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- Maximal_lotteries abstract "Maximal lotteries refers to a probabilistic voting system first considered by Germain Kreweras in 1965 and independently rediscovered and studied in more detail in 1984 by Peter C. Fishburn. The method uses preferential ballots and returns so-called maximal lotteries, i.e., probability distributions over the alternatives that are weakly preferred to any other probability distribution. Maximal lotteries satisfy the Condorcet criterion, the Smith criterion, reversal symmetry, polynomial runtime, and probabilistic versions of reinforcement, participation, and independence of clones.Maximal lotteries are equivalent to mixed maximin strategies (or Nash equilibria) of the symmetric zero-sum game given by the pairwise majority margins. As such, they can be computed using linear programming. In 2015, maximal lotteries were axiomatically characterized by showing that only maximal lotteries satisfy probabilisitic versions of population-consistency (a weakening of reinforcement), agenda-consistency, and composition-consistency (a strengthening of independence of clones).It was also shown that maximal lotteries satisfy a strong notion of Pareto efficiency and a weak notion of strategyproofness. In contrast to random dictatorship, maximal lotteries do not satisfy the standard notion of strategyproofness. Also, maximal lotteries are not monotonic in probabilities, i.e., it is possible that the probability of an alternative decreases when this alternative is ranked up. However, the probability of the alternative will remain positive.Maximal lotteries or variants thereof have been rediscovered multiple times by economists, mathematicians, political scientists, philosophers, and computer scientists.In particular, the support of maximal lotteries, which is known as the essential set or the bipartisan set, has been studied in detail.".
- Maximal_lotteries wikiPageExternalLink pnyx.dss.in.tum.de.
- Maximal_lotteries wikiPageID "46339461".
- Maximal_lotteries wikiPageLength "5737".
- Maximal_lotteries wikiPageOutDegree "26".
- Maximal_lotteries wikiPageRevisionID "680062646".
- Maximal_lotteries wikiPageWikiLink Category:Articles_created_via_the_Article_Wizard.
- Maximal_lotteries wikiPageWikiLink Category:Preferential_electoral_systems.
- Maximal_lotteries wikiPageWikiLink Condorcet_criterion.
- Maximal_lotteries wikiPageWikiLink Condorcet_winner.
- Maximal_lotteries wikiPageWikiLink Germain_Kreweras.
- Maximal_lotteries wikiPageWikiLink Independence_of_clones.
- Maximal_lotteries wikiPageWikiLink Independence_of_clones_criterion.
- Maximal_lotteries wikiPageWikiLink Linear_programming.
- Maximal_lotteries wikiPageWikiLink Minimax.
- Maximal_lotteries wikiPageWikiLink Minimax_strategy.
- Maximal_lotteries wikiPageWikiLink Monotonicity_criterion.
- Maximal_lotteries wikiPageWikiLink Nash_equilibria.
- Maximal_lotteries wikiPageWikiLink Nash_equilibrium.
- Maximal_lotteries wikiPageWikiLink Pareto_efficiency.
- Maximal_lotteries wikiPageWikiLink Participation.
- Maximal_lotteries wikiPageWikiLink Peter_C._Fishburn.
- Maximal_lotteries wikiPageWikiLink Polynomial_time.
- Maximal_lotteries wikiPageWikiLink Ranked_voting_system.
- Maximal_lotteries wikiPageWikiLink Reinforcement.
- Maximal_lotteries wikiPageWikiLink Reversal_symmetry.
- Maximal_lotteries wikiPageWikiLink Skew-symmetric_matrix.
- Maximal_lotteries wikiPageWikiLink Smith_criterion.
- Maximal_lotteries wikiPageWikiLink Strategyproof.
- Maximal_lotteries wikiPageWikiLink Support_(mathematics).
- Maximal_lotteries wikiPageWikiLink Time_complexity.
- Maximal_lotteries wikiPageWikiLink Voting_system.
- Maximal_lotteries wikiPageWikiLink Zero-sum_game.
- Maximal_lotteries wikiPageWikiLinkText "Maximal lotteries".
- Maximal_lotteries hasPhotoCollection Maximal_lotteries.
- Maximal_lotteries wikiPageUsesTemplate Template:Reflist.
- Maximal_lotteries subject Category:Articles_created_via_the_Article_Wizard.
- Maximal_lotteries subject Category:Preferential_electoral_systems.
- Maximal_lotteries comment "Maximal lotteries refers to a probabilistic voting system first considered by Germain Kreweras in 1965 and independently rediscovered and studied in more detail in 1984 by Peter C. Fishburn. The method uses preferential ballots and returns so-called maximal lotteries, i.e., probability distributions over the alternatives that are weakly preferred to any other probability distribution.".
- Maximal_lotteries label "Maximal lotteries".
- Maximal_lotteries wasDerivedFrom Maximal_lotteries?oldid=680062646.
- Maximal_lotteries isPrimaryTopicOf Maximal_lotteries.