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Voting Methods

Voting Methods. A presentation by Merin Jose Kashyap Uppuluri Shruti Vangari. Why Voting Methods?. Election statistics!. Implementation. authenticate. Admin Functionalities (1 to 3). User Functionalities (All). Admin Function after Voting. Condorcet Winner Method.

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Voting Methods

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  1. Voting Methods A presentation by Merin Jose Kashyap Uppuluri Shruti Vangari

  2. Why Voting Methods?

  3. Election statistics!

  4. Implementation authenticate

  5. Admin Functionalities (1 to 3)

  6. User Functionalities (All)

  7. Admin Function after Voting

  8. Condorcet Winner Method • A >M B just in case n1+n2+n5 > n3+n4+n6 (otherwise B ≥M A) • A >M C just in case n1+n2+n3 > n4+n5+n6 (otherwise C ≥M A) • B >M C just in case n1+n3+n4 > n2+n5+n6 (otherwise B ≥M C)

  9. Method I = Condorcet Winner • 19 rank Obama above Bush • 18 rank Obama above Palin • 11 rank Bush above Obama • 16 rank Bush above Palin • 12 rank Palin above Obama • 14 rank Palin above Bush 37 27 26

  10. Condorcet Winner Method

  11. Who is the winner? – Method I

  12. Borda Count Method BS(A)=(n−1) × #{i | i ranks A first} + (n−2) × #{i | i ranks A second} + … + 1 × #{i | i ranks A second to last} + 0 × #{i | i ranks A last}

  13. Who is the winner? – Method II 37 BS(Obama) = (3-1)*14 + (3-2)*9 + (3-3)*7 BS (Bush) = (3-1)*7 + (3-2)*9 + (3-3)*14 BS(Palin) = (3-1)*9 + (3-2)*8 + (3-3)*13 23 26

  14. Borda Count Method

  15. Who is the winner? – Method II

  16. Which method to adopt? == Confusion Matrix for Borda Count Method == a b c <-- classified as 11 1 0 | a = Yes 2 7 0 | b = No 1 0 0 | c = Tie == Confusion Matrix for Condorcet Winner Method == a b c <-- classified as 7 1 0 | a = Yes 2 5 1 | b = No 1 0 5 | c = Tie

  17. Decision Tree for Borda Count

  18. Decision Tree for Condorcet

  19. Comparison based on no. of Voters N=13 Winner as per Borda Candidate2 Candidate1 Candidate2 Candidate1 Candidate1 Candidate2 Candidate1 Candidate1 Tie Tie Winner as per Condorcet Discrepancy Discrepancy Discrepancy

  20. Comparison based on no. of Candidates N=4 Winner as per Borda Candidate1 Candidate4 Candidate4 Candidate4 Candidate1 Candidate1 Candidate3 Candidate4 Candidate3 Candidate1 Winner as per Condorcet Discrepancy Discrepancy

  21. Conclusion • Borda count does not satisfy the Condorcet winner criterion • The Borda Count Method - Rank sporting teams or academic institutions. • The Condorcet Method – Government Electoral System • When there is a tie in Condorcet winner, go for Borda Count

  22. Bibliography • Stanford encyclopedia of philosophy – Voting Methods • http://www.ctl.ua.edu/math103/voting/4popular.htm • http://theorem.ca/~mvcorks/code/voting_methods.html • http://www.nctm.org/resources/content.aspx?id=7934 • http://archives.math.utk.edu/software/msdos/discrete.math/voting/.html

  23. Questions?

  24. Thank You!!! 

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