over Pepsi
….over Coke
…over Dr. Pepper
68
68
58
1
9
4
83
58
1
4
1
Prefer Pepsi… 32
Prefer Coke…
32
17
Prefer
Dr.Pepper…
42
42
58
42
» Kemeny score of above example is 393
(68+68+58+83+58+58)
» Ranking (based on best possible Kemeny score)
is Sprite > Pepsi > Coke > Dr. Pepper
1st
2nd
3rd
4th
» A single voter cannot control the outcome
» Is a neutral method for the Condorcet criteria
» It allows for a fair vote, because all possible
preferences and rankings are taken into
consideration
» With large datasets/many different candidates,
the calculations for the popularity matrix and
the best overall Kemeny score can be VERY time
consuming
» In a nutshell, K-Y method involves considering
every possible order-of-preference sequence,
calculating a score for each such sequence, and
then choosing the sequence with the highest
score as the best fit
» From that best fit you can tell how the
candidates will be ranked (1st, 2nd, 3rd,…,etc)
» Not much information online besides on Wikipedia
pages and this site
˃ http://www.votefair.org/province.html
˃ I had to search through the Purdue Library to find relevant info
» Levin, J., & Nalebuff, B. (1995). An introduction to
vote-counting schemes. The Journal of Economic
Perspectives, 9. 15-16.
» Drissi, M., & Truchon, M. (2004). Maximum
likelihood approach to vote aggregation with
variable probabilities. Social Choice and Welfare,
23. 161-185.