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A formal proof of the Incompatibility of SD-Efficiency and SD-Strategy-Proofness

Manuel Eberl
2019
relatively weak kind of efficiency) and something known as strong SD-Strategy-Proofness is the rule of Random Dictatorship.  ...  and SMT solvers to prove a conjecture by Aziz et al. that no anonymous and neutral randomised voting rule (known as Social Decision Scheme) can fulfil the notions of both SD-Efficiency and SD-Strategy-Proofness  ...  [BBS16; BBG16] , I have written a fully machine-checked proof of the incompatibility of SD-Strategy-Proofness and SD-Efficiency using the Isabelle/HOL theorem prover and, based on this, a 'human-readable  ... 
doi:10.14459/2016md1485242 fatcat:cokomapajbgj3imaqa62smc6dq

Impossibilities for probabilistic assignment

Haris Aziz, Yoichi Kasajima
2017 Social Choice and Welfare  
We show that equal treatment of equals, efficiency, and strategy-proofness are incompatible. Moreover, anonymity, neutrality, efficiency, and weak strategy-proofness are incompatible.  ...  If we strengthen weak strategy-proofness to weak group strategy-proofness, then when agents have single-unit demands, anonymity, neutrality, efficiency, and weak group strategy-proofness become incompatible  ...  Acknowledgements We thank the editor, an associate editor, and an anonymous referee for their suggestions and comments.  ... 
doi:10.1007/s00355-017-1059-3 fatcat:ezwa6n3agjcpfkbdwbm677zdl4

Probabilistic assignment: an extension approach

Wonki Jo Cho
2018 Social Choice and Welfare  
Then we study their behavior, as well as that of the random priority rule, in terms of efficiency, no-envy, and strategy-proofness.  ...  The notion of strategy-proofness based on the sd-extension, which we call sd-strategy-proofness, says that for each agent, the lottery he obtains by reporting his preferences truthfully should stochastically  ...  them in terms of efficiency, no-envy, and strategy-proofness.  ... 
doi:10.1007/s00355-018-1110-z fatcat:ai52sfrf2rhjjkuzbdbkw3eqn4

Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving [article]

Florian Brandl, Felix Brandt, Manuel Eberl, Christian Geist
2017 arXiv   pre-print
Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggregation mechanism should not be manipulable.  ...  This settles an open problem and strengthens a number of existing theorems, including statements that were shown within the special domain of assignment.  ...  The Incompatibility of SD-efficiency and SD-strategy-proofness. Archive of Formal Proofs (2016). Table 1.  ... 
arXiv:1604.05692v4 fatcat:ixsi7gcfenexniafwl74qth5wa

On Popular Random Assignments [chapter]

Haris Aziz, Felix Brandt, Paul Stursberg
2013 Lecture Notes in Computer Science  
In this paper, we study the compatibility of popularity with other properties that have been considered in the literature on random assignments, namely efficiency, equal treatment of equals, envy-freeness  ...  One of the most fundamental and ubiquitous problems in microeconomics and operations research is how to assign objects to agents based on their individual preferences.  ...  of Aerospace Research and Development through grant AOARD-124056, and the Deutsche Forschungsgemeinschaft under grants BR 2312/7-1 and BR 2312/7-2.  ... 
doi:10.1007/978-3-642-41392-6_16 fatcat:hnw3utxaj5hblaa6s6dt7zsabi

On the tradeoff between efficiency and strategyproofness

Haris Aziz, Florian Brandl, Felix Brandt, Markus Brill
2018 Games and Economic Behavior  
We show that efficiency and strategyproofness are incompatible to some extent when preferences are defined using stochastic dominance (SD) and therefore introduce a natural weakening of SD based on Savage's  ...  Our main result is that strict maximal lotteries-an appealing class of social decision schemes due to Kreweras and Fishburn-satisfy SD-efficiency and STstrategyproofness.  ...  This material is based upon work supported by the Deutsche Forschungsgemeinschaft under grants BR 2312/7-1 and BR 2312/10-1.  ... 
doi:10.1016/j.geb.2018.03.005 fatcat:zixukcuwyfftfiekv2w3qdtpvq

Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving

Florian Brandl, Felix Brandt, Manuel Eberl, Christian Geist
2018 Journal of the ACM  
Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggregation mechanism should not be manipulable.  ...  This settles a conjecture by Aziz et al. [2013b] and strengthens a number of existing theorems, including statements that were shown within the special domain of assignment.  ...  The Result Our main result shows that efficiency and strategyproofness are incompatible with basic fairness properties.  ... 
doi:10.1145/3125642 fatcat:psgz7zepnnaslal6bnuhpwqkmq

Assignment Maximization

Mustafa Oguz Afacan, Inncio BB, Bertan Turhan
2017 Social Science Research Network  
Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated -in terms of number of assignments -in equilibrium.  ...  Those show that the difference in number of matched agents between the proposed mechanisms and others in the literature is large and significant.  ...  We show that maximizing the number of assignments is incompatible not only with fairness, but also with strategy-proofness (Proposition 1), and that no mechanism is maximal in equilibrium (Proposition  ... 
doi:10.2139/ssrn.3036416 fatcat:o4jakr4sc5gozbre46bntduw7e

Randomized Scheduling Mechanisms: Assigning Course Seats in a Fair and Efficient Way

Martin Bichler, Soeren Merting
2021 Production and operations management  
This is an interesting and frequent application of distributed scheduling, where payments cannot be used to implement the efficient allocation.  ...  The results of our empirical work shed light on the advantages that randomized scheduling mechanisms have over FCFS in the field, but also on the challenges.  ...  Acknowledgments We are grateful for valuable feedback from Nguyen Thanh and Rakesh Vohra. Financial support is acknowledged from the German Research Foundation (DFG) [Grant BI-1057 9/1]. Notes  ... 
doi:10.1111/poms.13449 fatcat:e3ma4kwktbcjrhdthdf3kmjk4e

Computational Social Choice: The First Ten Years and Beyond [chapter]

Haris Aziz, Felix Brandt, Edith Elkind, Piotr Skowron
2019 Lecture Notes in Computer Science  
Computational social choice is a research area at the intersection of computer science, mathematics, and economics that is concerned with aggregation of preferences of multiple agents.  ...  social choice, random assignment, and computer-aided theorem proving.  ...  The second result shows the incompatibility of SD-efficiency and weak SD-strategyproofness and strengthens a number of previous impossibilities [32] .  ... 
doi:10.1007/978-3-319-91908-9_4 fatcat:u5nezniajbe53lwvb6u3e3rfwy

Assigning Course Schedules: About Preference Elicitation, Fairness, and Truthfulness [article]

Martin Bichler, Sören Merting, Aykut Uzunoglu
2018 arXiv   pre-print
Bundled Probabilistic Serial (BPS) is a randomized mechanism satisfying ordinal efficiency, envy-freeness, and weak strategy-proofness.  ...  the average rank, the profile, and the popularity of the assignments.  ...  Gibbard (1977) showed that random dictatorship is the only anonymous and symmetric (in the sense of equal treatment of equals), strongly SD-strategy-proof, and ex post efficient assignment rule when preferences  ... 
arXiv:1812.02630v2 fatcat:2whh4hhyfvhzjgkkyoimq67bse

Strategy-proof allocation with outside option [article]

Jun Zhang
2021 arXiv   pre-print
The second result provides a sufficient condition for two strategy-proof mechanisms to be equivalent when the number of possible allocations is finite.  ...  The first result proves that, for individually rational and strategy-proof mechanisms, pinning down every agent's probability of choosing his outside option is equivalent to pinning down a mechanism.  ...  So under NI and Richness, not-strongly-bidominated mechanisms are on the efficiency frontier of IR and strategy-proof mechanisms. that p ′ ≻ sd i p and p ′ [A i ] ≤ p[A i ]. Suppose NI holds.  ... 
arXiv:2009.05311v2 fatcat:4nyul2jol5f4hl44sgw7j2lcyu

Fair solutions to the random assignment problem

Christian Basteck
2018 Journal of Mathematical Economics  
As an alternative, we present a solution, based on Walrasian equilibria, that is sd-efficient, in the weak sd-core from equal division and satisfies the strong sd-equal-division-lower-bound.  ...  Hylland and Zeckhauser's Walrasian Equilibria from Equal Incomes) are incompatible with the strong sd-equal-division-lower-bound.  ...  Bogomolnaia and Moulin [2001] show that no assignment mechanism satisfies sd-efficiency, equal treatment of equals and strategy proofness.  ... 
doi:10.1016/j.jmateco.2018.02.006 fatcat:qhmncoaflrh5pdhi7nozcayzpq

The Probabilistic Serial and Random Priority Mechanisms with Minimum Quotas [article]

Marek Bojko
2020 arXiv   pre-print
We show the mechanisms satisfy the same criteria as their classical counterparts: PS is ordinally efficient, envy-free and weakly strategy-proof; RP is strategy-proof, weakly envy-free but not ordinally  ...  The Probabilistic Serial (PS) and Random Priority (RP) mechanisms are generalised based on the same intuitive idea: Allow agents to consume their most preferred available object until the total mass of  ...  The RP mechanism is strategy-proof, treats equals equally; it is ex-post efficient but may incur unambiguous efficiency loss ex-ante, and so is not ordinally efficient.  ... 
arXiv:2012.11028v1 fatcat:h3g24ffpqjcydnslrrkhfqm2yy

Taxon Selection under Split Diversity

Bui Quang Minh, Steffen Klaere, Arndt von Haeseler
2009 Systematic Biology  
We illustrate our method using a case study of game birds ("Galliformes") and discuss the different choices of taxa based on our approach and PD.  ...  In this study, we provide an efficient dynamic programming algorithm for maximizing PD when splits in the trees or network form a circular split system.  ...  Gregory Ewing, Alethea Rea, Allen Rodrigo, and 3 anonymous referees provided helpful comments on the manuscript.  ... 
doi:10.1093/sysbio/syp058 pmid:20525611 fatcat:7r6wtxbqx5fl5e5krwqdqam35u
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