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Journal articles on the topic 'Single-peaked preferences'

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Published: 25 May 2024

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1

Fitzsimmons, Zack, and Martin Lackner. "Incomplete Preferences in Single-Peaked Electorates." Journal of Artificial Intelligence Research 67 (April 13, 2020): 797–833. http://dx.doi.org/10.1613/jair.1.11577.

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Incomplete preferences are likely to arise in real-world preference aggregation scenarios. This paper deals with determining whether an incomplete preference profile is single-peaked. This is valuable information since many intractable voting problems become tractable given singlepeaked preferences. We prove that the problem of recognizing single-peakedness is NP-complete for incomplete profiles consisting of partial orders. Despite this intractability result, we find several polynomial-time algorithms for reasonably restricted settings. In particular, we give polynomial-time recognition algorithms for weak orders, which can be viewed as preferences with indifference.

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2

Peters, Dominik, and Martin Lackner. "Preferences Single-Peaked on a Circle." Journal of Artificial Intelligence Research 68 (June 24, 2020): 463–502. http://dx.doi.org/10.1613/jair.1.11732.

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We introduce the domain of preferences that are single-peaked on a circle, which is a generalization of the well-studied single-peaked domain. This preference restriction is useful, e.g., for scheduling decisions, certain facility location problems, and for one-dimensional decisions in the presence of extremist preferences. We give a fast recognition algorithm of this domain, provide a characterisation by finitely many forbidden subprofiles, and show that many popular single- and multi-winner voting rules are polynomial-time computable on this domain. In particular, we prove that Proportional Approval Voting can be computed in polynomial time for profiles that are single-peaked on a circle. In contrast, Kemeny's rule remains hard to evaluate, and several impossibility results from social choice theory can be proved using only profiles in this domain.

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3

Bade, Sophie. "Matching with single-peaked preferences." Journal of Economic Theory 180 (March 2019): 81–99. http://dx.doi.org/10.1016/j.jet.2018.12.004.

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4

Conitzer, V. "Eliciting Single-Peaked Preferences Using Comparison Queries." Journal of Artificial Intelligence Research 35 (June 16, 2009): 161–91. http://dx.doi.org/10.1613/jair.2606.

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Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to simply ask agents to report their complete preferences. Rather, the agents' preferences, or at least the relevant parts thereof, need to be elicited. This is done by asking the agents a (hopefully small) number of simple queries about their preferences, such as comparison queries, which ask an agent to compare two of the alternatives. Prior work on preference elicitation in voting has focused on the case of unrestricted preferences. It has been shown that in this setting, it is sometimes necessary to ask each agent (almost) as many queries as would be required to determine an arbitrary ranking of the alternatives. In contrast, in this paper, we focus on single-peaked preferences. We show that such preferences can be elicited using only a linear number of comparison queries, if either the order with respect to which preferences are single-peaked is known, or at least one other agent's complete preferences are known. We show that using a sublinear number of queries does not suffice. We also consider the case of cardinally single-peaked preferences. For this case, we show that if the alternatives' cardinal positions are known, then an agent's preferences can be elicited using only a logarithmic number of queries; however, we also show that if the cardinal positions are not known, then a sublinear number of queries does not suffice. We present experimental results for all elicitation algorithms. We also consider the problem of only eliciting enough information to determine the aggregate ranking, and show that even for this more modest objective, a sublinear number of queries per agent does not suffice for known ordinal or unknown cardinal positions. Finally, we discuss whether and how these techniques can be applied when preferences are almost single-peaked.

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5

Amorós, Pablo. "Single-peaked preferences with several commodities." Social Choice and Welfare 19, no. 1 (January 1, 2002): 57–67. http://dx.doi.org/10.1007/s355-002-8325-6.

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6

Moreno, Bernardo. "Single-peaked preferences, endowments and population-monotonicity." Economics Letters 75, no. 1 (March 2002): 87–95. http://dx.doi.org/10.1016/s0165-1765(01)00576-6.

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7

Bonifacio, Agustín G. "Bribe-proof reallocation with single-peaked preferences." Social Choice and Welfare 44, no. 3 (September 26, 2014): 617–38. http://dx.doi.org/10.1007/s00355-014-0849-0.

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8

Lackner, Marie-Louise, and Martin Lackner. "On the likelihood of single-peaked preferences." Social Choice and Welfare 48, no. 4 (March 7, 2017): 717–45. http://dx.doi.org/10.1007/s00355-017-1033-0.

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9

Trick, Michael A. "Recognizing single-peaked preferences on a tree." Mathematical Social Sciences 17, no. 3 (June 1989): 329–34. http://dx.doi.org/10.1016/0165-4896(89)90060-7.

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10

Brown, Lindsey, Hoang Ha, and Jonathan K. Hodge. "Single-peaked preferences over multidimensional binary alternatives." Discrete Applied Mathematics 166 (March 2014): 14–25. http://dx.doi.org/10.1016/j.dam.2013.11.006.

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11

Hashimoto, Kazuhiko, and Takuma Wakayama. "Fair reallocation in economies with single-peaked preferences." International Journal of Game Theory 50, no. 3 (May 27, 2021): 773–85. http://dx.doi.org/10.1007/s00182-021-00767-z.

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12

Smeulders, B. "Testing a mixture model of single-peaked preferences." Mathematical Social Sciences 93 (May 2018): 101–13. http://dx.doi.org/10.1016/j.mathsocsci.2018.02.002.

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13

Ehlers, Lars. "Resource-monotonic allocation when preferences are single-peaked." Economic Theory 20, no. 1 (August 1, 2002): 113–31. http://dx.doi.org/10.1007/s001990100204.

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14

Berga, Dolors, and Bernardo Moreno. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences." Social Choice and Welfare 32, no. 2 (August 5, 2008): 275–98. http://dx.doi.org/10.1007/s00355-008-0323-y.

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15

Brandt, Felix, Markus Brill, Edith Hemaspaandra, and Lane A. Hemaspaandra. "Bypassing Combinatorial Protections: Polynomial-Time Algorithms for Single-Peaked Electorates." Journal of Artificial Intelligence Research 53 (July 22, 2015): 439–96. http://dx.doi.org/10.1613/jair.4647.

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For many election systems, bribery (and related) attacks have been shown NP-hard using constructions on combinatorially rich structures such as partitions and covers. This paper shows that for voters who follow the most central political-science model of electorates---single-peaked preferences---those hardness protections vanish. By using single-peaked preferences to simplify combinatorial covering challenges, we for the first time show that NP-hard bribery problems---including those for Kemeny and Llull elections---fall to polynomial time for single-peaked electorates. By using single-peaked preferences to simplify combinatorial partition challenges, we for the first time show that NP-hard partition-of-voters problems fall to polynomial time for single-peaked electorates. We show that for single-peaked electorates, the winner problems for Dodgson and Kemeny elections, though Theta-two-complete in the general case, fall to polynomial time. And we completely classify the complexity of weighted coalition manipulation for scoring protocols in single-peaked electorates.

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16

Brandt, Felix, Markus Brill, Edith Hemaspaandra, and Lane Hemaspaandra. "Bypassing Combinatorial Protections: Polynomial-Time Algorithms for Single-Peaked Electorates." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 4, 2010): 715–22. http://dx.doi.org/10.1609/aaai.v24i1.7637.

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For many election systems, bribery (and related) attacks have been shown NP-hard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice. This paper shows that for voters who follow the most central political-science model of electorates — single-peaked preferences — those protections vanish. By using single-peaked preferences to simplify combinatorial covering challenges, we show that NP-hard bribery problems — including those for Kemeny and Llull elections- — fall to polynomial time. By using single-peaked preferences to simplify combinatorial partition challenges, we show that NP-hard partition-of-voters problems fall to polynomial time. We furthermore show that for single-peaked electorates, the winner problems for Dodgson and Kemeny elections, though Θ2p-complete in the general case, fall to polynomial time. And we completely classify the complexity of weighted coalition manipulation for scoring protocols in single-peaked electorates.

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17

Chun, Youngsub. "The Separability Principle in Economies with Single-Peaked Preferences." Social Choice and Welfare 26, no. 2 (April 2006): 239–53. http://dx.doi.org/10.1007/s00355-006-0092-4.

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18

Kar, Anirban, and Özgür Kıbrıs. "Allocating multiple estates among agents with single-peaked preferences." Social Choice and Welfare 31, no. 4 (February 26, 2008): 641–66. http://dx.doi.org/10.1007/s00355-008-0301-4.

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19

Kasajima, Yoichi. "Probabilistic assignment of indivisible goods with single-peaked preferences." Social Choice and Welfare 41, no. 1 (June 6, 2012): 203–15. http://dx.doi.org/10.1007/s00355-012-0674-2.

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20

Herrero, Carmen, and Ricardo Martínez. "Allocation problems with indivisibilities when preferences are single-peaked." SERIEs 2, no. 4 (February 23, 2011): 453–67. http://dx.doi.org/10.1007/s13209-011-0046-7.

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21

Lepelley, Dominique. "Constant scoring rules, condorcet criteria and single-peaked preferences." Economic Theory 7, no. 3 (October 1996): 491–500. http://dx.doi.org/10.1007/bf01213662.

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22

Doghmi, Ahmed, and Abderrahmane Ziad. "Nash implementation in exchange economies with single-peaked preferences." Economics Letters 100, no. 1 (July 2008): 157–60. http://dx.doi.org/10.1016/j.econlet.2007.12.010.

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23

Ehlers, Lars, and Ton Storcken. "Arrow's Possibility Theorem for one-dimensional single-peaked preferences." Games and Economic Behavior 64, no. 2 (November 2008): 533–47. http://dx.doi.org/10.1016/j.geb.2008.02.005.

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24

Juarez, Ruben, and Jung S. You. "Optimality of the uniform rule under single-peaked preferences." Economic Theory Bulletin 7, no. 1 (March 28, 2018): 27–36. http://dx.doi.org/10.1007/s40505-018-0141-z.

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25

Thomson, William. "The Replacement Principle in Economies with Single-Peaked Preferences." Journal of Economic Theory 76, no. 1 (September 1997): 145–68. http://dx.doi.org/10.1006/jeth.1997.2294.

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26

Peters, Dominik, Lan Yu, Hau Chan, and Edith Elkind. "Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results." Journal of Artificial Intelligence Research 73 (January 12, 2022): 231–76. http://dx.doi.org/10.1613/jair.1.12332.

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A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced by Demange (1982), and subsequently Trick (1989b) described an efficient algorithm for deciding if a given profile is single-peaked on a tree. We study the complexity of multiwinner elections under several variants of the Chamberlin–Courant rule for preferences single-peaked on trees. We show that in this setting the egalitarian version of this rule admits a polynomial-time winner determination algorithm. For the utilitarian version, we prove that winner determination remains NP-hard for the Borda scoring function; indeed, this hardness results extends to a large family of scoring functions. However, a winning committee can be found in polynomial time if either the number of leaves or the number of internal vertices of the underlying tree is bounded by a constant. To benefit from these positive results, we need a procedure that can determine whether a given profile is single-peaked on a tree that has additional desirable properties (such as, e.g., a small number of leaves). To address this challenge, we develop a structural approach that enables us to compactly represent all trees with respect to which a given profile is single-peaked. We show how to use this representation to efficiently find the best tree for a given profile for use with our winner determination algorithms: Given a profile, we can efficiently find a tree with the minimum number of leaves, or a tree with the minimum number of internal vertices among trees on which the profile is single-peaked. We then explore the power and limitations of this framework: we develop polynomial-time algorithms to find trees with the smallest maximum degree, diameter, or pathwidth, but show that it is NP-hard to check whether a given profile is single-peaked on a tree that is isomorphic to a given tree, or on a regular tree.

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27

RAD, SOROUSH RAFIEE, and OLIVIER ROY. "Deliberation, Single-Peakedness, and Coherent Aggregation." American Political Science Review 115, no. 2 (February 22, 2021): 629–48. http://dx.doi.org/10.1017/s0003055420001045.

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Rational deliberation helps to avoid cyclic or intransitive group preferences by fostering meta-agreements, which in turn ensures single-peaked profiles. This is the received view, but this paper argues that it should be qualified. On one hand we provide evidence from computational simulations that rational deliberation tends to increase proximity to so-called single-plateaued preferences. This evidence is important to the extent that, as we argue, the idea that rational deliberation fosters the creation of meta-agreement and, in turn, single-peaked profiles does not carry over to single-plateaued ones, and the latter but not the former makes coherent aggregation possible when the participants are allowed to express indifference between options. On the other hand, however, our computational results show, against the received view, that when the participants are strongly biased towards their own opinions, rational deliberation tends to create irrational group preferences, instead of eliminating them. These results are independent of whether the participants reach meta-agreements in the process, and as such they highlight the importance of rational preference change and biases towards one’s own opinion in understanding the effects of rational deliberation.

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28

Flores-Szwagrzak, Karol. "The replacement principle in networked economies with single-peaked preferences." Social Choice and Welfare 47, no. 4 (September 1, 2016): 763–89. http://dx.doi.org/10.1007/s00355-016-0991-y.

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29

Klaus, Bettina, Hans Peters, and Ton Storcken. "Strategy-proof division with single-peaked preferences and individual endowments." Social Choice and Welfare 15, no. 2 (March 2, 1998): 297–311. http://dx.doi.org/10.1007/s003550050106.

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30

K?br?s, �zg�r. "Constrained allocation problems with single-peaked preferences: An axiomatic analysis." Social Choice and Welfare 20, no. 3 (June 1, 2003): 353–62. http://dx.doi.org/10.1007/s003550200183.

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31

Lepelley, Dominique. "Condorcet efficiency of positional voting rules with single-peaked preferences." Economic Design 1, no. 1 (December 1994): 289–99. http://dx.doi.org/10.1007/bf02716627.

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32

Weymark, John A. "A unified approach to strategy-proofness for single-peaked preferences." SERIEs 2, no. 4 (May 12, 2011): 529–50. http://dx.doi.org/10.1007/s13209-011-0064-5.

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33

Bhardwaj, Bhavook, Rajnish Kumar, and Josué Ortega. "Fairness and efficiency in cake-cutting with single-peaked preferences." Economics Letters 190 (May 2020): 109064. http://dx.doi.org/10.1016/j.econlet.2020.109064.

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34

Duggan, John. "May’s theorem in one dimension." Journal of Theoretical Politics 29, no. 1 (July 9, 2016): 3–21. http://dx.doi.org/10.1177/0951629815603694.

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This paper provides three versions of May’s theorem on majority rule, adapted to the one-dimensional model common in formal political modeling applications. The key contribution is that single peakedness of voter preferences allows us to drop May’s restrictive positive responsiveness axiom. The simplest statement of the result holds when voter preferences are single peaked and linear (no indifferences), in which case a voting rule satisfies anonymity, neutrality, Pareto, and transitivity of weak social preference if and only if the number of individuals is odd and the rule is majority rule.

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35

Klaus, Bettina, and Panos Protopapas. "On strategy-proofness and single-peakedness: median-voting over intervals." International Journal of Game Theory 49, no. 4 (November 17, 2020): 1059–80. http://dx.doi.org/10.1007/s00182-020-00728-y.

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AbstractWe study correspondences that choose an interval of alternatives when agents have single-peaked preferences over locations and ordinally extend their preferences over intervals. We extend the main results of Moulin (Public Choice 35:437–455, 1980) to our setting and show that the results of Ching (Soc Choice Welf 26:473–490, 1997) cannot always be similarly extended. First, strategy-proofness and peaks-onliness characterize the class of generalized median correspondences (Theorem 1). Second, this result neither holds on the domain of symmetric and single-peaked preferences, nor can in this result min/max continuity substitute peaks-onliness (see counter-Example 3). Third, strategy-proofness and voter-sovereignty characterize the class of efficient generalized median correspondences (Theorem 2).

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36

Thomson, William. "The replacement principle in public good economies with single-peaked preferences." Economics Letters 42, no. 1 (January 1993): 31–36. http://dx.doi.org/10.1016/0165-1765(93)90169-d.

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37

Chatterji, Shurojit, Arunava Sen, and Huaxia Zeng. "A characterization of single-peaked preferences via random social choice functions." Theoretical Economics 11, no. 2 (May 2016): 711–33. http://dx.doi.org/10.3982/te1972.

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38

Long, Yan. "Strategy-proof group selection under single-peaked preferences over group size." Economic Theory 68, no. 3 (June 19, 2018): 579–608. http://dx.doi.org/10.1007/s00199-018-1135-7.

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39

Ehlers, Lars, Hans Peters, and Ton Storcken. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences." Journal of Economic Theory 105, no. 2 (August 2002): 408–34. http://dx.doi.org/10.1006/jeth.2001.2829.

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40

Escoffier, Bruno, Olivier Spanjaard, and Magdaléna Tydrichová. "Recognizing single-peaked preferences on an arbitrary graph: Complexity and algorithms." Discrete Applied Mathematics 348 (May 2024): 301–19. http://dx.doi.org/10.1016/j.dam.2024.02.009.

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41

MORDESON, JOHN N., LANCE NIELSEN, and TERRY D. CLARK. "SINGLE PEAKED FUZZY PREFERENCES IN ONE-DIMENSIONAL MODELS: DOES BLACK'S MEDIAN VOTER THEOREM HOLD?" New Mathematics and Natural Computation 06, no. 01 (March 2010): 1–16. http://dx.doi.org/10.1142/s1793005710001566.

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Black's Median Voter Theorem is among the more useful mathematical tools available to political scientists for predicting choices of political actors based on their preferences over a finite set of alternatives within an institutional or constitutional setting. If the alternatives can be placed on a single-dimensional continuum such that the preferences of all players descend monotonically from their ideal point, then the outcome will be the alternative at the median position. We demonstrate that the Median Voter Theorem holds for fuzzy preferences. Our approach considers the degree to which players prefer options in binary relations.

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42

Harless, Patrick. "Solidarity with respect to small changes in preferences in public good economies with single-peaked preferences." Mathematical Social Sciences 75 (May 2015): 81–86. http://dx.doi.org/10.1016/j.mathsocsci.2015.02.006.

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43

Chun, Youngsub. "Distributional properties of the uniform rule in economies with single-peaked preferences." Economics Letters 67, no. 1 (April 2000): 23–27. http://dx.doi.org/10.1016/s0165-1765(99)00250-5.

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44

Herrero, Carmen, and Ricardo Martínez. "Up methods in the allocation of indivisibilities when preferences are single-peaked." TOP 16, no. 2 (March 26, 2008): 272–83. http://dx.doi.org/10.1007/s11750-008-0043-6.

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45

Klaus, Bettina. "A Note on the Separability Principle in Economies with Single-Peaked Preferences." Social Choice and Welfare 26, no. 2 (April 2006): 255–61. http://dx.doi.org/10.1007/s00355-006-0096-0.

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46

Wakayama, Takuma. "Bribe-proofness for single-peaked preferences: characterizations and maximality-of-domains results." Social Choice and Welfare 49, no. 2 (July 7, 2017): 357–85. http://dx.doi.org/10.1007/s00355-017-1068-2.

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47

Klaus, Bettina, and Panos Protopapas. "Solidarity for public goods under single-peaked preferences: characterizing target set correspondences." Social Choice and Welfare 55, no. 3 (April 23, 2020): 405–30. http://dx.doi.org/10.1007/s00355-020-01245-3.

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48

Gehrlein, William V. "The expected likelihood of transitivity for probabilistic choosers with single-peaked preferences." Mathematical Social Sciences 25, no. 2 (February 1993): 143–55. http://dx.doi.org/10.1016/0165-4896(93)90049-o.

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49

Escoffier, Bruno, Hugo Gilbert, and Adèle Pass-Lanneau. "Iterative Delegations in Liquid Democracy with Restricted Preferences." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 02 (April 3, 2020): 1926–33. http://dx.doi.org/10.1609/aaai.v34i02.5562.

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Liquid democracy is a collective decision making paradigm which lies between direct and representative democracy. One main feature of liquid democracy is that voters can delegate their votes in a transitive manner so that: A delegates to B and B delegates to C leads to A delegates to C. Unfortunately, because voters' preferences over delegates may be conflicting, this process may not converge. There may not even exist a stable state (also called equilibrium). In this paper, we investigate the stability of the delegation process in liquid democracy when voters have restricted types of preference on the agent representing them (e.g., single-peaked preferences). We show that various natural structures of preference guarantee the existence of an equilibrium and we obtain both tractability and hardness results for the problem of computing several equilibria with some desirable properties.

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50

Amorós, Pablo. "Efficiency and income redistribution in the single-peaked preferences model with several commodities." Economics Letters 63, no. 3 (June 1999): 341–49. http://dx.doi.org/10.1016/s0165-1765(99)00047-6.

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