1. Robust Winners and Winner Determination Policies under Candidate Uncertainty JOEL OREN, UNIVERSITY OF TORONTO JOINT WORK WITH CRAIG BOUTILIER, JÉRÔME LANG AND HÉCTOR PALACIOS. 1

2. Motivation – Winner Determination under Candidate Uncertainty A committee, with preferences over alternatives: Prospective projects. Goals. Costly determination of availabilities: Market research for determining the feasibility of a project: engineering estimates, surveys, focus groups, etc. “Best” alternative depends on available ones. 2 a b c 4 voters 3 voters 2 voters a b c b c a c a b Winner a ? ? ? c

3. Efficient Querying Policies for Winner Determination a b c 4 voters 3 voters 2 voters a b c b c a c a b Winner ? ? 3

4. The Formal Model a c C b b 3 voters 2 voters a c b c a c a b Y (available) U (unknown) 4

5. Querying & Decision Making a c C b b 3 voters 2 voters a c b c a c a b 0.5 0.70.4 ? a b ? 5

6. Computing a Robust Winner Y x 6

7. 7

8. The Query Policy Goal: design a policy for finding correct winner. Can be represented by a decision tree. Example for the vote profile (plurality): abcde, abcde, adbec, bcaed, bcead, cdeab, cbade, cdbea a b a wins c c wins a wins b b wins c a wins U a b c d a b b c 8

9. Winner Determination Policies as Trees a b a wins c c wins a wins b b wins c a wins 9

10. a b a wins c c wins a wins b b wins c a wins Recursively Finding Optimal Decision Trees 10

11. Myopically Constructing Decision Trees 11

12. Empirical Results 0.30.50.9 Method Plurality, DP4.13.42.7 Plurality, Myopic4.13.52.8 Borda, DP3.72.71.7 Borda, Myopic3.72.71.7 Average cost (# of queries) 12

13. Empirical Results 0.30.50.9 Method Plurality, DP4.13.42.7 Plurality, Myopic4.13.52.8 Borda, DP3.72.71.7 Borda, Myopic3.72.71.7 Average cost (# of queries) 13

14. Additional Results 14

15. Conclusions & Future Directions A framework for querying candidates under a probabilistic availability model. Connections to control of elections. Two algorithms for generating decision trees: DP, Myopic. Future directions: 1.Ways of pruning the decision trees (depend on the voting rules). 2.Sample-based methods for reducing training set size. 3.Deeper theoretical study of the query complexity. 15