# Brittany Vacchiano. » Voting procedure in which voters can vote for as many candidate as they wish » Each candidate approved of receives one vote » Single.

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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

» Ballot 1 » x Pepsi x Sprite Coke » Ballot 2 » x Pepsi Sprite x Coke » Ballot 3 » Pepsi x Sprite Coke » Ballot 4 » Pepsi x Sprite x Coke » Winner – Sprite (3 votes)

» 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…over Pepsi….over Coke…over Dr. Pepper Prefer Sprite… 68 58 Prefer Pepsi…328358 Prefer Coke…321758 Prefer Dr.Pepper… 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

» 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 1 st 2 nd 3 rd 4 th …over Sprite…over Pepsi….over Coke…over Dr. Pepper Prefer Sprite… 68 58 Prefer Pepsi…328358 Prefer Coke…321758 Prefer Dr.Pepper… 42 194194 141141

» 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 (1 st, 2 nd, 3 rd,…,etc)

» Not much information online besides on Wikipedia pages and this site ˃http://www.votefair.org/province.htmlhttp://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.

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