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\n  \n 2023\n \n \n (1)\n \n \n
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\n \n\n \n \n Pritchard, G.; and Wilson, M. C.\n\n\n \n \n \n \n \n Asymptotic welfare performance of Boston assignment algorithms.\n \n \n \n \n\n\n \n\n\n\n Stochastic Systems, 13(2): 247–270. 2023.\n \n\n\n\n
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@Article{PrWi2022,\n  author  = {Pritchard, Geoffrey and Wilson, Mark C.},\n  journal = {Stochastic Systems},\n  abstract  = {We make a detailed analysis of three key algorithms (Serial Dictatorship\nand the naive and adaptive variants of the Boston algorithm) for the housing alloca-\ntion problem, under the assumption that agent preferences are chosen iid uniformly\nfrom linear orders on the items. We compute limiting distributions (with respect to\nsome common utility functions) as $n\\to\\infty$ of both the utilitarian welfare and the or-\nder bias. To do this, we compute limiting distributions of the outcomes for an arbitrary\nagent whose initial relative position in the tiebreak order is $\\theta\\in [0, 1]$, as a function of θ.\nWe expect that these fundamental results on the stochastic processes underlying these\nmechanisms will have wider applicability in future. Overall our results show that the\ndifferences in utilitarian welfare performance of the three algorithms are fairly small,\nbut the differences in order bias are much greater. Also, Naive Boston beats Adaptive\nBoston, which beats Serial Dictatorship, on both welfare and order bias.\n},\n  title   = {Asymptotic welfare performance of Boston assignment algorithms},\n  year    = {2023},\n  number  = {2},\n  pages   = {247--270},\n  volume  = {13},\n  doi     = {},\n  keywords = {social choice,assignment},\n  url_paper = {https://pubsonline.informs.org/doi/abs/10.1287/stsy.2022.0104},\n  url_slides = {https://www.dropbox.com/s/1jk218g16pp8qas/Mark_Wilson.pdf?dl=0},\n}\n\n
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\n We make a detailed analysis of three key algorithms (Serial Dictatorship and the naive and adaptive variants of the Boston algorithm) for the housing alloca- tion problem, under the assumption that agent preferences are chosen iid uniformly from linear orders on the items. We compute limiting distributions (with respect to some common utility functions) as $n\\to∞$ of both the utilitarian welfare and the or- der bias. To do this, we compute limiting distributions of the outcomes for an arbitrary agent whose initial relative position in the tiebreak order is $θ∈ [0, 1]$, as a function of θ. We expect that these fundamental results on the stochastic processes underlying these mechanisms will have wider applicability in future. Overall our results show that the differences in utilitarian welfare performance of the three algorithms are fairly small, but the differences in order bias are much greater. Also, Naive Boston beats Adaptive Boston, which beats Serial Dictatorship, on both welfare and order bias. \n
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\n  \n 2021\n \n \n (2)\n \n \n
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\n \n\n \n \n DiPilla, M.; and Wilson, M. C.\n\n\n \n \n \n \n \n New algorithms for school choice.\n \n \n \n \n\n\n \n\n\n\n ,8pp. 2021.\n \n\n\n\n
\n\n\n\n \n \n \"New paper\n  \n \n \n \"New slides\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 12 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@Article{DiWi2021,\n  author     = {DiPilla, Morgan and Wilson, Mark C.},\n  title      = {New algorithms for school choice},\n  pages      = {8pp},\n  journal    = {},\n  abstract   = {Algorithms for the school choice problem have been widely studied. A\nsmall number of algorithms for producing a solution dominate the\nliterature, for example Serial Dictatorship (SD) and the Deferred\nAcceptance (DA) algorithm. One main reason for the dominance of these\nalgorithms is their good (worst-case) axiomatic behaviour with respect\nto notions of Pareto efficiency, justified envy and manipulation.\nHowever if we shift the focus to fairness, social welfare, the\ninevitable tradeoffs between incompatible axioms, and average-case\nanalysis, it is far from clear that these algorithms are the last word.\n\nWe introduce a 6-parameter family of 40 inequivalent algorithms derived\nfrom DA, most of which have not appeared (to our knowledge) in the\nliterature before. The family includes SD and the naive and adaptive\nversions of the Boston mechanism, the most commonly used school choice\nalgorithm other than SD and DA. We investigate agent welfare, order bias\nand stability via numerical simulation, under the assumption of truthful\npreferences. We find that some of the new algorithms are worthy of much\nmore study. In particular, when we consider order bias, some of the new\nalgorithms clearly outperform the classic ones, while losing almost\nnothing in stability and utilitarian welfare.}, \n  keywords   = {social choice, assignment},\n  url_paper  = {https://markcwilson.site/Research/Outputs/DiWi2021.pdf},\n  url_slides = {},\n  year       = {2021},\n}\n\n\n
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\n Algorithms for the school choice problem have been widely studied. A small number of algorithms for producing a solution dominate the literature, for example Serial Dictatorship (SD) and the Deferred Acceptance (DA) algorithm. One main reason for the dominance of these algorithms is their good (worst-case) axiomatic behaviour with respect to notions of Pareto efficiency, justified envy and manipulation. However if we shift the focus to fairness, social welfare, the inevitable tradeoffs between incompatible axioms, and average-case analysis, it is far from clear that these algorithms are the last word. We introduce a 6-parameter family of 40 inequivalent algorithms derived from DA, most of which have not appeared (to our knowledge) in the literature before. The family includes SD and the naive and adaptive versions of the Boston mechanism, the most commonly used school choice algorithm other than SD and DA. We investigate agent welfare, order bias and stability via numerical simulation, under the assumption of truthful preferences. We find that some of the new algorithms are worthy of much more study. In particular, when we consider order bias, some of the new algorithms clearly outperform the classic ones, while losing almost nothing in stability and utilitarian welfare.\n
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\n \n\n \n \n Freeman, R.; Pritchard, G.; and Wilson, M. C.\n\n\n \n \n \n \n \n Order Symmetry: a new fairness criterion for assignment algorithms.\n \n \n \n \n\n\n \n\n\n\n ,44pp. 2021.\n \n\n\n\n
\n\n\n\n \n \n \"Order paper\n  \n \n \n \"Order slides\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 14 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@Article{FrPW2021,\n  author  = {Freeman, Rupert and Pritchard, Geoffrey and Wilson, Mark C.},\n  journal = {},\n  abstract  = {We introduce a new fairness criterion, order symmetry, for\nassignment mechanisms that match $n$ objects to $n$ agents with ordinal\npreferences over the objects. An assignment mechanism is order symmetric\nwith respect to some probability measure over preference profiles if\nevery agent is equally likely to receive their favorite object, every\nagent is equally likely to receive their second favorite, and so on.\nWhen associated with a sufficiently symmetric probability measure, order\nsymmetry is a relaxation of anonymity that, crucially, can be satisfied\nby discrete assignment mechanisms. Furthermore, it can be achieved\nwithout sacrificing other desirable axiomatic properties satisfied by\nexisting mechanisms. In particular, we show that it can be achieved in\nconjunction with strategyproofness and ex post efficiency via the top\ntrading cycles mechanism (but not serial dictatorship). We additionally\ndesign a novel mechanism that is both order symmetric and ordinally\nefficient. The practical utility of order symmetry is substantiated by\nsimulations on Impartial Culture and Mallows-distributed preferences for \nfour common assignment mechanisms.},\n  title   = {Order Symmetry: a new fairness criterion for assignment algorithms},\n  year    = {2021},\n  number  = {},\n  pages   = {44pp},\n  volume  = {},\n  doi     = {},\n  keywords = {social choice,assignment},\n  url_paper = {https://osf.io/preprints/socarxiv/xt37c/},\n  url_slides = {https://www.youtube.com/watch?v=qdyEspDXa90&list=PLKz9ISqcKAGCKccL_XdTCfo7WBRGMS21i&index=5},\n}\n\n
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\n We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match $n$ objects to $n$ agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.\n
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\n  \n 2019\n \n \n (3)\n \n \n
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\n \n\n \n \n Wilson, M. C.\n\n\n \n \n \n \n \n Inputs, Algorithms, Quality Measures: More Realistic Simulation in Social Choice.\n \n \n \n \n\n\n \n\n\n\n In The Future of Economic Design, pages 165-171. Springer, Cham, 2019.\n \n\n\n\n
\n\n\n\n \n \n \"Inputs, paper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 4 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@incollection{wilson2019inputs,\n  title={Inputs, Algorithms, Quality Measures: More Realistic Simulation in Social Choice},\n  author={Wilson, Mark C.},\n  booktitle={The Future of Economic Design},\n  pages={165-171},\n  year={2019},\n  publisher={Springer, Cham},\n  keywords={social choice, simulation},\n  url_Paper={https://markcwilson.site/Research/Outputs/FED.pdf},\n  abstract={Much of my research deals with trying to evaluate the performance of\nsocial choice \\emph{algorithms} via simulations, which requires\nappropriate \\emph{inputs} and \\emph{quality measures}. All three areas\noffer substantial scope for improvement in the coming years. For\nconcreteness and because of my own limited experience, I focus on the\nallocation of indivisible goods and on voting, although many of the\nideas are more broadly applicable.}\n}\n\n
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\n Much of my research deals with trying to evaluate the performance of social choice \\emphalgorithms via simulations, which requires appropriate \\emphinputs and \\emphquality measures. All three areas offer substantial scope for improvement in the coming years. For concreteness and because of my own limited experience, I focus on the allocation of indivisible goods and on voting, although many of the ideas are more broadly applicable.\n
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\n \n\n \n \n Ianovski, E.; and Wilson, M. C.\n\n\n \n \n \n \n \n Manipulability of consular election rules.\n \n \n \n \n\n\n \n\n\n\n Social Choice and Welfare, 52(2): 363-393. 2019.\n \n\n\n\n
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@article{ianovski2019manipulability,\n  title={Manipulability of consular election rules},\n  author={Ianovski, Egor and Wilson, Mark C.},\n  journal={Social Choice and Welfare},\n  volume={52},\n  number={2},\n  pages={363-393},\n  year={2019},\n  publisher={Springer Berlin Heidelberg},\n  keywords={social choice, voting},\n  url_Paper={https://arxiv.org/abs/1611.07102},\n  url_Link={https://link.springer.com/article/10.1007/s00355-018-1152-2},\n  abstract={The Gibbard-Satterthwaite theorem is a cornerstone of social choice\ntheory, stating that an onto social choice function cannot be both\nstrategy-proof and non-dictatorial if the number of alternatives is at\nleast three. The Duggan-Schwartz theorem proves an analogue in the case\nof set-valued elections: if the function is onto with respect to\nsingletons, and can be manipulated by neither an optimist nor a\npessimist, it must have a weak dictator. However, the assumption that\nthe function is onto with respect to singletons makes the\nDuggan-Schwartz theorem inapplicable to elections which necessarily\nselect a committee with multiple members. In this paper we make a start\non this problem by considering elections which elect a committee of size\ntwo (such as the consulship of ancient Rome). We establish that if such\na \\emph{consular election rule} cannot be expressed as the union of two\ndisjoint social choice functions, then strategy-proofness implies the\nexistence of a dictator. Although we suspect that a similar result holds\nfor larger sized committees, there appear to be many obstacles to\nproving it, which we discuss in detail.}\n}\n\n
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\n The Gibbard-Satterthwaite theorem is a cornerstone of social choice theory, stating that an onto social choice function cannot be both strategy-proof and non-dictatorial if the number of alternatives is at least three. The Duggan-Schwartz theorem proves an analogue in the case of set-valued elections: if the function is onto with respect to singletons, and can be manipulated by neither an optimist nor a pessimist, it must have a weak dictator. However, the assumption that the function is onto with respect to singletons makes the Duggan-Schwartz theorem inapplicable to elections which necessarily select a committee with multiple members. In this paper we make a start on this problem by considering elections which elect a committee of size two (such as the consulship of ancient Rome). We establish that if such a \\emphconsular election rule cannot be expressed as the union of two disjoint social choice functions, then strategy-proofness implies the existence of a dictator. Although we suspect that a similar result holds for larger sized committees, there appear to be many obstacles to proving it, which we discuss in detail.\n
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\n \n\n \n \n Hadjibeyli, B.; and Wilson, M. C.\n\n\n \n \n \n \n \n Distance rationalization of anonymous and homogeneous voting rules.\n \n \n \n \n\n\n \n\n\n\n Social Choice and Welfare, 52(3): 559-583. 2019.\n \n\n\n\n
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@article{hadjibeyli2019distance,\n  title={Distance rationalization of anonymous and homogeneous voting rules},\n  author={Hadjibeyli, Benjamin and Wilson, Mark C.},\n  journal={Social Choice and Welfare},\n  volume={52},\n  number={3},\n  pages={559-583},\n  year={2019},\n  publisher={Springer Berlin Heidelberg},\n  keywords={social choice, voting},\n  url_Paper={https://link.springer.com/content/pdf/10.1007/s00355-018-1156-y.pdf},\n  abstract={The concept of distance rationalizability of voting rules has been\nexplored in recent years by several authors. Most previous work has\ndealt with a definition in terms of preference profiles. However, most\nvoting rules in common use are anonymous and homogeneous. In this case\nthere is a much more succinct representation (using the voting simplex)\nof the inputs to the rule. This representation has been widely used in\nthe voting literature, but rarely in the context of distance\nrationalizability. Recently, the present authors showed, as a special\ncase of general results on quotient spaces, exactly how to connect\ndistance rationalizability on profiles for anonymous and homogeneous\nrules to geometry in the simplex. In this article we develop the\nconnection for the important special case of votewise distances,\nrecently introduced and studied by Elkind, Faliszewski and Slinko in\nseveral papers. This yields a direct interpretation in terms of\nwell-developed mathematical topics not seen before in the voting\nliterature, namely Kantorovich (also called Wasserstein) distances and\nthe geometry of Minkowski spaces. As an application of this approach, we\nprove some positive and some negative results about the decisiveness of\ndistance rationalizable anonymous and homogeneous rules. The positive\nresults connect with the recent theory of hyperplane rules, while the\nnegative ones deal with distances that are not metrics, controversial\nnotions of consensus, and the fact that the $\\ell^1$-norm is not\nstrictly convex. We expect that the above novel geometric interpretation\nwill aid the analysis of rules defined by votewise distances, and the\ndiscovery of new rules with desirable properties.}\n}\n\n
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\n The concept of distance rationalizability of voting rules has been explored in recent years by several authors. Most previous work has dealt with a definition in terms of preference profiles. However, most voting rules in common use are anonymous and homogeneous. In this case there is a much more succinct representation (using the voting simplex) of the inputs to the rule. This representation has been widely used in the voting literature, but rarely in the context of distance rationalizability. Recently, the present authors showed, as a special case of general results on quotient spaces, exactly how to connect distance rationalizability on profiles for anonymous and homogeneous rules to geometry in the simplex. In this article we develop the connection for the important special case of votewise distances, recently introduced and studied by Elkind, Faliszewski and Slinko in several papers. This yields a direct interpretation in terms of well-developed mathematical topics not seen before in the voting literature, namely Kantorovich (also called Wasserstein) distances and the geometry of Minkowski spaces. As an application of this approach, we prove some positive and some negative results about the decisiveness of distance rationalizable anonymous and homogeneous rules. The positive results connect with the recent theory of hyperplane rules, while the negative ones deal with distances that are not metrics, controversial notions of consensus, and the fact that the $\\ell^1$-norm is not strictly convex. We expect that the above novel geometric interpretation will aid the analysis of rules defined by votewise distances, and the discovery of new rules with desirable properties.\n
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\n  \n 2017\n \n \n (1)\n \n \n
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\n \n\n \n \n Lo, J.; and Wilson, M. C.\n\n\n \n \n \n \n \n New algorithms for matching problems.\n \n \n \n \n\n\n \n\n\n\n arXiv preprint arXiv:1703.04225. 2017.\n \n\n\n\n
\n\n\n\n \n \n \"New paper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 10 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@article{lo2017new,\n  title={New algorithms for matching problems},\n  author={Lo, Jacky and Wilson, Mark C.},\n  journal={arXiv preprint arXiv:1703.04225},\n  year={2017},\n  keywords={social choice, allocation, algorithms},\n  url_Paper={http://arxiv.org/abs/1703.04225},\n  abstract={The standard two-sided and one-sided matching problems, and the closely\nrelated school choice problem, have been widely studied from an\naxiomatic viewpoint. A small number of algorithms dominate the\nliterature. For two-sided matching, the Gale-Shapley algorithm; for\none-sided matching, (random) Serial Dictatorship and Probabilistic\nSerial rule; for school choice, Gale-Shapley and the Boston mechanisms.\nThe main reason for the dominance of these algorithms is their good\n(worst-case) axiomatic behaviour with respect to notions of efficiency\nand strategyproofness. However if we shift the focus to fairness, social\nwelfare, tradeoffs between incompatible axioms, and average-case\nanalysis, it is far from clear that these algorithms are optimal. We\ninvestigate new algorithms several of which have not appeared (to our\nknowledge) in the literature before. We give a unified presentation in\nwhich algorithms for 2-sided matching yield 1-sided matching algorithms\nin a systematic way. In addition to axiomatic properties, we investigate\nagent welfare using both theoretical and computational approaches. We\nfind that some of the new algorithms are worthy of consideration for\ncertain applications. In particular, when considering welfare under\ntruthful preferences, some of the new algorithms outperform the classic\nones.}\n}\n\n
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\n The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the Gale-Shapley algorithm; for one-sided matching, (random) Serial Dictatorship and Probabilistic Serial rule; for school choice, Gale-Shapley and the Boston mechanisms. The main reason for the dominance of these algorithms is their good (worst-case) axiomatic behaviour with respect to notions of efficiency and strategyproofness. However if we shift the focus to fairness, social welfare, tradeoffs between incompatible axioms, and average-case analysis, it is far from clear that these algorithms are optimal. We investigate new algorithms several of which have not appeared (to our knowledge) in the literature before. We give a unified presentation in which algorithms for 2-sided matching yield 1-sided matching algorithms in a systematic way. In addition to axiomatic properties, we investigate agent welfare using both theoretical and computational approaches. We find that some of the new algorithms are worthy of consideration for certain applications. In particular, when considering welfare under truthful preferences, some of the new algorithms outperform the classic ones.\n
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\n  \n 2016\n \n \n (1)\n \n \n
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\n \n\n \n \n Hadjibeyli, B.; and Wilson, M. C.\n\n\n \n \n \n \n \n Distance rationalization of social rules.\n \n \n \n \n\n\n \n\n\n\n arXiv preprint arXiv:1610.01902. 2016.\n \n\n\n\n
\n\n\n\n \n \n \"Distance paper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@article{hadjibeyli2016distance,\n  title={Distance rationalization of social rules},\n  author={Hadjibeyli, Benjamin and Wilson, Mark C.},\n  journal={arXiv preprint arXiv:1610.01902},\n  year={2016},\n  keywords={social choice, voting},\n  url_Paper={http://arxiv.org/abs/1610.01902},\n  abstract={The concept of distance rationalizability of social choice rules has\nbeen explored in recent years by several authors. We deal here with\nseveral foundational questions, and unify, correct, and generalize\nprevious work. For example, we study a new question involving uniqueness\nof representation in the distance rationalizability framework, and\npresent a counterexample. For rules satisfying various axiomatic\nproperties such as anonymity, neutrality and homogeneity, the standard\nprofile representation of input can be compressed substantially. We\nexplain in detail using quotient constructions how distance\nrationalizability is interpreted in this situation. This enables us to\nconnect the theory of distance rationalizability with geometric concepts\nsuch as Earth Mover distance and optimal transportation. We give\nimproved sufficient conditions for distance rationalizable rules to\nsatisfy anonymity, neutrality, homogeneity, consistency and continuity.}\n}\n\n\n
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\n The concept of distance rationalizability of social choice rules has been explored in recent years by several authors. We deal here with several foundational questions, and unify, correct, and generalize previous work. For example, we study a new question involving uniqueness of representation in the distance rationalizability framework, and present a counterexample. For rules satisfying various axiomatic properties such as anonymity, neutrality and homogeneity, the standard profile representation of input can be compressed substantially. We explain in detail using quotient constructions how distance rationalizability is interpreted in this situation. This enables us to connect the theory of distance rationalizability with geometric concepts such as Earth Mover distance and optimal transportation. We give improved sufficient conditions for distance rationalizable rules to satisfy anonymity, neutrality, homogeneity, consistency and continuity.\n
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\n  \n 2014\n \n \n (1)\n \n \n
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\n \n\n \n \n Emery, M.; and Wilson, M. C.\n\n\n \n \n \n \n \n Iterated Regret Minimization in Voting Games.\n \n \n \n \n\n\n \n\n\n\n In COMSOC 2014, Pittsburgh, June 23-25, 2014, pages 12pp, 2014. \n \n\n\n\n
\n\n\n\n \n \n \"IteratedPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@inproceedings{EmWi2014,\n  author    = {Miranda Emery and\n               Mark C. Wilson},\n  title     = {Iterated Regret Minimization in Voting Games},\n  booktitle = {COMSOC 2014, Pittsburgh, June 23-25, 2014},\n  pages     = {12pp},\n  year      = {2014},\n  keywords={social choice, voting, game theory},\n url   = {http://www.cs.cmu.edu/~arielpro/comsoc-14/papers/EmeryWilson2014.pdf},\n  abstract={The game-theoretic solution concept Iterated Regret Minimization (IRM)\nwas introduced recently by Halpern and Pass. We give the first\napplication of IRM to simultaneous voting games. We study positional\nscoring rules in detail and give theoretical results demonstrating the\nbias of IRM toward sincere voting. We present comprehensive simulation\nresults of the effect on social welfare of IRM compared to both sincere\nand optimal voting. The results fit into a broader research theme of the\nwelfare consequences of strategic voting.}\n}\n\n\n
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\n The game-theoretic solution concept Iterated Regret Minimization (IRM) was introduced recently by Halpern and Pass. We give the first application of IRM to simultaneous voting games. We study positional scoring rules in detail and give theoretical results demonstrating the bias of IRM toward sincere voting. We present comprehensive simulation results of the effect on social welfare of IRM compared to both sincere and optimal voting. The results fit into a broader research theme of the welfare consequences of strategic voting.\n
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\n  \n 2013\n \n \n (1)\n \n \n
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\n \n\n \n \n Pritchard, G.; Reyhani, R.; and Wilson, M. C.\n\n\n \n \n \n \n \n Power measures derived from the sequential query process.\n \n \n \n \n\n\n \n\n\n\n Mathematical Social Sciences, 65(3): 174-180. 2013.\n \n\n\n\n
\n\n\n\n \n \n \"Power paper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@article{pritchard2013power,\n  title={Power measures derived from the sequential query process},\n  author={Pritchard, Geoffrey and Reyhani, Reyhaneh and Wilson, Mark C.},\n  journal={Mathematical Social Sciences},\n  volume={65},\n  number={3},\n  pages={174-180},\n  year={2013},\n  publisher={North-Holland},\n  keywords={social choice, cooperative games},\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0165489612001096?casa_token=4x3gmLGuiPIAAAAA:9crEC8R6F3yj1ut1S482WqW3UPlxOvAyL6-gzldpHWnpp7qYgbMYugOhgwxefm-mB6TFBETE_Q},\n  abstract={We study a basic sequential model for the discovery of winning\ncoalitions in a simple game, well known from its use in defining the\nShapley-Shubik power index. We derive in a uniform way a family of\nmeasures of collective and individual power in simple games, and show\nthat, as for the Shapley-Shubik index, they extend naturally to measures\nfor TU-games. In particular, the individual measures include all\nweighted semivalues. We single out the simplest measure in our family\nfor more investigation, as it is new to the literature as far as we\nknow. Although it is very different from the Shapley value, it is\nclosely related in several ways, and is the natural analogue of the\nShapley value under a nonstandard, but natural, definition of simple\ngame. We illustrate this new measure by calculating its values on some\nstandard examples.}\n}\n\n
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\n We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual power in simple games, and show that, as for the Shapley-Shubik index, they extend naturally to measures for TU-games. In particular, the individual measures include all weighted semivalues. We single out the simplest measure in our family for more investigation, as it is new to the literature as far as we know. Although it is very different from the Shapley value, it is closely related in several ways, and is the natural analogue of the Shapley value under a nonstandard, but natural, definition of simple game. We illustrate this new measure by calculating its values on some standard examples.\n
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\n  \n 2012\n \n \n (2)\n \n \n
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\n \n\n \n \n Reyhani, R.; and Wilson, M. C.\n\n\n \n \n \n \n \n Best reply dynamics for scoring rules.\n \n \n \n \n\n\n \n\n\n\n In Proceedings of the 20th European Conference on Artificial Intelligence, pages 672-677, 2012. IOS Press\n \n\n\n\n
\n\n\n\n \n \n \"Best paper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@inproceedings{reyhani2012best,\n  title={Best reply dynamics for scoring rules},\n  author={Reyhani, Reyhaneh and Wilson, Mark C.},\n  booktitle={Proceedings of the 20th European Conference on Artificial Intelligence},\n  pages={672-677},\n  year={2012},\n  organization={IOS Press},\n  keywords={social choice, voting},\n  url_Paper={https://ebooks.iospress.nl/doi/10.3233/978-1-61499-098-7-672},\n  abstract={We consider best-reply dynamics for voting games in which all players\nare strategic and no coalitions are formed. We study the class of\nscoring rules, show convergence of a suitably restricted version for the\nplurality and veto rules, and failure of convergence for other rules\nincluding $k$-approval and Borda. In particular, for 3 candidates\nconvergence fails for all rules other than plurality and veto. We give a\nunified proof for the convergence of these two rules. Our proofs in the\ncase of plurality improve the known bound on convergence, and the other\nconvergence results are new.}\n}\n\n
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\n We consider best-reply dynamics for voting games in which all players are strategic and no coalitions are formed. We study the class of scoring rules, show convergence of a suitably restricted version for the plurality and veto rules, and failure of convergence for other rules including $k$-approval and Borda. In particular, for 3 candidates convergence fails for all rules other than plurality and veto. We give a unified proof for the convergence of these two rules. Our proofs in the case of plurality improve the known bound on convergence, and the other convergence results are new.\n
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\n \n\n \n \n Reyhani, R.; Wilson, M. C.; and Khazaei, J.\n\n\n \n \n \n \n \n Coordination via Polling in Plurality Voting Games under Inertia.\n \n \n \n \n\n\n \n\n\n\n In COMSOC 2012, Krakow, September 11-13, 2012, pages 359-370, 2012. \n \n\n\n\n
\n\n\n\n \n \n \"CoordinationPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@inproceedings{RWK2012,\n  author    = {Reyhaneh Reyhani and\n               Mark C. Wilson and Javad Khazaei},\n  title     = {Coordination via Polling in Plurality Voting Games\nunder Inertia},\n  booktitle = {COMSOC 2012, Krakow, September 11-13, 2012},\n  pages     = {359-370},\n  year      = {2012},\n  keywords={social choice, voting, game theory},\n  url       = {http://home.agh.edu.pl/~faliszew/COMSOC-2012/proceedings/paper_52.pdf},\n  abstract={We discuss a general model for strategic voting in plurality elections\nunder uncertainty, using the concept of inertia to deal with information\nand risk attitude of agents. The model is flexible enough to be used for\nhuman societies and artificially designed multiagent systems. Under some\nfurther assumptions we show that a sequence of pre-election polls can\nhelp agents to coordinate on an equilibrium outcome. This mechanism is\nclosely related to the STV voting rule and gives insight into the\npolitical science principle known as Duverger's law.}\n}\n\n\n
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\n We discuss a general model for strategic voting in plurality elections under uncertainty, using the concept of inertia to deal with information and risk attitude of agents. The model is flexible enough to be used for human societies and artificially designed multiagent systems. Under some further assumptions we show that a sequence of pre-election polls can help agents to coordinate on an equilibrium outcome. This mechanism is closely related to the STV voting rule and gives insight into the political science principle known as Duverger's law.\n
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\n  \n 2011\n \n \n (1)\n \n \n
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\n \n\n \n \n Ianovski, E.; Yu, L.; Elkind, E.; and Wilson, M. C.\n\n\n \n \n \n \n \n The Complexity of Safe Manipulation under Scoring Rules.\n \n \n \n \n\n\n \n\n\n\n In IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16-22, 2011, pages 246-251, 2011. \n \n\n\n\n
\n\n\n\n \n \n \"ThePaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@inproceedings{IYEW2011,\n  author    = {Egor Ianovski and\n               Lan Yu and\n               Edith Elkind and\n               Mark C. Wilson},\n  title     = {The Complexity of Safe Manipulation under Scoring Rules},\n  booktitle = {{IJCAI} 2011, Proceedings of the 22nd International Joint Conference\n               on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16-22,\n               2011},\n  pages     = {246-251},\n  year      = {2011},\n keywords={social choice, voting, algorithms},\n url       = {http://ijcai.org/papers11/Papers/IJCAI11-052.pdf},\n abstract={Slinko and White have recently introduced a new model of coalitional\nmanipulation of voting rules under limited communication, which they\ncall safe strategic voting". The computational aspects of this model\nwere first studied by Hazon and Elkind, who provide polynomial-time\nalgorithms for finding a safe strategic vote under $k$-approval and the\nBucklin rule. In this paper, we answer an open question of Hazon and\nElkind by presenting a polynomial-time algorithm for finding a safe\nstrategic vote under the Borda rule. Our results for Borda generalize to\nseveral interesting classes of scoring rules.}\n }\n\n
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\n Slinko and White have recently introduced a new model of coalitional manipulation of voting rules under limited communication, which they call safe strategic voting\". The computational aspects of this model were first studied by Hazon and Elkind, who provide polynomial-time algorithms for finding a safe strategic vote under $k$-approval and the Bucklin rule. In this paper, we answer an open question of Hazon and Elkind by presenting a polynomial-time algorithm for finding a safe strategic vote under the Borda rule. Our results for Borda generalize to several interesting classes of scoring rules.\n
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\n  \n 2010\n \n \n (1)\n \n \n
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\n \n\n \n \n Reyhani, R.; and Wilson, M. C.\n\n\n \n \n \n \n \n The Probability of Safe Manipulation.\n \n \n \n \n\n\n \n\n\n\n In COMSOC 2010, Düsseldorf, September 13-16, 2010, pages 423-430, 2010. \n \n\n\n\n
\n\n\n\n \n \n \"ThePaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@inproceedings{ReWi2010,\n  author    = {Reyhaneh Reyhani and\n               Mark C. Wilson},\n  title     = {The Probability of Safe Manipulation},\n  booktitle = {COMSOC 2010, D\\"{u}sseldorf, September 13-16, 2010},\n  pages     = {423-430},\n  year      = {2010},\n  keywords={social choice, voting},\n  url       = {http://ccc.cs.uni-duesseldorf.de/COMSOC-2010/papers/comsoc2010.pdf},\n  abstract={The concept of safe manipulation has recently been introduced by Slinko\nand White. We show how to compute the asymptotic probability that a safe\nmanipulation exists for a given scoring rule under the uniform\ndistribution on voting situations (the so- called Impartial Anonymous\nCulture). The technique used is computation of volumes of convex\npolytopes. We present explicit numerical results in the 3-candidate\ncase.}\n}\n\n\n
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\n The concept of safe manipulation has recently been introduced by Slinko and White. We show how to compute the asymptotic probability that a safe manipulation exists for a given scoring rule under the uniform distribution on voting situations (the so- called Impartial Anonymous Culture). The technique used is computation of volumes of convex polytopes. We present explicit numerical results in the 3-candidate case.\n
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\n  \n 2009\n \n \n (1)\n \n \n
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\n \n\n \n \n Pritchard, G.; and Wilson, M. C.\n\n\n \n \n \n \n \n Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour.\n \n \n \n \n\n\n \n\n\n\n Mathematical Social Sciences, 58(1): 35-57. 2009.\n \n\n\n\n
\n\n\n\n \n \n \"Asymptotics paper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@article{pritchard2009asymptotics,\n  title={Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour},\n  author={Pritchard, Geoffrey and Wilson, Mark C.},\n  journal={Mathematical Social Sciences},\n  volume={58},\n  number={1},\n  pages={35-57},\n  year={2009},\n  publisher={North-Holland},\n  keywords={social choice, voting, computation},\n  url_Paper={https://www.sciencedirect.com/science/article/abs/pii/S0165489609000225},\n  abstract={We consider the problem of manipulation of elections using positional\nvoting rules under Impartial Culture voter behaviour. We consider both\nthe logical possibility of coalitional manipulation, and the number of\nvoters that must be recruited to form a manipulating coalition. It is\nshown that the manipulation problem may be well approximated by a very\nsimple linear program in two variables. This permits a comparative\nanalysis of the asymptotic (large-population) manipulability of the\nvarious rules. It is seen that the manipulation resistance of positional\nrules with 5 or 6 (or more) candidates is quite different from the more\ncommonly analyzed 3- and 4-candidate cases.}\n}\n\n
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\n We consider the problem of manipulation of elections using positional voting rules under Impartial Culture voter behaviour. We consider both the logical possibility of coalitional manipulation, and the number of voters that must be recruited to form a manipulating coalition. It is shown that the manipulation problem may be well approximated by a very simple linear program in two variables. This permits a comparative analysis of the asymptotic (large-population) manipulability of the various rules. It is seen that the manipulation resistance of positional rules with 5 or 6 (or more) candidates is quite different from the more commonly analyzed 3- and 4-candidate cases.\n
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\n  \n 2007\n \n \n (2)\n \n \n
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\n \n\n \n \n Wilson, M. C.; and Pritchard, G.\n\n\n \n \n \n \n \n Probability calculations under the IAC hypothesis.\n \n \n \n \n\n\n \n\n\n\n Mathematical Social Sciences, 54(3): 244-256. 2007.\n \n\n\n\n
\n\n\n\n \n \n \"Probability paper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n\n\n\n
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@article{wilson2007probability,\n  title={Probability calculations under the IAC hypothesis},\n  author={Wilson, Mark C. and Pritchard, Geoffrey},\n  journal={Mathematical Social Sciences},\n  volume={54},\n  number={3},\n  pages={244-256},\n  year={2007},\n  publisher={North-Holland},\n  keywords={social choice, voting, computation},\n  url_Paper={https://www.sciencedirect.com/science/article/abs/pii/S0165489607000443},\n  abstract={We show how powerful algorithms recently developed for counting lattice\npoints and computing volumes of convex polyhedra can be used to compute\nprobabilities of a wide variety of events of interest in social choice\ntheory. Several illustrative examples are given.}\n}\n\n
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\n We show how powerful algorithms recently developed for counting lattice points and computing volumes of convex polyhedra can be used to compute probabilities of a wide variety of events of interest in social choice theory. Several illustrative examples are given.\n
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\n \n\n \n \n Pritchard, G.; and Wilson, M. C.\n\n\n \n \n \n \n \n Exact results on manipulability of positional voting rules.\n \n \n \n \n\n\n \n\n\n\n Social Choice and Welfare, 29(3): 487-513. 2007.\n \n\n\n\n
\n\n\n\n \n \n \"Exact paper\n  \n \n \n \"Exact link\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@article{pritchard2007exact,\n  title={Exact results on manipulability of positional voting rules},\n  author={Pritchard, Geoffrey and Wilson, Mark C.},\n  journal={Social Choice and Welfare},\n  volume={29},\n  number={3},\n  pages={487-513},\n  year={2007},\n  publisher={Springer-Verlag},\n  keywords={social choice, voting},\n  url_Paper={https://link.springer.com/content/pdf/10.1007/s00355-007-0216-5.pdf},\n  url_Link={https://link.springer.com/article/10.1007/s00355-007-0216-5},\n  abstract={We consider 3-candidate elections under a general scoring rule and\nderive precise conditions for a given voting situation to be\nstrategically manipulable by a given coalition of voters. We present an\nalgorithm that makes use of these conditions to compute the minimum size\n$M$ of a manipulating coalition for a given voting situation. The\nalgorithm works for any voter preference model - here we present\nnumerical results for IC and for IAC, for a selection of scoring rules,\nand for numbers of voters up to 150. A full description of the\ndistribution of $M$ is obtained, generalizing all previous work on the\ntopic. The results obtained show interesting phenomena and suggest\nseveral conjectures. In particular we see that rules {``} between\nplurality and Borda{"} behave very differently from those {``} between\nBorda and antiplurality{"}.}\n}\n\n
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\n We consider 3-candidate elections under a general scoring rule and derive precise conditions for a given voting situation to be strategically manipulable by a given coalition of voters. We present an algorithm that makes use of these conditions to compute the minimum size $M$ of a manipulating coalition for a given voting situation. The algorithm works for any voter preference model - here we present numerical results for IC and for IAC, for a selection of scoring rules, and for numbers of voters up to 150. A full description of the distribution of $M$ is obtained, generalizing all previous work on the topic. The results obtained show interesting phenomena and suggest several conjectures. In particular we see that rules `` between plurality and Borda\" behave very differently from those `` between Borda and antiplurality\".\n
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