Voting and Math

1. Voting and Math Kelsey, Ashleigh, Alex, Nick, Justin MAT 142 Final Project

2. Table of Contents • Vocab • Types of Voting • Borda Count • Pairwise Comparison • Proxy Voting • Delegated Voting

3. Vocab Voter Preference Tables: • These types of tables list different rankings of the candidates along with the number of voters who chose each specific ranking. They are often used to depict the voting patterns in a ranked election. Notice that the preference schedule compactly summarizes the votes in the election by grouping identical preference ballots together along with a count of how many voters cast each identical preference ballot. • From the perspective of the instant runoff method, which is when voters rank the candidates in order of preference and their ballots are counted as one vote for their first choice candidate, we can conclude that the winner would be [w] because you can add the number of ballots cast for first choice W, and see that there are 23 people who ranked was first choice, whereas the other would be 19 and 18. • With the Borda Count Method, which is a single-winner election method in which voters rank candidates in order of preference, B would be the winner. You can find that out by doing the math, the total points would be W=112, P=123, and B=125. Ex Number of Ballots Cast 9 14 15 4 2 16 1st Choice w w p p b b 2nd Choice p b b w w p 3rd Choice b p w b p w

4. Vocab Cont. The Majority Criterion • This is when a single-winner voting system criterion is used to compare systems. The criterion states that if one candidate is preferred by a majority (more than 50%) of voters, then that candidate must win. This is similar to the instant runoff method. • If candidate X receives a majority of the votes, then candidate X should be declared the winner. The Head-to-Head Criterion • If candidate X is favored when compared head-to-head (individually) with each of the other candidates, then candidate X should be declared the winner. • You’re competing head-to-head with candidate A and you win; then you go head-to-head with candidate B and also win. The fair and logical conclusion would be that you beat both so you should be the overall winner.

5. Vocab Cont. The Monotonicity Criterion • If candidate X wins an election, and in a subsequent election, the only changes are changes in favor of candidate X, then candidate X should be declared the winner. Arrow’s Impossibility Theorem • It is mathematically impossible to create any system of voting, involving three or more candidates that satisfies all four fairness criteria. This theorem states that, when voters have three or more distinct alternatives options, no voting system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting a specific set of criteria.

6. Borda Count • Each voter ranks all of the candidates. If there are k candidates each candidate receives k points for each first-choice vote, (k-1) points for each second-choice vote, (k-2) points for each third-choice vote, and so on. The candidate with the most total points is declared the winner. • BordaCount is currently used for the election of two ethnic minority members of the National Assembly of Slovenia, and, in modified forms, to select presidential election candidates in Kiribati and to elect members of the Parliament of Nauru. It is also used throughout the world by various private organizations and competitions. • The Borda count is classified as a positional voting system because each rank on the ballot is worth a certain number of points. Other positional methods include first-past-the-post(plurality) voting. • Referenceshttp://wiki.electorama.com/wiki/Borda_count Wikipedia

7. Borda Count Cont. There is a formula that you can use it takes awhile but this is the main formula for it: 4( )+3( )+2( )+1( )= ? You do this for each person in the race. Paul:1140 Rita:1500 Sarah:1200 Tim:1160

8. Pairwise Comparison • Wikipedia: generally refers to any process of comparing entities in pairs to judge which of each pair is preferred, or has a greater amount of some quantitative property Book definition: Each voter ranks all of the candidates. For each possible pairing of candidates, the candidate with the most votes receives 1 point; if there is a tie, each candidate receives ½ point. The candidate who receives the most points is declared the winner. • Simple Definition: The most random method of voting, that actually makes sense...

9. Pairwise Comparison Cont. • Most commonly used for the Analytical Hierarchy Process, “a structured technique for helping people deal with complex decisions.

10. Proxy Voting • Proxy voting is a procedure that allows one person to authorize someone else to vote on his behalf. It is most commonly used by lawmakers in the legislative process, in elections, and in corporate shareholder meetings. Proxy voting is recognized under a number of popular rules of order, including Riddick's Rules of Parliamentary Procedure™, but is prohibited under others, such as The Standard Code of Parliamentary Procedure™. Such rules are normally adopted by an organization at its inception. One receive a proxy ballot in the mail along with an informational booklet called a proxy statement describing the issues to be voted on. They return a form by mail agreeing to have their vote cast by proxy. Issues commonly decided by proxy vote include electing directors to the board, approving a merger or acquisition, and approving a stock compensation plan. • In elected government, proxy voting is often employed in the committee process, to allow legislators to vote on bills and resolutions in absentia. Though specific rules often vary among governments and committees, generally, a legislator who expects to miss a committee vote must submit his proxy vote to the chairman or committee staff, in writing, prior to the vote taking place. A proxy vote does not count towards a committee's quorum, so there must be enough members present to establish a quorum before any proxy votes on a given question can be counted.

11. Delegated Voting • In delegated voting, the proxy is transitive and the transfer is recursive. • Put simply, the vote can be further delegated to the proxy's proxy, and so on. • This process is also known as transitive voting, delegable proxy, and asset voting, Liquid Democracy and Augmented Democracy.

12. Delegated Voting Cont. • An early proposal of delegate voting was that of Lewis Carroll in 1884. • More recent proposals are by Mikael Nordfors, Bryan Ford, James Green-Armytageand Michael Allan. • Delegate voting is used by the Swedish local political party Demoex. Demoex won their first seat in the city council of Vallentuna, Sweden, in 2002. The first years of activity in the party have been evaluated by Mitthögskolan • University in a paper by Karin Ottesen in 2003 • In Demoex, a voter can also vote directly, even if she has delegated her vote to a proxy; the direct vote overrules the proxy vote. It is also possible to change the proxy at any time.