PL EN


2016 | 26 | 2 | 87-106
Article title

On types of responsiveness in the theory of voting

Content
Title variants
Languages of publication
EN
Abstracts
EN
In mathematics, monotonicity is used to denote the nature of the connection between variables. Hence for example, a variable is said to be a monotonically increasing function of another variable if an increase in the value of the latter is always associated with an increase in the other variable. In the theory of voting and the measurement of a priori voting power one encounters, not one, but several concepts that are closely related to the mathematical notion of monotonicity. We deal with such notions focusing particularly on their role in capturing key aspects of plausible opinion aggregation. Further, we outline approaches to analyzing the relationship of opinion aggregation and voting power and thereby contribute to our understanding of major components that determine the outcome of voting.
Year
Volume
26
Issue
2
Pages
87-106
Physical description
Contributors
  • University of Hamburg, Center of Conflict Resolution (CCR), Mittelweg 177, 20148 Hamburg, Germany.
  • Public Choice Research Center (PCRC), University of Turku, Publicum (Assistentinkatu 7) 20014 Turun yliopisto, Finland
author
  • Public Choice Research Centre and Department of Philosophy, Contemporary History and Political Science, University of Turku, Assistentinkatu 7, 20500 Turku, Finland
References
  • ALESKEROV F.T., Arrovian aggregation models, Kluwer, Dordrecht 1999.
  • ALESKEROV F.T., Categories of Arrovian voting schemes, [in:] K. Arrow, A. Sen, K. Suzumura (Eds.), Handbook of Social Choice and Welfare, Elsevier, Amsterdam 2002, 95.
  • ALONSO-MEIJIDE J.M., BOWLES C., Power indices restricted by a priori unions can be easily computed and are useful. A generating function-based application to the IMF, Annals of Operations Research, 2005, 137, 21.
  • ALONSO-MEIJIDE J.M., HOLLER M.J., Freedom of choice and weighted monotonicity of power, Metro- economica, 2009, 60 (4), 571.
  • ALONSO-MEIJIDE J.M., CASAS-MENDEZ B., FIESTRAS-JANEIRO G., HOLLER M.J., The Deegan–Packel index for simple games with a priori unions, Quality and Quantity, 2011, 45 (2), 425.
  • ALONSO-MEIJIDE J.M., BOWLES C., HOLLER M.J., NAPEL S., Monotonicity of power in games with a priori unions, Theory and Decision, 2009, 66, 17.
  • ALONSO-MEIJIDE J.M., ALVARES-MOZOS M., FIESTRAS-JANEIRO G., The Banzhaf value when some players are incompatible, [in:] M.J. Holler, M. Widgrén (Eds.), Essays in honor of Hannu Nurmi, Vol. I, Homo Oeconomicus, 2009, 26, 403.
  • BERG S., HOLLER M.J., Randomized decision rules in voting games: A model of strict proportional power, Quality and Quantity, 1986, 20, 419.
  • BERTINI C., GAMBARELLI G., STACH I., A public help index, [in:] M. Braham, F. Steffen (Eds.), Power, Freedom, and Voting. Essays in Honour of Manfred J. Holler, Springer Verlag, Heidelberg 2008, 83.
  • BRAHAM M., HOLLER M.J., The impossibility of a preference-based power index, Journal of Theoreti-cal Politics, 2005, 17, 137.
  • BRAMS S.J., Game Theory and Politics, Free Press, New York 1975.
  • DEEGAN J., PACKEL E.W., A new index of power for simple n-person games, International Journal of Game Theory, 1979, 7, 113.
  • FELSENTHAL D.S., Review of paradoxes afflicting procedures for electing a single candidate, [in:] D.S. Felsenthal, M. Machover (Eds.), Electoral Systems: Paradoxes, Assumptions, and Procedures, Springer Verlag, Berlin 2012, 19.
  • FELSENTHAL D.S., MACHOVER M., The measurement of Voting Power. Theory and Practice, Problems and Paradoxes, Edward Elgar, Cheltenham 1998.
  • FELSENTHAL D.S., NURMI H., Two types of participation failure under nine voting methods in variable electorates, Public Choice, 2016, 168 (1), 115.
  • FELSENTHAL D.S., TIDEMAN N., Varieties of monotonicity and participation under five voting methods, Theory and Decision, 2013, 75, 59.
  • FISHBURN P., BRAMS S., Paradoxes of preferential voting, Mathematics Magazine, 1983, 56, 207.
  • FREIXAS J., GAMBARELLI G., Common properties among power indices, Control and Cybernetics, 1997, 4, 591.
  • FREIXAS J., KURZ S., The cost of getting local monotonicity, European Journal of Operational Research, 2016, 251, 600.
  • GAMBARELLI G., Minimax apportionments, Group Decision and Negotiation, 1999, 8, 441.
  • GAMBARELLI G., HOLUBIEC J., Power indices and democratic apportionments, [in:] M. Fedrizzi, J. Kacprzyk (Eds.), Proc. 8th Italian-Polish Symposium on Systems Analysis and Decision Support in Economics and Technology, Omnitech Press, Warsaw 1990, 240.
  • GAMBARELLI G., PALESTINI A., Minimax multi-district apportionments, [in:] M.J. Holler, H. Nurmi (Eds.), Power, Voting and Voting Power. 30 Years After, Springer Verlag, Berlin 2013, 169.
  • HOLLER M.J., Forming coalitions and measuring voting power, Political Studies, 1982, 30, 262.
  • HOLLER M.J., Strict proportional power in voting bodies, Theory and Decision, 1985, 19, 249.
  • HOLLER M.J., Power, monotonicity and expectations, Control and Cybernetics, 1997, 26, 605.
  • HOLLER M.J., LI X., From public good index to public value. An axiomatic approach and generaliza-tion, Control and Cybernetics, 1995, 24, 257.
  • HOLLER M.J., NAPEL S., Local monotonicity of power. Axiom or just a property, Quality and Quantity, 2004, 38, 637.
  • HOLLER M.J., NAPEL S., Monotonicity of power and power measures, Theory and Decision, 2004, 56, 93.
  • HOLLER M.J., NURMI H., Measurement of power, probabilities, and alternative models of man, Quality and Quantity, 2010, 44, 833.
  • HOLLER M.J., NURMI H., Reflections on power, voting, and voting power, [in:] M.J. Holler, H. Nurmi (Eds.), Power, Voting, and Voting Power. 30 Years After, Springer Verlag, Berlin 2013, 1.
  • HOLLER M.J., NURMI H., Aspects of power overlooked by power indices, [in:] R. Fara, D. Leech, M. Salles (Eds.), Voting Power and Procedures. Essays in Honour of Dan Felsenthal and Moshé Machover, Springer Verlag, Berlin 2014, 205.
  • HOLLER M.J., NURMI H., Pathology or revelation? The public good index, [in:] R. Fara, D. Leech, M. Salles (Eds.), Voting Power and Procedures: Essays in Honour of Dan Felsenthal and Moshé Machover, Springer Verlag, Berlin 2014, 247.
  • HOLLER M.J., ONO R., STEFFEN F., Constrained monotonicity and the measurement of power, Theory and Decision, 2001, 50, 385.
  • HOLLER M.J., PACKEL E.W., Power, luck and the right index, Zeitschrift für Nationalökonomie, 1983, 43, 21.
  • KANIOVSKI S., KURZ S., The average representation – a cornucopia of power indices? Homo Oeco-nomicus, 2015, 32 (2), 169.
  • KILGOUR D.M., The Shapley value for cooperative games with quarelling, [in:] A. Rapoport (Ed.), Game Theory as a Theory of Conflict Resolution, Reidel, Boston 1974.
  • LAGERSPETZ E., Social choice in the real world, Scandinavian Political Studies, 1993, 16 (1), 1.
  • MASKIN E., The theory of implementation in Nash equilibrium, [in:] L. Hurwicz, D. Schmeidler, H. Sonnenschein (Eds.), Social Goals and Social Organization. Essays in Memory of Elisha Pazner, Cambridge University Press, Cambridge 1985, 173.
  • MOULIN H., Condorcet’s principle implies the no show paradox, Journal of Economic Theory, 1988, 45, 53.
  • NAPEL S., The Holler–Packel axiomatization of the public good index completed, Homo Oeconomicus, 1999, 15, 513.
  • NAPEL S.WIDGRÉN M., The possibility of a preference-based power index, Journal of Theoretical Pol-itics, 2005, 17, 377.
  • NURMI H., Comparing voting systems, Reidel, Dordrecht 1987.
  • NURMI H., Voting procedures under uncertainty, Springer Verlag, Berlin 2002
  • NURMI H., On the relevance of theoretical results to voting system choice, [in:] D. Felsenthal, M. Machover (Eds.), Electoral Systems. Paradoxes, Assumptions, and Procedures, Springer Verlag, Berlin 2012, 255.
  • PÉREZ J., Incidence of no show paradoxes in Condorcet choice functions, Investigaciones Economicas, 1995, 14, 139.
  • PÉREZ J., The strong no show paradoxes are common flaw in Condorcet voting correspondences, Social Choice and Welfare, 2001, 18, 601.
  • RICHELSON J.T., Majority Rule and Collective Choice, Mimeo 1980.
  • TURNOVEC F., Monotonicity and power indices, [in:] T.J. Stewart, P.S. van den Honert (Eds.), Trends in Multicriteria Decision Making. Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin 2008, 465.
  • TURNOVEC F., Strict proportional power and optimal quota, Homo Oeconomicus, 2011, 27 (4), 463.
  • WEBER M., Class, status and party, [in:] H.H. Gerth, C.W. Mills (Eds.), Essays from Max Weber, Routledge and Kegan Paul, London 1948 [1924].
  • WIDGRÉN M., On the probabilistic relationship between the public good index and the normalized Banzhaf index, [in:] M.J. Holler, G. Owen (Eds.), Power Measures, Vol. 2, Homo Oeconomicus, 2002, 19 (3), 373.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-06e2fa26-0961-49da-8b87-0ea655f225dc
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.