2000 character limit reached
Network Preference Dynamics using Lattice Theory (2310.00179v2)
Published 29 Sep 2023 in cs.MA
Abstract: Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume, revise their preferences as they gain more information about other agents. Exploiting the ordered algebraic structure of preferences, we introduce a message-passing algorithm for heterogeneous agents distributed over a network to update their preferences based on aggregations of the preferences of their neighbors in a graph. We demonstrate the existence of equilibrium points of the resulting global dynamical system of local preference updates and provide a sufficient condition for trajectories to converge to equilibria: stable preferences. Finally, we present numerical simulations demonstrating our preliminary results.
- M. C. Munger, Choosing in groups: Analytical politics revisited. Cambridge University Press, 2015.
- M. J. Osborne and A. Rubinstein, A course in game theory. MIT press, 1994.
- A. Gibbard, “Manipulation of voting schemes: a general result,” Econometrica: journal of the Econometric Society, pp. 587–601, 1973.
- M. A. Satterthwaite, “Strategy-proofness and arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions,” Journal of economic theory, vol. 10, no. 2, pp. 187–217, 1975.
- Yale university press, 2012.
- A. F. Beardon, J. C. Candeal, G. Herden, E. Induráin, and G. B. Mehta, “The non-existence of a utility function and the structure of non-representable preference relations,” Journal of Mathematical Economics, vol. 37, no. 1, pp. 17–38, 2002.
- K. Eliaz and E. Ok, “Indifference or indecisiveness? choice-theoretic foundations of incomplete preferences,” Games and Economic Behavior, vol. 56, pp. 61–86, 2006.
- J. C. Harsanyi, “Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility,” Journal of political economy, vol. 63, no. 4, pp. 309–321, 1955.
- G. J. Stigler and G. S. Becker, “De gustibus non est disputandum,” The american economic review, vol. 67, no. 2, pp. 76–90, 1977.
- S. O. Hansson, “Changes in preferences,” Theory and Decision, vol. 38, no. 1, pp. 1–28, 1995.
- H. Riess and R. Ghrist, “Diffusion of information on networked lattices by gossip,” in 2022 IEEE Conference on Decision and Control (CDC), (Cancun, Mexico), 2022.
- H. Riess, M. Munger, and M. M. Zavlanos, “Max-plus synchronization in decentralized trading systems,” arXiv preprint arXiv:2304.00210, 2023.
- F. Karacal and R. Mesiar, “Aggregation functions on bounded lattices,” International Journal of General Systems, vol. 46, no. 1, pp. 37–51, 2017.
- C. P. Chambers and A. D. Miller, “Rules for aggregating information,” Social Choice and Welfare, vol. 36, no. 1, pp. 75–82, 2011.
- J.-P. Barthélemy and M. F. Janowitz, “A formal theory of consensus,” SIAM Journal on Discrete Mathematics, vol. 4, no. 3, pp. 305–322, 1991.
- B. Jean-Pierre, L. Bruno, and M. Bernard, “On the use of ordered sets in problems of comparison and consensus of classifications,” Journal of Classification, 1986.
- H. Attiya, M. Herlihy, and O. Rachman, “Atomic snapshots using lattice agreement,” Distributed Computing, vol. 8, pp. 121–132, 1995.
- H. Noorazar, “Recent advances in opinion propagation dynamics: A 2020 survey,” The European Physical Journal Plus, vol. 135, pp. 1–20, 2020.
- M. H. DeGroot, “Reaching a consensus,” Journal of the American Statistical association, vol. 69, no. 345, pp. 118–121, 1974.
- J. Hansen and R. Ghrist, “Opinion dynamics on discourse sheaves,” SIAM Journal on Applied Mathematics, vol. 81, no. 5, pp. 2033–2060, 2021.
- J. Ghaderi and R. Srikant, “Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate,” Automatica, vol. 50, no. 12, pp. 3209–3215, 2014.
- R. Hegselmann and U. Krause, “Opinion dynamics and bounded confidence intervals,” Journal of Artificial Societies and Social Simulation, vol. 5, no. 3, 2002.
- V. D. Blondel, J. M. Hendrickx, and J. N. Tsitsiklis, “On krause’s multi-agent consensus model with state-dependent connectivity,” IEEE Transactions on Automatic Control, 2009.
- M. Hayhoe, F. Alajaji, and B. Gharesifard, “A polya contagion model for networks,” IEEE Transactions on Control of Network Systems, vol. 5, no. 4, pp. 1998–2010, 2017.
- American Mathematical Soc., 1940.
- Springer, 2008.
- A. Dudzik and P. Veličković, “Graph neural networks are dynamic programmers,” arXiv preprint arXiv:2203.15544, 2022.
- A. Dudzik, T. von Glehn, R. Pascanu, and P. Veličković, “Asynchronous algorithmic alignment with cocycles,” arXiv preprint arXiv:2306.15632, 2023.
- S. A. Tailor, F. Opolka, P. Lio, and N. D. Lane, “Do we need anisotropic graph neural networks?,” in International Conference on Learning Representations, 2021.
- University of Michigan press, 1965.
- A. Tarski, “On the calculus of relations,” The Journal of Symbolic Logic, vol. 6, no. 3, pp. 73–89, 1941.
- B. Knaster, “Un theoreme sur les functions d’ensembles,” Ann. Soc. Polon. Math., vol. 6, pp. 133–134, 1928.
- A. Tarski, “A lattice-theoretical fixpoint theorem and its applications,” Pacific journal of Mathematics, vol. 5, no. 2, pp. 285–309, 1955.
- P. Cousot and R. Cousot, “Constructive versions of tarski’s fixed point theorems,” Pacific journal of Mathematics, vol. 82, no. 1, pp. 43–57, 1979.
- M. G. Kendall, “A new measure of rank correlation,” Biometrika, vol. 30, no. 1/2, pp. 81–93, 1938.
- J. H. Kim and V. H. Vu, “Generating random regular graphs,” in Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, pp. 213–222, 2003.
Collections
Sign up for free to add this paper to one or more collections.