Skip to main content
SpringerLink
Log in

Structured Preferences: A Literature Survey

  • SURVEY ARTICLES
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

A survey of papers on practically significant restrictions on the preference profile of a collective is carried out, including single-peaked preferences, group-separable preferences, preferences with the single-crossing property, and Euclidean preferences and their extensions. Both ordinal and dichotomous preferences are considered. For structured preferences, we present characterization in terms of forbidden subprofiles and the probability of the appearance of a profile with a given property. For group-separable preferences, we describe an algorithm for constructing a hierarchical tree. Structured preferences leading to a unique stable matching in the marriage problem are considered separately.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. Aleskerov, F.T., Arrovian Aggregation Models, Dordrecht: Kluwer Acad. Publ., 1999.

    Book  MATH  Google Scholar 

  2. Arrow, K.J., Social Choice and Individual Values, New York: Wiley, 1951.

    MATH  Google Scholar 

  3. Gibbard, A., Manipulation of voting schemes: a general result, Econometrica, 1973, vol. 41, no. 4, pp. 587–601.

    Article  MathSciNet  MATH  Google Scholar 

  4. Satterthwaite, M.A., Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions, J. Econ. Theory, 1975, vol. 10, no. 2, pp. 187–217.

    Article  MathSciNet  MATH  Google Scholar 

  5. Dasgupta, P. and Maskin, E., On the robustness of majority rule, J. Eur. Econ. Assoc., 2008, vol. 6, no. 5, pp. 949–973.

    Article  Google Scholar 

  6. Xefteris, D., How robust is majority voting as a social choice rule?, Oxford Econ. Pap., 2014, vol. 66, no. 4, pp. 1006–1018.

  7. Aşan, G. and Sanver, M.R., Another characterization of the majority rule, Econ. Lett., 2002, vol. 75, no. 3, pp. 409–413.

  8. Campbell, D.E. and Kelly, J.S., A simple characterization of majority rule, Econ. Theory, 2000, vol. 15, no. 3, pp. 689–700.

    Article  MathSciNet  MATH  Google Scholar 

  9. Dasgupta, P. and Maskin, E., Strategy-proofness, independence of irrelevant alternatives, and majority rule, Am. Econ. Rev. Insights, 2020, vol. 2, no. 4, pp. 459–474.

    Article  Google Scholar 

  10. May, K.O., A set of independent necessary and sufficient conditions for simple majority decisions, Econometrica, 1952, vol. 20, no. 4, pp. 680–684.

    Article  MathSciNet  MATH  Google Scholar 

  11. Woeginger, G.J., A new characterization of the majority rule, Econ. Lett., 2003, vol. 81, no. 1, pp. 89–94.

    Article  MathSciNet  MATH  Google Scholar 

  12. Gehrlein, W.V., Condorcet’s Paradox, Heidelberg: Springer, 2006.

    MATH  Google Scholar 

  13. Xefteris, D., A necessary and sufficient single-profile condition for transitivity of the majority rule relation, Econ. Lett., 2012, vol. 116, no. 3, pp. 516–518.

    Article  MathSciNet  MATH  Google Scholar 

  14. Aleskerov, F., Categories of Arrovian voting schemes, in Handbook of Social Choice and Welfare, Arrow, K., Sen, A., and Suzumura, K., Eds., Amsterdam: Elsevier Science, 2002, pp. 95–129.

  15. Dittrich, T., Eine vollständige Klassifkation von Condorcet Domains für kleine Alternativenmengen, Dissertation, Karlsruher Inst. Technol. (KIT) 2018.

  16. Li, G., Puppe, C., and Slinko, A., Towards a classification of maximal peak-pit Condorcet domains, Math. Soc. Sci., 2021, vol. 113, pp. 191–202.

    Article  MathSciNet  MATH  Google Scholar 

  17. Galambos, Á. and Reiner, V., Acyclic sets of linear orders via the Bruhat orders, Soc. Choice Welfare, 2008. vol. 30, pp. 245–264.

  18. Danilov, V.I. and Koshevoy, G.A., Maximal Condorcet domains, Order, 2013, vol. 30, no. 1, pp. 181–194.

    Article  MathSciNet  MATH  Google Scholar 

  19. Danilov, V.I., Karzanov, A.V., and Koshevoy, G.A., Condorcet domains of tiling type, Discrete Appl. Math., 2012, vol. 160, pp. 933–940.

    Article  MathSciNet  MATH  Google Scholar 

  20. Karpov, A. and Slinko, A., Constructing large peak-pit Condorcet domains, Theory Decis., 2022.

  21. Polyakov, N.L. and Shamolin, M.V., Reduction theorems in collective choice theory, Itogi Nauki Tekh. Ser. Sovrem. Mat. Prilozh. Tematicheskii Obz., 2020, vol. 174, pp. 46–51.

    Google Scholar 

  22. Danilov, V.I., Karzanov, A.V., and Koshevoy, G.A., Majority rule on rhombus tilings and Condorcet super-domains, Discrete Appl. Math., 2021, vol. 292, pp. 85–96.

    Article  MathSciNet  MATH  Google Scholar 

  23. Inada, K., A note on the simple majority decision rule, Econometrica, 1964, vol. 32, no. 4, pp. 525–531.

    Article  MathSciNet  Google Scholar 

  24. Inada, K., The simple majority decision rule, Econometrica, 1969, vol. 37, no. 3, pp. 490–506.

    Article  MATH  Google Scholar 

  25. Sen, A.K., A possibility theorem on majority decisions, Econometrica, 1966, vol. 34, no. 2, pp. 491–499.

    Article  MATH  Google Scholar 

  26. Mirrlees, J., An exploration in the theory of optimal income taxation, Rev. Econ. Stud., 1971, vol. 38, pp. 175–208.

    Article  MATH  Google Scholar 

  27. Roberts, K., Voting over income tax schedules, J. Public Econ., 1977, vol. 8, no. 3, pp. 329–340.

    Article  Google Scholar 

  28. Elkind, E., Lackner, M., and Peters, D., Structured preferences, in Trends in Computational Social Choice, Endriss, U., Ed., 2017, pp. 187–207.

  29. Karpov, A., On the number of group-separable preference profiles, Group Decis. Negot., 2019, vol. 28, no. 3, pp. 501–517.

    Article  Google Scholar 

  30. Chen, J. and Finnendahl, U.P., On the number of single-peaked narcissistic or single-crossing narcissistic preference profiles, Discrete Math., 2018, vol. 341, pp. 1225–1236.

    Article  MathSciNet  MATH  Google Scholar 

  31. Durand, S., Finding sharper distinctions for conditions of transitivity of the majority method, Discrete Appl Math., 2003, vol. 131, pp. 577–595.

    Article  MathSciNet  MATH  Google Scholar 

  32. Karpov, A., The likelihood of single-peaked preferences under classical and new probability distribution assumptions, Soc. Choice Welfare, 2020, vol. 55, pp. 629–644.

    Article  MathSciNet  MATH  Google Scholar 

  33. Lackner, M.L. and Lackner, M., On the likelihood of single-peaked preferences, Soc. Choice Welfare, 2017, vol. 48, no. 4, pp. 717–745.

    Article  MathSciNet  MATH  Google Scholar 

  34. Kim, K.H. and Roush, F.W., Special domains and nonmanipulability, Math. Soc. Sci., 1980, vol. 1, pp. 85–92.

    Article  MathSciNet  MATH  Google Scholar 

  35. Sato, S., Circular domains, Rev. Econ. Des., 2010, vol. 14, pp. 331–342.

    MathSciNet  MATH  Google Scholar 

  36. Achuthankutty, G. and Roy, S., Dictatorship on top-circular domains, Theory Decis., 2018, vol. 86, pp. 479–493.

    Article  MathSciNet  MATH  Google Scholar 

  37. Peters, D. and Lackner, M., Preferences single-peaked on a circle, J. Artif. Intell. Res., 2020, vol. 68, pp. 463–502.

    Article  MathSciNet  MATH  Google Scholar 

  38. Ozdemir, U. and Sanver, M.R., Dictatorial domains in preference aggregation, Soc. Choice Welfare, 2007, vol. 28, pp. 61–76.

    Article  MathSciNet  MATH  Google Scholar 

  39. Monjardet, B., Acyclic domains of linear orders: a survey, in The mathematics of preference, choice and order, Essays in honor of Peter C. Fishburn, Brams, S., Gehrlein, W.V., and Roberts, F.S., Eds., Heidelberg: Springer, 2009, pp. 139–160.

  40. Fishburn, P.C., Acyclic sets of linear orders, Soc. Choice Welfare, 1996, vol. 14, pp. 113–124.

    Article  MathSciNet  MATH  Google Scholar 

  41. Danilov, V.I., Karzanov, A.V., and Koshevoi, G.A., Condorcet domains and rhombus tilings, Ekon. Mat. Metody, 2010, vol. 46, no. 4, pp. 55–68.

    Google Scholar 

  42. Labbe, J.-P. and Lange, C., Cambrian acyclic domains: counting c-singletons, Order, 2020, vol. 37, pp. 571–603.

    Article  MathSciNet  MATH  Google Scholar 

  43. Kreweras, G., Les décisions collectives, Math. Sci. Hum., 1963, vol. 2, pp. 25–35.

    Google Scholar 

  44. Bartholdi, J. and Trick, M., Stable matching with preferences derived from a psychological model, Oper. Res. Lett., 1986, vol. 5, no. 4, pp. 165–169.

    Article  MathSciNet  MATH  Google Scholar 

  45. Escoffier, B., Lang, J., and Ozturk, M., Single-peaked consistency and its complexity, in Proc. 18th Eur. Conf. Artif. Intell. (ECAI 2008), Ghallab, M., Spyropoulos, C.D., Fakotakis, N., and Avouris, N., Eds., 2008, pp. 366–370.

  46. Black, D., On the rationale of group decision-making, J. Polit. Econ., 1948, vol. 56, pp. 23–34.

    Article  Google Scholar 

  47. Brandt, F., Brill, M., Hemaspaandra, E., and Hemaspaandra, L.A., Bypassing combinatorial protections: polynomial-time algorithms for single-peaked electorates, J. Artif. Intell. Res., 2015, vol. 53, pp. 439–496.

    Article  MathSciNet  MATH  Google Scholar 

  48. Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., and Rothe, J., The shield that never was: societies with single-peaked preferences are more open to manipulation and control, Inf. Comput., 2011, vol. 209, no. 2, pp. 89–107.

    Article  MathSciNet  MATH  Google Scholar 

  49. Veselova, Yu.A., Computational complexity of manipulation: a survey, Autom. Remote Control, 2016, vol. 77, no. 3, pp. 369–388.

    Article  MathSciNet  MATH  Google Scholar 

  50. Puppe, C., The single-peaked domain revisited: a simple global characterization, J. Econ. Theory, 2018, vol. 176, pp. 55–80.

    Article  MathSciNet  MATH  Google Scholar 

  51. Slinko, A., Condorcet domains satisfying Arrow’s single-peakedness, J. Math. Econ., 2019, vol. 84, pp. 166–175.

    Article  MathSciNet  MATH  Google Scholar 

  52. Liversidge, G., Counting Condorcet domains, 2020.

  53. Weisstein, E.W., Permutation pattern. From MathWorld–A Wolfram web resource, 2020. .

  54. Ballester, M.A. and Haeringer, G., A characterization of the single-peaked domain, Soc. Choice Welfare, 2011, vol. 36, pp. 305–322.

    Article  MathSciNet  MATH  Google Scholar 

  55. Demange, G., Single-peaked orders on a tree, Math. Soc. Sci., 1982, vol. 3, no. 4, pp. 389–396.

    Article  MathSciNet  MATH  Google Scholar 

  56. Nehring, K. and Puppe, C., The structure of strategy-proof social choice—part I: General characterization and possibility results on median spaces, J. Econ. Theory, 2007, vol. 135, no. 1, pp. 269–305.

    Article  MathSciNet  MATH  Google Scholar 

  57. Escoffier, B., Spanjaard, O., and Tydrichová, M., Recognizing single-peaked preferences on an arbitrary graph: complexity and algorithms, in Proc. 13th Int. Symp. (SAGT 2020), Harks, T. and Klimm, M., Eds. (Augsburg, 2020), pp. 291–306.

  58. Trick, M.A., Recognizing single-peaked preferences on a tree, Math. Soc. Sci., 1989, vol. 17, no. 3, pp. 329–334.

    Article  MathSciNet  MATH  Google Scholar 

  59. Sliwinski, J. and Elkind, E., Preferences single-peaked on a tree: sampling and tree recognition, in Proc. Twenty-Eighth Int. Joint Conf. Artif. Intell. (IJCAI-19), Kraus, S., Ed., pp. 580–586.

  60. Peters, D. and Elkind, E., Preferences single-peaked on nice trees, in Proc. 30th AAAI Conf. Artif. Intell. (AAAI 2016), 2016, pp. 594–600.

  61. Peters, D., Yu, L., Chan, H., and Elkind, E., Preferences single-peaked on a tree: multiwinner elections and structural results, J. Artif. Intell. Res., 2022, vol. 73, pp. 231–276.

    Article  MathSciNet  MATH  Google Scholar 

  62. Duchi, E., A code for square permutations and convex permutominoes, Discrete Math. Theor. Comput. Sci., 2019. vol. 21, no. 2, #2.

  63. Erdelyi, G., Lackner, M., and Pfandler, A., Computational aspects of nearly single-peaked electorates, J. Artif. Intell. Res., 2017, vol. 58, pp. 297–337.

    Article  MathSciNet  MATH  Google Scholar 

  64. Sui, X., Nienaber, A., and Boutilier, C., Multidimensional single-peaked consistency and its approximations, in Proc. Twenty-Third Int. Joint Conf. Artif. Intell. (IJCAI-13), Rossi, F., Ed., pp. 367–374, Beijing, 2013, pp. 375–382.

  65. Faliszewski, P., Hemaspaandra, E., and Hemaspaandra, L.A., The complexity of manipulative attacks in nearly single-peaked electorates, Artif. Intell., 2014, vol. 207, pp. 69–99.

    Article  MathSciNet  MATH  Google Scholar 

  66. Menon, V. and Larson, K., Reinstating combinatorial protections for manipulation and bribery in single-peaked and nearly single-peaked electorates, Proc. 30th AAAI Conf. Artif. Intell. (AAAI. 2016), 2016, pp. 565–571.

  67. Yang, Y., Manipulation with bounded single-peaked width: a parameterized study, Proc. 13th Int. Joint Conf. Auton. Agents Multiagent Syst., Bordini, R.H., Elkind, E., Weiss, G., and Yolum, P., Eds., 2015, pp. 77–85.

  68. Yang, Y., Complexity of controlling nearly single-peaked elections revisited, Proc. 17th Int. Conf. Auton. Agents Multiagent Syst. (AAMAS 2018), Dastani, M., Sukthankar, G., Andre, E., and Koenig, S., Eds., 2018, pp. 2139–2141.

  69. Yang, Y., On the complexity of constructive control under nearly single-peaked preferences, Proc. 24th Eur. Conf. Artif. Intell. (ECAI 2020) (Santiago de Compostela, 2020).

  70. Yang, Y. and Guo, J., Controlling elections with bounded single-peaked width, Proc. 13th Int. Conf. Auton. Agents Multiagent Syst. (AAMAS 2014), Lomuscio, A., Scerri, P., Bazzan, A., and Huhns, M., Eds., (Paris, 2014), pp. 629–636.

  71. Yang, Y. and Guo, J., The control complexity of r-approval: From the single-peaked case to the general case, J. Comput. Syst. Sci., 2017, vol. 89, pp. 432–449.

    Article  MathSciNet  MATH  Google Scholar 

  72. Yang, Y. and Guo, J., Parameterized complexity of voter control in multi-peaked elections, Theory Comput. Syst., 2018, vol. 62, no. 8, pp. 1798–1825.

    Article  MathSciNet  MATH  Google Scholar 

  73. Cornaz, D., Galand, L., and Spanjaard, O., Bounded single-peaked width and proportional representation, Proc. 24th Eur. Conf. Artif. Intell. (ECAI 2020) (2012), pp. 270–275.

  74. Cornaz, D., Galand, L., and Spanjaard, O., Kemeny elections with bounded single-peaked or single-crossing width, Proc. Twenty-Third Int. Joint Conf. Artif. Intell. (IJCAI-2013) (2013), pp. 76–82.

  75. Fitzsimmons, Z. and Lackner, M., Incomplete preferences in single-peaked electorates, J. Artif. Intell. Res., 2020, vol. 67, pp. 797–833.

    Article  MathSciNet  MATH  Google Scholar 

  76. Tideman, T.N., Independence of clones as a criterion for voting rules, Soc. Choice Welfare, 1987, vol. 4, no. 3, pp. 185–206.

    Article  MathSciNet  MATH  Google Scholar 

  77. Elkind, E., Faliszewski, P., and Slinko, A., Clone structures in voters’ preferences, Proc. 13th ACM Conf. Electron. Commer. (EC-12) (Valencia, 2012), pp. 496–513.

  78. Booth, K.S. and Lueker, G.S., Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. Syst. Sci., 1976, vol. 13, pp. 335–379.

    Article  MathSciNet  MATH  Google Scholar 

  79. Faliszewski, P., Karpov, A., and Obraztsova, S., The complexity of election problems with group-separable preferences, Auton. Agents Multi-Agent Syst., 2022, vol. 36, article ID 18.

  80. Kitaev, S., Separable permutations, in Patterns in Permutations and Words. Monographs in Theoretical Computer Science, Berlin: Springer-Verlag, 2011, pp. 57–66.

  81. Ferrari, L., Enhancing the connections between patterns in permutations and forbidden configurations in restricted elections, J. Discrete Math. Sci. Cryptography, 2022, vol. 25, no. 6, pp. 1613–1631.

    Article  MATH  Google Scholar 

  82. Liu, P., Random assignments on sequentially dichotomous domains, Games Econ. Behav., 2020, vol. 121, pp. 565–584.

    Article  MathSciNet  MATH  Google Scholar 

  83. Liu, P. and Zeng, H., Random assignments on preference domains with a tier structure, J. Math. Econ., 2019, vol. 84, pp. 176–194.

    Article  MathSciNet  MATH  Google Scholar 

  84. Skowron, P., Yu, L., Faliszewski, P., and Elkind, E., The complexity of fully proportional representation for single-crossing electorates, Theor. Comput. Sci., 2015, vol. 569, no. 2, pp. 43–57.

    Article  MathSciNet  MATH  Google Scholar 

  85. Bredereck, R., Chen, J., and Woeginger, G.J., A characterization of the single-crossing domain, Soc. Choice Welfare, 2013, vol. 41, no. 4, pp. 989–998.

    Article  MathSciNet  MATH  Google Scholar 

  86. Stanley, R.P., On the number of reduced decompositions of elements of Coxeter groups, Eur. J. Combinatorics, 1984, vol. 5, pp. 359–372.

    Article  MathSciNet  MATH  Google Scholar 

  87. Slinko, A., Qinggong Wu, and Xing Zheng Wu, A characterization of preference domains that are single-crossing and maximal Condorcet, Econ. Lett., 2021, vol. 204, no. 109918.

  88. Puppe, C. and Slinko, A., Condorcet domains, median graphs and the single-crossing property, Econ. Theory, 2019, vol. 67, no. 1, pp. 285–318.

    Article  MathSciNet  MATH  Google Scholar 

  89. Constantinescu, A.C. and Elkind, E., Proportional representation under single-crossing preferences revisited, Proc. Thirty-Fifth AAAI Conf. Artif. Intell. (AAAI-21) (2021), pp. 5286–5293.

  90. Bredereck, R., Chen, J., and Woeginger, G.J., Are there any nicely structured preference profiles nearby? Math. Soc. Sci., 2016, vol. 79, pp. 61–73.

  91. Jaeckle, F., Peters, D., and Elkind, E., On recognising nearly single-crossing preferences, Proc. 32nd AAAI Conf. Artif. Intell. (AAAI-2018) (2018), pp. 1079–1086.

  92. Cohen, N., Elkind, E., and Lakhani, F., Single-crossing implementation, 2019.

  93. Elkind, E., Faliszewski, P., Lackner, M., and Obraztsova, S., The complexity of recognizing incomplete single-crossing preferences, Proc. Twenty-Ninth AAAI Conf. Artif. Intell. (AAAI-2015) (Austin, 2015), pp. 865–871.

  94. Lakhani, F., Peters, D., and Elkind, E., Correlating preferences and attributes: Nearly single-crossing profiles, Proc. Twenty-Eighth Int. Joint Conf. Artif. Intell. (IJCAI-19), pp. 414–420.

  95. Elkind, E., Faliszewski, P., and Skowron, P., A characterization of the single-peaked single-crossing domain, Soc. Choice Welfare, 2020, vol. 54, pp. 167–181.

    Article  MathSciNet  MATH  Google Scholar 

  96. Berg, S. and Perlinger, T., Single-peaked compatible preference profiles: some combinatorial results, Soc. Choice Welfare, 2006, vol. 27, no. 1, pp. 89–102.

    Article  MathSciNet  MATH  Google Scholar 

  97. Hotelling, H., Stability in competition, Econ. J., 1929, vol. 153, no. 39, pp. 41–57.

    Article  Google Scholar 

  98. Downs, A., An Economic Theory of Democracy, New York: Harper and Row, 1957.

    Google Scholar 

  99. Chen, J. and Grottke, S., Small one-dimensional Euclidean preference profiles, Soc. Choice Welfare, 2021, vol. 57, pp. 117–144.

    Article  MathSciNet  MATH  Google Scholar 

  100. Chen, J., Pruhs, K.R., and Woeginger, G.J., The one-dimensional Euclidean domain: finitely many obstructions are not enough, Soc. Choice Welfare, 2017, vol. 48, pp. 409–432.

    Article  MathSciNet  MATH  Google Scholar 

  101. Tucker, A., A structure theorem for the consecutive 1’s property, J. Comb. Theory B, 1972, vol. 12, no. 2, pp. 153–162.

    Article  MathSciNet  MATH  Google Scholar 

  102. Knoblauch, V., Recognizing one-dimensional Euclidean preference profiles, J. Math. Econ., 2010, vol. 46, pp. 1–5.

    Article  MathSciNet  MATH  Google Scholar 

  103. Elkind, E. and Faliszewski, P., Recognizing 1-Euclidean preferences: an alternative approach, Proc. 13th Int. Symp. (SAGT 2014), Lavi, R., Ed., (Haifa, 2014), pp. 146–157.

  104. Peters, D., Recognising multidimensional Euclidean preferences, Proc. 31st AAAI Conf Artif. Intell. (AAAI-2017) (2017), pp. 642–648.

  105. Salop, S., Monopolistic competition with outside goods, Bell J. Econ., 1979, vol. 10, pp. 141–156.

    Article  Google Scholar 

  106. Peeters, R., Saran, R., and Yuksel, A.M., Strategic party formation on a circle and Durverger’s law, Soc. Choice Welfare, 2016, vol. 47, pp. 729–759.

    Article  MathSciNet  MATH  Google Scholar 

  107. Gale, D. and Shapley, L.S., College admissions and the stability of marriage, Am. Math. Mon., 1962, vol. 69, no. 1, pp. 9–14.

    Article  MathSciNet  MATH  Google Scholar 

  108. Eeckhout, J., On the uniqueness of stable marriage matchings, Econ. Lett., 2000, vol. 69, no. 1, pp. 1–8.

    Article  MathSciNet  MATH  Google Scholar 

  109. Karpov, A., A necessary and sufficient condition for uniqueness consistency in the stable marriage matching problem, Econ. Lett., 2019, vol. 178, pp. 63–65.

    Article  MathSciNet  MATH  Google Scholar 

  110. Sankararaman, A., Basu, S., and Sankararaman, K.A., Dominate or delete: decentralized competing bandits in serial dictatorship, Proc. 24th Int. Conf. Artif. Intell. Stat. (AISTATS 2021), (San Diego, 2021).

  111. Basu, S., Sankararaman, K.A., and Sankararaman, A., Beyond log \({}^{2} \)(T) regret for decentralized bandits in matching markets, Proc. 38th Int. Conf. Mach. Learn. (PMLR 139) (2021).

  112. Brams, S.J. and Fishburn, P.C., Approval voting, Am. Polit. Sci. Rev., 1978, vol. 72, pp. 831–847.

    Article  MATH  Google Scholar 

  113. Aziz, H., Brill, M., Conitzer, V., Elkind, E., Freeman, R., and Walsh, T., Justified representation in approval-based committee voting, Soc. Choice Welfare, 2017, vol. 48, no. 2, pp. 461–485.

    Article  MathSciNet  MATH  Google Scholar 

  114. Bogomolnaia, A. and Moulin, H., Random matching under dichotomous preferences, Econometrica, 2004, vol. 72, pp. 257–279.

    Article  MathSciNet  MATH  Google Scholar 

  115. Bogomolnaia, A., Moulin, H., and Stong, R., Collective choice under dichotomous preferences, J. Econ. Theory, 2005, vol. 122, no. 2, pp. 165–184.

    Article  MathSciNet  MATH  Google Scholar 

  116. Duddy, C., Fair sharing under dichotomous preferences, Math. Soc. Sci., 2015, vol. 73, pp. 1–5.

    Article  MathSciNet  MATH  Google Scholar 

  117. Aziz, H., Harrenstein, P., Lang, J., and Wooldridge, M., Boolean hedonic games, Proc. 15th Int. Conf. Princ. Knowl. Representation Reasoning (KR-2016) (2016), pp. 166–175.

  118. Elkind, E. and Lackner, M., Structure in dichotomous preferences, Proc. 24th Int. Joint Conf. Artif. Intell. (IJCAI-2015) (2015), pp. 2019–2025.

  119. Blin, G., Rizzi, R., and Vialette, S., A faster algorithm for finding minimum Tucker submatrices, Proc. 6th Conf. Computability Eur. (CiE’10) (Ponta Delgada, 2010), pp. 69–77.

  120. Safe, M.D., Circularly compatible ones, D-circularity, and proper circular-arc bigraphs, SIAM J. Discrete Math., 2021, vol. 35, no. 2, pp. 707–751.

    Article  MathSciNet  MATH  Google Scholar 

  121. Pe’er, I., Pupko, T., Shamir, R., and Sharan, R., Incomplete directed perfect phylogeny, SIAM J. Comput., 2004, vol. 33, no. 3, pp. 590–607.

    Article  MathSciNet  MATH  Google Scholar 

  122. Terzopoulou, Z., Karpov, A., and Obraztsova, S., Restricted domains of dichotomous preferences with possibly incomplete information, Proc. 35th AAAI Conf. Artif. Intell. (AAAI 2021) (2021), pp. 5726–5733.

  123. Brewbaker, C., A combinatorial interpretation of the poly-Bernoulli numbers and two Fermat analogues, Integers, 2008, vol. 8, no. 1, A2.

  124. Weisstein, E.W., Stirling number of the second kind. MathWorld—a Wolfram web resource. .

  125. Yang, Y., On the tree representations of dichotomous preferences, in Proc. Twenty-Eighth Int. Joint Conf. Artif. Intell. (IJCAI-2019), Kraus, S., Ed., 2019, P. 644–650.

  126. Ju, H.-K. and Seo, S., Enumeration of (0, 1)-matrices avoiding some 2 \(\times \) 2 matrices, Discrete Math., 2012, vol. 312, no. 16, pp. 2473–2481.

    Article  MathSciNet  MATH  Google Scholar 

  127. Mattei, N. and Walsh, T., Preflib: a library of preference data, in Proc. Third Int. Conf. Algorithmic Decis. Theory (ADT 2013). Lect. Notes Artif. Intell., 2013, pp. 259–270.

  128. Boehmer, N. and Schaar, N., Collecting, classifying, analyzing, and using real-world elections, 2022.

Download references

ACKNOWLEDGMENTS

The author thanks F.T. Aleskerov, the participants of the Moscow-wide seminar “Expert assessments and data analysis” held on March 11, 2020 at the Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, the participants of the seminar “Mathematical economics” held at the Central Economics and Mathematics Institute of the Russian Academy of Sciences on November 9, 2021, and an anonymous referee for valuable comments.

Funding

This article is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE University).

Author information

Authors and Affiliations

  1. HSE University, Moscow, 101000, Russia

    A. V. Karpov

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    A. V. Karpov

Authors
  1. A. V. Karpov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Karpov.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karpov, A.V. Structured Preferences: A Literature Survey. Autom Remote Control 83, 1329–1354 (2022). https://doi.org/10.1134/S0005117922090016

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117922090016

Keywords

Search

Navigation