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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 A presentation by Merin Jose Kashyap Uppuluri Shruti Vangari
Implementation authenticate
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)
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
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}
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
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
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
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
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
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