Practical Algorithms for Computing STV Chunheng Jiang, Sujoy Sikdar, Hejun Wang, Lirong Xia, Zhibing Zhao Single Transferable vote β’ π candidates β’ π β 1 rounds β’ At each round: ο Eliminate a candidate with lowest plurality score β’ Last remaining candidate is the winner Single Transferable Vote: Multi-round voting 2 1 3 β» β» β» β» β» β» β» plurality score 4 β» # votes 4 3 3 4 2 1 3 Winner! 4 6 How should ties be broken? β» β» β» β» 3 β» β» β» β» 4 3 1 2 4 3 Parallel-Universe-Tiebreaking (PUT) β STV [Conitzer et al. 2009] Ties are real β’ 9.2% of Preflib profiles have more than one STV co-winners. β’ On average 1.1 co-winners in Preflib data. β’ Greater transparency in voting rule implementation. β’ Random elimination of ties not the solution. β’ Computing all co-winners for STV, and other rules is NP-hard. [Conitzer et al. β09, Mattei et al. β14] When COMSOC starts β’ Complexity of Kemeny and Dodgsonβs rule [Bartholdi et al. β89] β’ Computing Kemeny winners: β’ 104 algorithms compared [Ali and Meila, β12] β’ STV has been overlooked. β’ Used in Australia, Canada, India, UK, US β’ Computing winners using Map Reduce [Csar et al. β17] β’ P-complete for STV using fixed tie breaking Main messages β’ Winner computation has been overlooked β’ STV, ranked pairs, Coombs, Baldwinβ¦ β’ Standard search algorithms work for small elections β’ New frontier: Machine learning for COMSOC Winner Determination Problem β’ Input: Preferences β’ Output: co-Winners β’ Criteria β’ Running time β’ Early discovery Online, high frequency voting Want: Anytime algorithms RPI Grand Marshall Week β’ The Grand Marshal (GM) is the highest elected student leader of RPI [wiki] β’ Annually since 1865 β’ 152 GMs β’ A full week of events β’ active campaigning β’ debates β’ primary/general elections Online voting becomes real β’ RPI switched to βonlineβ voting in 2015 β’ Google form β’ Long line β’ Only vote for top choice β’ We can build a better system β’ Rank the candidates? Yes β’ Complicated mechanism? No β’ Live results? Maybe β’ Cyber security? Disclaimer: I am not advocating for online voting Online Preference Reporting and Aggregation Live Results Include picture As an AI search/exploration problem β» β» β» β» 3 β» β» β» β» 4 3 1 2 4 3 Standard tricks β¦ β¦ β¦ β¦ Store in cache β¦ β’ Caching β’ Pruning β’ Reduction β’ Sampling X Prune Experimental Setup β’ Preflib data β’ Synthetic data β’ Profiles generated i.i.d. β’ Only use hard cases: at least one tie in the execution of STV Caching helps Depth First Exploration no caching with caching Peak in avg. # co-winners around n=20 Early discovery: # co-winners / # states proportion of co-winners pruning, caching plain π = 30, π = 30 Avg. co-winners: 7.4 Exploring more intelligently β’ Prioritize states that lead to a new winner β’ Priority function: β’ To aid early discovery β’ Reduce # nodes expanded β’ Idea for priority function β’ If we had better knowledge of co-winners in each state πΌ1 β # πππ€ π€ππππππ + πΌ2 β ππππ‘β + πΌ3 β #πππ€ π€ππππππ β ππππ‘β estimated by machine learning Machine Learning for STV β’ Features β’ Weighted Majority graph β’ Positional matrix β’ Borda, Copeland, Maximin score β’ LP relaxation β’ Learning algorithms tried: β’ Neural networks β’ Logistic β’ SVM β linear, rbf β’ Deep learning Machine learning for early discovery (π = 20, π = 20) Ground truth -48% NN -35% Summary and future work β’ Winner determination problem revisited β’ STV, ranked pairs, Coombs, Baldwinβ¦ β’ Standard AI algorithms may work β’ Machine learning can help β’ Deep learning β’ Reinforcement learning β’ New frontier: Machine learning for COMSOC β’ Other multi-round rules β’ Other classical COMSOC problems: Kemeny, multi-winner rules, manipulation, bribery, margin of victory, possible/necessary winners β’ Measuring and visualizing consensus: voting blocs β’ Designing new rules [Xia β13 AAMAS] Thank You Thank You
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