An approach from bankruptcy rules applied to the apportionment problem in proportional electoral systems

• Authors: SÁNCHEZ-SORIANO Joaquín , LLORCA Natividad , ALGABA Encarnación
• Languages of publication: EN

Abstracts

EN

(Discrete) bankruptcy problems associated with apportionment problems have been defined. The authors studied which allocations for apportionment problems have been obtained when (discrete) bankruptcy rules were applied to the associated bankruptcy problems. They have shown that the (discrete) constrained equal losses rule coincides with the greatest remainder method for apportionment problems. Furthermore, new properties related to governability have been proposed for apportionment methods. Finally, several apportionment methods satisfying governability properties have been applied to the case of the Spanish Elections in 2015.

Keywords

EN

apportionment rules; bankruptcy rules; standard of comparisons; proportional electoral sys-tems; governability

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2016
• Volume: 26
• Issue: 2
• Pages: 127-145

Contributors

author

SÁNCHEZ-SORIANO Joaquín

• Center of Operations Research (CIO), Miguel Hernandez University of Elche, Avinguda de la Uni-versitat d’Elx, 03202 Elx, Alicante, Spain

author

LLORCA Natividad

• Center of Operations Research (CIO), Miguel Hernandez University of Elche, Avinguda de la Uni-versitat d’Elx, 03202 Elx, Alicante, Spain

author

ALGABA Encarnación

• Department of Applied Mathematics II, University of Seville, Camino Descubrimientos, S/N. Isla Cartuja, C.P: 41092 Sevilla), Spain

References

• AUMANN R.J., MASCHLER M., Game theoretic analysis of a bankruptcy problem from the Talmud, Journal of Economic Theory, 1985, 36, 195.
• BALINSKI M.L., RAMIREZ V., Parametric methods of apportionment, rounding and production, Math-ematical Social Sciences, 1999, 37, 107.
• BALINSKI M.L., YOUNG H.P., A new method for congressional apportionment, Proceedings of the Na-tional Academy of Sciences of the United States of America, USA, 1974, 71, 4602.
• BALINSKI M.L., YOUNG H.P., On Huntington methods of apportionment, SIAM Journal on Applied Mathematics, 1977, 33, 607.
• BALINSKI M.L., YOUNG H.P., Fair representation. Meeting the ideal of one man, one vote, Yale Uni-versity Press, New Haven 1982.
• CHEN S., Systematic favorability in claims problems with indivisibilities, Social Choice and Welfare, 2015, 44, 283.
• CURIEL I., A multifaceted analysis of the electoral system of the Republic of Suriname, Operations Research and Decisions, 2014, 24, 29.
• DE FRUTOS M.A., Coalitional manipulations in a bankruptcy problem, Review of Economic Design, 1999, 4, 255.
• [9] FERNANDEZ GARCIA F.R., Sobre repartos ..., Universidad de Sevilla, Sevilla 2008 (in Spanish).
• [10] FRAGNELLI V., GAGLIARDO S., GASTALDI F., Integer solutions to bankruptcy problems with non-inte-ger claims, TOP, 2014, 22, 892.
• FRAGNELLI V., GAGLIARDO S., GASTALDI F., Bankruptcy problems with non-integer claims: definition and characterizations of the ICEA Solution, TOP, 2015, forthcoming.
• GALLAGHER M., Proportionality, disproportionality and electoral systems, Electoral Studies, 1991, 10, 33.
• GAMBARELLI G., Minimax apportionments, Group Decision and Negotiation, 1999, 8, 441.
• GAMBARELLI G., PALESTINI A., Minimax multi-district apportionments, Homo Oeconomicus, 2007, 23, 335.
• GIMENEZ-GOMEZ J.M., MARCO M.C., A new approach for bounding awards in bankruptcy problems, Social Choice and Welfare, 2014, 43, 447.
• GIMENEZ-GOMEZ J.M., VILELLA C., A note on discrete claims problems, CREIP, Working paper No. 19, 2012.
• HERRERO C., MARTINEZ R., Egalitarian rules in claims problems with indivisible goods, Instituto Va-lenciano de Investigaciones Económicas, IVIE-WP-AD, 2004, 20, 1.
• HERRERO C., MARTINEZ R., Up methods in the allocation of indivisibilities when preferences are sin-gle-peaked, TOP, 2008, 16, 272–283.
• HERRERO C., MARTINEZ R., Balanced allocation methods for claim problems with indivisibilities, So-cial Choice and Welfare, 2008, 30, 603.
• HOROWITZ D.L., Electoral systems. A primer for decision makers, Journal of Democracy, 2003, 14, 115.
• LIJPHARDT A., Degrees of proportionality of proportional representation formulas, [in:] B. Grofman, A. Lijphardt (Eds.), Electoral laws and their political consequences, Agathon, New York 1986, 170.
• LUCAS W.F., The apportionment problem, [in:] S.J. Brams, W.F. Lucas, P.D. Straffin Jr. (Eds.), Polit-ical and Related Models, Springer-Verlag, New York 1983, 358.
• LUCAS-ESTAÑ M.C., GOZALVEZ J., SÁNCHEZ-SORIANO J., PULIDO M., CALABUIG D., Multi-channel ra-dio resource distribution policies in heterogeneous traffic scenarios, [in:] Proceedings IEEE 66th Ve-hicular Technology Conference (VTC2007-Fall), Baltimore 2007, 1674.
• LUCAS-ESTAÑ M.C., GOZALVEZ J., SÁNCHEZ-SORIANO J., Bankruptcy-based radio resource manage-ment for multimedia mobile networks, Transactions on Emerging Telecommunications Technologies, 2012, 23, 186.
• MAIER S., ZACHARIASSEN P., ZACHARIASSEN M., Divisor-based bipropotional apportionment in elec-toral systems: a real-life benchmark study, Management Science, 2010, 56, 373.
• MARTINEZ-PUJALTE A.L., Los sistemas electorales españoles: Evaluación y propuestas de reforma, Editorial Dykinson S.L., 2010 (in Spanish).
• MERCIK J.W., A priori veto power of the President of Poland, Operations Research and Decisions, 2009, 19, 61.
• MOULIN H., The proportional random allocation of indivisible units, Social Choice and Welfare, 2002, 19, 381.
• MOULIN H., STONG R., Fair queuing and other probabilistic allocation methods, Mathematics of Operations Research, 2002, 27, 1.
• MOULIN H., STONG, R., Filling a multicolor urn: an axiomatic analysis, Games and Economic Behav-ior, 2003, 45, 242.
• PULIDO M., BORM P., HENDRICKX R., LLORCA N., SÁNCHEZ-SORIANO J., Compromise solutions for bankruptcy situations with references, Annals of Operations Research, 2008, 158, 131.
• PULIDO M., SÁNCHEZ-SORIANO J., LLORCA N., Game theory techniques for university management. A generalized bankruptcy model, Annals of Operations Research, 2002, 109, 129.
• SÁNCHEZ-SORIANO J., Aspectos numéricos de la democracia, [in:] A.L. Martínez-Pujalte (Ed.), Los Sistemas Electorales Españoles: Evaluación y propuestas de reforma, Editorial Dykinson S.L., 2010, 175 (in Spanish).
• THOMSON W., Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey, Mathematical Social Sciences, 2003, 45, 249.
• THOMSON W., Axiomatic and game-theoretic analysis of bankruptcy and taxation problems. A survey, Mathematical Social Sciences, 2015, 74, 41.
• YOUNG H.P., Equity in theory and practice, Princeton University Press, Princeton 1994.

Identifiers

DOI

10.5277/ord160208