Randomized Algorithms for Lexicographic Inference

References

• Ailon N, Charikar M, Newman A (2008) Aggregating inconsistent information: Ranking and clustering. J. ACM 55(5):1–27.Crossref, Google Scholar
• Bartholdi J, Tovey CA, Trick MA (1989) Voting schemes for which it can be difficult to tell who won the election. Soc. Choice Welfare 6(2):157–165.Crossref, Google Scholar
• Beggs S, Cardell S, Hausman J (1981) Assessing the potential demand for electric cars. J. Econometrics 17(1):1–19.Crossref, Google Scholar
• Belloni A, Freund R, Selove M, Simester D (2008) Optimizing product line designs: Efficient methods and comparisons. Management Sci. 54(9):1544–1552.Link, Google Scholar
• Bertsimas D, Mišić VV (2017) Robust product line design. Oper. Res. 65(1):19–37.Link, Google Scholar
• Bertsimas D, Mišić VV (2019) Exact first-choice product line optimization. Oper. Res. Forthcoming.Google Scholar
• Bettman JR, Luce MF, Payne JW (1998) Constructive consumer choice processes. J. Consumer Res. 25(3):187–217.Crossref, Google Scholar
• Billings RS, Scherer LL (1988) The effects of response mode and importance on decision-making strategies: Judgment versus choice. Organ. Behav. Human Decision Processes 41(1):1–19.Crossref, Google Scholar
• Box GEP, Hunter WG, Hunter JS (1978) Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building (Wiley, New York).Google Scholar
• Bridges D (1983) A numerical representation of intransitive preferences on a countable set. J. Econom. Theory 30(1):213–217.Crossref, Google Scholar
• Bröder A (2000) Assessing the empirical validity of the “take-the-best” heuristic as a model of human probabilistic inference. J. Experiment. Psych. Learn. Memory Cognition 26(5):1332–1346.Crossref, Google Scholar
• Bröder A, Schiffer S (2003) Take the best versus simultaneous feature matching: Probabilistic inferences from memory and effects of representation format. J. Experiment. Psych. General 132(2):277–293.Crossref, Google Scholar
• Byrd RH, Nocedal J, Schnabel RB (1994) Representations of quasi-Newton matrices and their use in limited memory methods. Math. Programming 63(4):129–156.Crossref, Google Scholar
• Campos V, Glover F, Laguna M, Martí R (2001) An experimental evaluation of a scatter search for the linear ordering problem. J. Global Optim. 21(4):397–414.Crossref, Google Scholar
• Charon I, Hudry O (2007) A survey on the linear ordering problem for weighted or unweighted tournaments. 4OR 5(1):5–60.Crossref, Google Scholar
• Charon I, Hudry O (2010) An updated survey on the linear ordering problem for weighted or unweighted tournaments. Ann. Oper. Res. 175(1):107–158.Crossref, Google Scholar
• Chateauneuf A (1987) Continuous representation of a preference relation on a connected topological space. J. Math. Econom. 16(2):139–146.Crossref, Google Scholar
• Chen KD, Hausman WH (2000) Technical note: Mathematical properties of the optimal product line selection problem using choice-based conjoint analysis. Management Sci. 46(2):327–332.Link, Google Scholar
• Debreu G (1954) Representation of a preference ordering by a numerical function. Thrall RM, Coombs CH, Davis RL, eds. Decision Processes (John Wiley, New York), 159–165.Google Scholar
• DeSarbo WS, Fong DKH, Liechty JC (2005) Dynamic models incorporating individual heterogeneity: Utility evolution in conjoint analysis. Marketing Sci. 24(2):285–293.Link, Google Scholar
• Dieckmann A, Dippold K, Dietrich H (2009) Compensatory versus noncompensatory models for predicting consumer preferences. Judgment Decision Making 4(3):200–213.Google Scholar
• Drolet A, Luce MF (2004) Cognitive load and trade-off avoidance. J. Consumer Res. 31(1):63–77.Crossref, Google Scholar
• Fishburn P (1974) Lexicographic orders, utilities and decision rules: A survey. Management Sci. 20(11):1442–1471.Link, Google Scholar
• Floudas CA, Visweswaran V (1995) Quadratic optimization. Horst R, Pardalos PM, eds. Handbook of Global Optimization, Nonconvex Optimization and Its Applications, vol. 2 (Springer, Boston), 217–269.Crossref, Google Scholar
• Garcia CG, Pérez-Brito D, Campos V, Martí R (2006) Variable neighborhood search for the linear ordering problem. Comput. Oper. Res. 33(12):3549–3565.Crossref, Google Scholar
• Gigerenzer G, Hoffrage U, Kleinbolting H (1991) Probabilistic mental models: A Brunswikian theory of confidence. Psych. Rev. 98(4):506–528.Crossref, Google Scholar
• Goemans MX, Williamson DP (1995) Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42(6):1115–1145.Crossref, Google Scholar
• Green PE, Krieger AM (1985) Models and heuristics for product line selection. Marketing Sci. 4(1):1–19.Link, Google Scholar
• Grötschel M, Jünger M, Reinelt G (1984) A cutting plane algorithm for the linear ordering problem. Oper. Res. 32(6):1195–1220.Link, Google Scholar
• Hoffman M, Gelman A (2014) The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. J. Machine Learn. Res. 15(1):1351–1381.Google Scholar
• Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591.Google Scholar
• Knoblauch V (2000) Lexicographic orders and preference representation. J. Math. Econom. 34(2):255–267.Crossref, Google Scholar
• Kohli R, Jedidi K (2007) Representation and inference of lexicographic preference structures and their variants. Marketing Sci. 26(3):380–399.Link, Google Scholar
• Kohli R, Jedidi K (2015) Error theory for elimination by aspects. Oper. Res. 63(3):512–526.Link, Google Scholar
• Kohli R, Krishnamurti R (1987) A heuristic approach to product design. Management Sci. 33(12):1523–1533.Link, Google Scholar
• Laguna M, Martí R, Campos V (1999) Intensification and diversification with elite tabu search solutions for the linear ordering problem. Comput. Oper. Res. 26(12):1217–1230.Crossref, Google Scholar
• Martí R, Reinelt G (2011) The Linear Ordering Problem: Exact and Heuristic Methods in Combinatorial Optimization, Applied Mathematical Sciences, vol. 175 (Springer-Verlag, Berlin, Heidelberg).Crossref, Google Scholar
• Martignon L, Hoffrage U (1999) Why does one reason decision making work? Gigerenzer G, Todd PM, the ABC Research Group, eds. Simple Heuristics That Make Us Smart (Oxford University Press, New York), 119–140.Google Scholar
• Martignon L, Hoffrage U (2002) Fast, frugal and fit: Simple heuristics for paired comparison. Theory Decision 52(1):29–71.Crossref, Google Scholar
• Motwani R, Raghavan P (1995) Randomized Algorithms (Cambridge University Press, New York).Crossref, Google Scholar
• Neal RM (1998) Regression and classification using Gaussian process priors. Bernardo JM, Berger JO, Dawid AO, Smith AFM, eds. Bayesian Statistics, vol. 6 (Oxford University Press, New York), 475–501.Google Scholar
• Papadimitriou CH, Steiglitz K (1998) Combinatorial Optimization: Algorithms and Complexity (Dover Publications, New York).Google Scholar
• Payne JW (1982) Contingent decision behavior. Psych. Bull. 92(2):382–402.Crossref, Google Scholar
• Pinelis I (2015) Exact upper and lower bounds on the difference between the arithmetic and geometric means. Bull. Australian Math. Soc. 92(1):149–158.Crossref, Google Scholar
• Schiavinotto T, Stützle T (2004) The linear ordering problem: Instances, search space analysis and algorithms. J. Math. Model. Algorithms 3(4):367–402.Crossref, Google Scholar
• Schkade DA, Johnson EJ (1989) Cognitive processes in preference reversals. Organ. Behav. Human Decision Processes 44(2):203–231.Crossref, Google Scholar
• Schmitt M, Martignon L (2006) On the complexity of learning lexicographic strategies. J. Machine Learn. 7(29):55–83.Google Scholar
• Slovic P (1975) Choice between equally valued alternatives. J. Experiment. Psych. Human Perception Performance 1(3):280–287.Crossref, Google Scholar
• Toubia O, Hauser JR, Simester DI, Dahan E (2003) Fast polyhedral adaptive conjoint estimation. Marketing Sci. 22(3):273–303.Link, Google Scholar
• Tversky A (1972) Choice by elimination. J. Math. Psych. 9(4):341–367.Crossref, Google Scholar
• Tversky A, Sattath S, Slovic P (1988) Contingent weighting in judgment and choice. Psych. Rev. 95(3):371–384.Crossref, Google Scholar
• van Zuylen A, Williamson DP (2008) Deterministic algorithms for rank aggregation and other ranking and clustering problems. Kaklamanis C, Skutella M, eds. Approximation and Online Algorithms. WAOA 2007. Lecture Notes in Computer Science, vol. 4927 (Springer, Berlin, Heidelberg), 260–273.Crossref, Google Scholar
• Wakker P (1988) Continuity of preference relations for separable topologies. Internat. Econom. Rev. 29(1):105–110.Crossref, Google Scholar
• Yee M, Dahan E, Hauser JR, Orlin J (2007) Greedoid-based noncompensatory inference. Marketing Sci. 26(4):532–549.Link, Google Scholar