But, how?? Explaining all possible positional, pairwise voting paradoxes & prop. Don Saari Institute for Math Behavioral Sciences University of California, Irvine CA 92697-5100 3 A>B>C 4 A>C>B 6 C>B>A 2 B>C>A 2 B>A>C Vote for one (1, 0, 0): A Vote for two (1, 1, 0): B Borda (2, 1, 0): C Paired comparisons? B>A, A>C, C>B, a cycle How would you explain, create, this example? Approval voting? Cumulative voting? Any of the 13 possible rankings is a sincere outcome Standard approach since Borda, Condorcet, Arrow: “Proof” by example Put forth “desirable properties that a voting rule “must” satisfy Example: “Will voting rule always elect Condorcet winner?” What have we accomplished? y impressive results (and difficult), but … er above challenges? Why paradoxes? Arrow? sensus -- even among those in voting theory? My approach was influenced by: n -- paradoxes, which are properties, n=7, 10 50 Nurmi -- Nothing goes right For a price ….. Need new approach Rather than “select rule and find supporting properties” Science approach is to find all properties and identify appropriate rules.
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But, how?? Explaining all possible positional, pairwise voting paradoxes & prop. Don Saari Institute for Math Behavioral Sciences University of California,
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But, how??
Explaining all possible positional, pairwise voting paradoxes & prop.
Don SaariInstitute for Math Behavioral Sciences
University of California, Irvine CA 92697-5100
3 A>B>C4 A>C>B6 C>B>A2 B>C>A2 B>A>C
Vote for one (1, 0, 0):A
Vote for two (1, 1, 0):BBorda (2, 1, 0):C
Paired comparisons?
B>A, A>C, C>B, a cycle
How would you explain, create, this example?
Approval voting? Cumulative voting?Any of the 13 possible rankings is a
sincere outcomeStandard approach since Borda, Condorcet,
Arrow:“Proof” by example
Put forth “desirable properties that a voting rule “must” satisfy