Brittany Vacchiano Voting Methods Voting procedure in which

Brittany Vacchiano Voting Methods

» 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 Approval

» » » » » 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 Approval Example

» 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 Advantages of Approval

» 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 Kemeny-Young

» Basically…. ˃ Compares every possible sequence of preferential choices and then associates those sequences with a Kemeny Score ˃ Judges which candidate is preferred over others Kemeny-Young Cont’d

» Suppose you had a ballot with 4 candidates: Sprite, Coke, Pepsi and Dr. Pepper » Those preferences can be expressed in a popularity matrix Kemeny-Young Example

…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 1 st 2 nd 3 rd 4 th

Advantages of K-Y » 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 Disadvantages of K-Y » 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) Still confused about K-Y?

» 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. Sources