A New Way to Aggregate Preferences: Application to Eurovision Song Contests

Transcription

1 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion New Way to ggregate Preferences: pplication to urovision Song ontests Jérémy esson and éline Robardet Institut National des Sciences ppliquées de Lyon - France Friday September 7 J. esson,. Robardet New Way to ggregate Preferences

2 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Outline orda and ondorcet Ranked Voting Methods Principles Limits Graph representation Formalization xperimentation on the urovision Song ontests 4 onclusion J. esson,. Robardet New Way to ggregate Preferences

3 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Five individual preferences Principles Limits J. esson,. Robardet New Way to ggregate Preferences

4 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion orda count output Principles Limits J. esson,. Robardet New Way to ggregate Preferences

5 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion ondorcet majority rule Principles Limits Preferences J. esson,. Robardet New Way to ggregate Preferences

6 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Limit of orda count Principles Limits J. esson,. Robardet New Way to ggregate Preferences

7 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Limit of orda count Principles Limits J. esson,. Robardet New Way to ggregate Preferences

8 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Limit of orda count Principles Limits J. esson,. Robardet New Way to ggregate Preferences

9 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Limit of orda count Principles Limits J. esson,. Robardet New Way to ggregate Preferences

10 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Limit of ondorcet count Principles Limits Preferences 4? J. esson,. Robardet New Way to ggregate Preferences

11 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Limit of ondorcet count Principles Limits Preferences 4? J. esson,. Robardet New Way to ggregate Preferences

12 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Graph representation Formalization Graph representation of voters rankings Voter Voter Voter > > > > > > G m J. esson,. Robardet New Way to ggregate Preferences

13 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Graph representation Formalization Graph representation of voters rankings Voter Voter Voter > > > > > > G O J. esson,. Robardet New Way to ggregate Preferences

14 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Graph representation Formalization Problem formalization omputing an order G O such that: the number of votes of G m in conflict with G O is minimized the number of comparable candidates in G O is maximized J. esson,. Robardet New Way to ggregate Preferences

15 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Graph representation Formalization Problem formalization omputing an order G O such that: the number of votes of G m in conflict with G O is minimized the number of comparable candidates in G O is maximized efinition G O G m G O is a G (G O ) α minimizing (G O ) J. esson,. Robardet New Way to ggregate Preferences

16 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Graph representation Formalization omputational aspects ata mining framework takes advantages from an appropriate enumeration process that turns the constraints and objective function to be monotonic: If G G, (G ) (G ) If the enumeration starts from G m and consists in removing arcs, and are monotonic. The G constraint is ensured by construction: at least one arc by cycle is removed. J. esson,. Robardet New Way to ggregate Preferences

17 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion Graph representation Formalization omputational aspects lgorithm It proceeds in two phases: omputing all cycles of G m. Generating the partial orders by removing at least one arc of each cycle: If a current solution G is such that (G) < α, then this branch is ended. If (G) is greater or equal to an already extracted partial order, then this branch is ended. If G is a G, then G is the current best solution. 4 lse, another arc is chosen. J. esson,. Robardet New Way to ggregate Preferences

18 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion omputational aspects Graph representation Formalization numeration tree Min = ycles Min Min 4 Min Min Min Min Min J. esson,. Robardet New Way to ggregate Preferences 4 4 Min Min Min Min Min Min

19 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion urovision Song ontest result for the year 975 Israel Switzerland 7 5 ustria 0 0 Italy France 9 Monaco 4 4 elgium United_kingdom Yugoslavia Norway Spain Ireland 4 Germany 4 6 Netherlands Finland Greece Portugal Luxembourg J. esson,. Robardet New Way to ggregate Preferences

20 orda and ondorcet Ranked Voting Methods xperimentation on the urovision Song ontests onclusion onclusion The new method to aggregate vote preferences preserves most of pairwise preferences embedded in the ranking votes, uses a parameter to make the partial order converge towards a total order. minimizes a function which increases during the enumeration First results show coherent order with the orda method but better synthesizes votes. dditional experimentation, especially to further study the impact of parameter α, is on going. J. esson,. Robardet New Way to ggregate Preferences