Abstract
We place ourselves in a decision making setting where a set of agents needs to collectively decide upon a set of alternatives characterised by their features. We introduce the notion of unshared features and show that if such features do not exist then we can reach a Condorcet consensus. We provide a deliberation protocol that ensures that, after its completion, the number of unshared features of the decision problem can only be reduced.
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Notes
- 1.
The pairwise majority aggregation method is known to be unanimous, independent to irrelevant alternatives and non-dictatorial.
- 2.
Please note that Dietrich et al. [6] suppose that agents can have a preference relation over features and thus they can discriminate between two alternatives satisfying the same number of desired features. Intuitively, the importance given to a feature depends on the context.
- 3.
In this case, the Condorcet winner is the most preferred alternative of the median voter [3].
- 4.
Case of the Condorcet paradox for example.
- 5.
Please note that for simplicity purposes, we assume here that both phases always succeed, i.e. all the agents manage to agree on a set of desired features and on the features satisfied by the alternatives.
- 6.
This observation is in line with the experimental results obtained by List et al. [12] in 2012.
References
Arrow, K.J.: Social Choice and Individual Values. Wiley, New York (1951)
Besnard, P., Hunter, A.: A logic-based theory of deductive arguments. Artif. Intell. 128(1–2), 203–235 (2001)
Black, D.: The median voter theorem. J. Polit. Econ. 56(1), 23–34 (1948)
Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D.: Handbook of Computational Social Choice, 1st edn. Cambridge University Press, New York (2016)
de Condorcet, M.J.A.N.C.M.: Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. L’imprimerie royale (1785)
Dietrich, F., List, C.: Where do preferences come from ? Int. J. Game Theory 42(3), 613–637 (2013)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77(2), 321–357 (1995)
Gehrlein, W.V.: Consistency in measures of social homogeneity: a connection with proximity to single peaked preferences. Qual. Quant. 38(2), 147–171 (2004)
Gehrlein, W.V.: Probabilities of election outcomes with two parameters: the relative impact of unifying and polarizing candidates. Rev. Econ. Des. 9(4), 317–336 (2005)
Guilbaud, G.T.: Les théories de l’intérêt général et le problème logique de l’agrégation. Économie appliquée 5, 501–584 (1952)
Inada, K.I.: A note on the simple majority decision rule. Econometrica: J. Econometric Soc. 32, 525–531 (1964)
List, C., Luskin, R.C., Fishkin, J.S., McLean, I.: Deliberation, single-peakedness, and the possibility of meaningful democracy: evidence from deliberative polls. J. Politics 75(1), 80–95 (2012)
Niemi, R.G.: Majority decision-making with partial unidimensionality. Am. Polit. Sci. Rev. 63(2), 488–497 (1969)
Searle, J.R.: Speech Acts: An Essay in the Philosophy of Language, vol. 626. Cambridge University Press, Cambridge (1969)
Sen, A.K.: A possibility theorem on majority decisions. Econometrica: J. Econometric Soc. 34, 491–499 (1966)
Tsetlin, I., Regenwetter, M., Grofman, B.: The impartial culture maximizes the probability of majority cycles. Soc. Choice Welf. 21(3), 387–398 (2003)
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Boixel, A., Bisquert, P., Croitoru, M. (2019). Deliberation Towards Transitivity with Unshared Features. In: Baldoni, M., Dastani, M., Liao, B., Sakurai, Y., Zalila Wenkstern, R. (eds) PRIMA 2019: Principles and Practice of Multi-Agent Systems. PRIMA 2019. Lecture Notes in Computer Science(), vol 11873. Springer, Cham. https://doi.org/10.1007/978-3-030-33792-6_1
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