From Argumentation Frameworks to Voting Systems and Back

• Autorzy: Benedetti I. , Bistarelli S.

Identyfikatory

DOI

10.3233/FI-2017-1459

• Języki publikacji: EN

Abstrakty

EN

Formal voting theories are established and can be used to determine if a voting system is fair or not in order to preserve democracy. There are a lot of voting systems described in the literature, with several properties, useful in many contexts. The Argumentation Framework is based on the exchange and the evaluation of interacting arguments which may represent information of various kinds. We show that Argumentation Frameworks can be interpreted within a voting theory and considered as voting methods. Using a mapping that associates an argument to a candidate and attacks to votes, we define a bidirectional mapping between the two theories and investigate how fairness criteria defined for voting systems can be re-interpreted within Argumentation Framework. We also show how voting ballots can be seen as suitable semantics for Argumentation Frameworks.

Słowa kluczowe

EN

Argumentation Framework; voting system; arrow fairness criteria; balloting systems; dichotomic preferences

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 150, nr 1
• Strony: 25--48
• Opis fizyczny: Bibliogr. 35 poz., rys., tab.

Twórcy

autor

Benedetti I.

• Dipartimento di Matematica e Informatica, Università di Perugia, Perugia, Italy

autor

Bistarelli S.

• Dipartimento di Matematica e Informatica, Università di Perugia, Perugia, Italy

Bibliografia

• [1] Arrow KJ. A Difficulty in the Concept of Social Welfare. The Journal of Political Economy, 1950: 58 (4): 328-346. URL http://www.jstor.org/stable/1828886.
• [2] Hodge JK, Klima RE. The mathematics of voting and elections: a hands-on approach, volume 22 of Mathematical World. American Mathematical Society, Providence, RI, 2005. ISBN: 0-8218-3798-2.
• [3] Modgil S. Reasoning about preferences in argumentation frameworks. Artif. Intell., 2009. 173 (9-10): 901— 934.
• [4] Dung PM. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning; logic programming and n-person games. Artif. Intell., 1995; 77 (2): 321—357. doi: http://dx.doi.org/10.1016/0004- 3702(94)00041-X.
• [5] Baroni P, Caminada M, Giacomin M. An introduction to argumentation semantics. Knowledge Eng. Review, 2011; 26 (4): 365-410. URL https://doi.org/10.1017/S0269888911000166.
• [6] Benedetti I, Bistarelli S, Piersanti P. On Relating Voting Systems and Argumentation Frameworks. In Giordano L, Gliozzi V, Pozzato GL (eds.), Proceedings of the 29th Italian Conference on Computational Logic, Torino, Italy, June 16-18, 2014., volume 1195 of CEUR Workshop Proceedings. CEUR-WS.org, 2014 pp. 309-313. URL http://ceur-ws.org/Vol-1195/short1.pdf.
• [7] Caminada M. Comparing Two Unique Extension Semantics for Formal Argumentation: Ideal and Eager. In: Proceedings of the 19th Benelux Conference on Artificial Intelligence (BNAIC2007), volume 7, 2007 pp. 81-87.
• [8] Moulin H. Axioms of cooperative decision making, volume 15 of Econometric Society Monographs, Cambridge University Press, 1988. ISBN-10: 0521360552, 13: 978-0521360555.
• [9] Arrow KJ, Sen AK, Suzumura K. Handbook of Social Choice and Welfare, volume 1 of Handbooks in Economics series. North Holland, Elsevier, 2002. ISBN: 978-0-444-50894-2.
• [10] Kilgour MD. Approval balloting in multi-winner elections. In: Laslier JF, Sanver MR (eds.). Handbook of approval voting, pp. 105-124. Springer, 2010. doi: 10.1007/978-3-642-02839-7_6.
• [11] Vorsatz M. Approval voting on dichotomous preferences. Soc Choice Welfare, 2007; 28 ( 1): 127-141. doi: 10.1007/s00355-006-0149-4.
• [12] Maniquet F, Mongin P. Approval voting and Arrow’s impossibility Theorem. Social Choice and Welfare 2015; 44 (3): 519-532. doi: 10.1007/s00355-014-0847-2.
• [13] Arrow KJ Social Choice and Individual Values. John Wiley & Sons, Inc., New York, London, Sydney, 1963, ISBN-10: 0300013647, 13: 978-0300013641.
• [14] Colomer J (ed.). The Handbook of Electoral System Choice. Palgrave Macmillan UK, 2004. doi: 10.1057/9780230522749.
• [15] Yu NN. A one-shot proof of Arrow’s impossibility theorem. Econom. Theory, 2012; 50 (2): 523-525. doi: 10.1007/s00199-012-0693-3.
• [16] Geanakoplos J. Three brief proofs of Arrow’s impossibility theorem. Econom. Theory, 2005; 26 (1): 211-215.
• [17] Goodin RE, List C. A conditional defense of Plurality rule: Generalizing May’s Theorem in a Restricted Informational Environment. American Journal of Political Science, 2006; 50 (4): 940-949. URL http://eprints.lse.ac.uk/5818/.
• [18] Baigent N. Preference Proximity and Anonymous Social Choice. The Quarterly Journal of Economics, 1987; 102 (1): 161-169. doi: 10.2307/1884686.
• [19] Arrow KJ, Sen AK, Suzumura K. Handbook of social choice and Welfare, volume 2 of Handbooks in Economics series. North Holland, Elsevier, 2010. ISBN: 978-0-444-82914-6..
• [20] Chichilnisky G. Social choice and the topology of spaces of preferences. Advances in Mathematics, 1980; 37 (2): 165-176. doi: 10.1016/0001-8708(80)90032-8.
• [21] Kura A (ed.). Electoral College and Presidential Elections. Nova Science Publishers, 2001.
• [22] Hix S, Hyland B (eds.). The Political System of the European Union. The European Union Series. Palgrave Macmillan, 2011. ISBN-13: 978-0230249820, 10: 0230249825.
• [23] Caminada M, Pigozzi G. On judgment aggregation in abstract argumentation. Autonomous Agents and Multi-Agent Systems, 2011; 22 (1): 64-102. doi: 10.1007/s10458-009-9116-7.
• [24] Awad E, Booth R, Tohm F, Rahwan I. Judgement aggregation in multi-agent argumentation. Journal of Logic and Computation, 2015. doi: 10.1093/logcom/exv055. URL http://logcom.oxfordjournals.org/content/early/2015/08/19/logcom.exv055.abstract.
• [25] Leite J, Martins J. Social Abstract Argumentation. In: Walsh T (ed.), IJCAI. IJCAI/AAAI, 2011 pp. 2287-2292. ISBN: 978-1-57735-516-8.
• [26] Eğilmez S, Martins J, Leite J. Extending Social Abstract Argumentation with Votes on Attacks. In: Theory and Applications of Formal Argumentation, Second International Workshop, TAFA 2013, Revised Selected papers, volume 8306 of Lecture Notes in Computer Science. Springer, 2014 pp. 16-31. doi: 10.1007/978-3-642-54373-9_2.
• [27] Evripidou V, Toni F. Argumentation and Voting for an Intelligent User Empowering Business Directory on the Web. In: Web Reasoning and Rule Systems, Proceedings of the 6th International Conference, RR 2012, volume 7497 of Lecture Notes in Computer Science. Springer, 2012 pp. 209-212. doi: 10.1007/978-3-642-33203-6_16.
• [28] Trojahn dos Santos C, Quaresma P, Vieira R, Isaac A. Comparing Argumentation Frameworks for Composite Ontology Matching. In: McBurney P, Rahwan I, Parsons S, Maudet N (eds.), Argumentation in Multi-Agent Systems, 6th International Workshop, ArgMAS 2009. Revised Selected and Invited Papers, volume 6057 of Lecture Notes in Computer Science. Springer, 2010 pp. 305-320. doi: 10.1007/978-3-642-12805-9_18.
• [29] Ontañón S, Plaza E. An Argumentation-Based Framework for Deliberation in Multi-agent Systems. In: Rahwan I, Parsons S, Reed C (eds.), Argumentation in Multi-Agent Systems, 4th International Workshop. ArgMAS 2007. Revised Selected and Invited Papers, volume 4946 of Lecture Notes in Computer Science. Springer, 2008 pp. 178-196. doi: 10.1007/978-3-540-78915-4_12.
• [30] Konieczny S, Pino Pérez R. Logic based merging. J. Philos. Logic, 2011; 40 (2): 239-270. doi:10.1007/s10992-011-9175-5. URL http://dx.doi.org/10.1007/s10992-011-9175-5.
• [31] Sosa-Toranzo C, Schlesinger F, Ferretti E, Errecalde M. Integrating a voting protocol within an argumentation-based BDI System. In: Proceedings of XVI Congreso Argentino de Ciencias de la Computacin (CACIC), XI Workshop Agentes y Sistemas Inteligentes (WASI). 2010 pp. 82-91. URL http://sedici.unlp.edu.ar/handle/10915/18812.
• [32] Pukelsheim F. Electoral reform in Germany: A positive twist to negative voting weights? In: Voting Power in Practice Summer Workshop, Assessing Alternative Voting Procedures. 2010.
• [33] Galam S. Sociophysics: A Physicist’s Modeling of Psycho-Political Phenomena (Understanding Complex Systems). Springer-Verlag, 2012. doi: 10.1007/978-1-4614-2032-3.
• [34] Bistarelli S, Santini F. A Common Computational Framework for Semiring-based Argumentation Systems In: Coelho H, Studer R, Wooldridge M (eds.), ECAI 2010 - 19th European Conference on Artificial Intelligence, Lisbon, Portugal, August 16-20, 2010, Proceedings, volume 215 of Frontiers in Artificial Intelligence and Applications. IOS Press, 2010 pp. 131-136. ISBN: 978-1-60750-605-8. URL http://www.booksonline.iospress.nl/Content/View.aspx?piid=17728.
• [35] Bistarelli S, Santini F. Coalitions of Arguments: An Approach with Constraint Programming. Fundam. Inform., 2013; 124 (4): 383-401. doi: 10.3233/FI-2013-840. URL http://dx.doi.org/10.3233/FI-2013-840.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).