Once Again: The Positivist Weight Formula
DOI:
https://doi.org/10.52292/j.dsc.2026.4804Keywords:
Alexy's Weight Formula, Positivist Weight Formula, Proportionality, Laws of Balancing, Intensity of Judicial ReviewAbstract
In normative systems where the German model of proportionality has been adopted as law, the two “laws of balancing” (substantive and epistemic) form the normative framework of balancing. Thus, a decision of balancing (legislative or judicial) is legitimate if and only if it does not violate such “laws”. Yet, the problem is that, despite the consensus about their content, their mathematical expression in Alexy’s weight formula is highly criticizable, mainly because it does not consider that they are mere limits of discretion (and not norms of preference). Attempting to express the constant of direct proportionality included in each one of them, a formula is presented, containing only the variables representing the normative content of such “laws”. It is an equation that aims to be the mathematical correct formulation of the internal justification of a balancing decision.
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References
Alexy, R. (2014a). Constitutional Rights and Proportionality. Revus, 22, 51-65.
Alexy, R. (2014b). Formal Principles: Some Replies to Critics. International Journal of Constitutional Law, 12(3), 511-524.
Alexy, R. (2006). Discourse Theory and Fundamental Rights. En A. Menendez (ed.), Arguing for Fundamental Rights (pp. 15-32). Dordrecht: Springer.
Alexy, R. (2003). On Balancing and Subsumption. A Structural Comparison. Ratio Juris, 16(4), 433-449.
Bana e Costa, C. y Vansnick, J. (1994). Macbeth. An Internal Path Towards the Construction of Cardinal Value Functions. International Transactions in Operational Research, 1(4), 489-500.
Barak, A. (2013). Proportionality. Constitutional Rights and their Limitations. Cambridge: Cambridge University Press.
Bernal Pulido, C. (2007). El Principio de Proporcionalidad y los Derechos Fundamentales. 3a ed. Madrid: Centro de Estudios Políticos y Constitucionales.
Bernal Pulido, C. (2006). On Alexy ́s Weight Formula. En A. Menéndez (ed). Arguing for Fundamental Rights (pp. 101-110). Dordrecht: Springer.
Borowski, M. (2013). On Apples and Oranges. Comment on Niels Petersen. German Law Journal, 14, 1409-1420.
Chang, R. (2002). Make Comparisons Count. Londres: Routledge.
Clerico, L. (2008). El Examen de Proporcionalidad en el Derecho Constitucional. Buenos Aires: Eudeba.
DeVellis, R. (2017). Scale Development, 4ta ed. Los Angeles: Sage.
Duarte, D. (2021). From Constitutional Discretion to the Positivist Weight Formula. En J. Sieckmann (ed.), Proportionality, Balancing, and Rights: Robert Alexy’s Theory of Constitutional Rights (pp. 21-73). Cham: Springer.
Duarte, D. (2018). Gains and Losses in Balancing Social Rights. En D. Duarte y J. Silva Sampaio (eds.), Proportionality in Law: An Analytic Perspective (pp. 49-70). Cham: Springer.
Duarte, D. (2010). Normative Conditions of Balancing: Drawing Up The Boundaries of Normative Conflicts That Lead to Balances. En J.
Sieckmann (ed.), Legal Reasoning: the Methods of Balancing (pp. 51-62). Stuttgart: Franz Steiner Verlag.
Guibourg, R. (2010). On Alexy´s Weighing Formula. En J. Sieckmann (ed.), Legal Reasoning: the Methods of Balancing (pp. 145-160). Stuttgart: Franz Steiner Verlag.
Habermas, J. (1996). Between Facts and Norms. Cambridge: The MIT Press.
Hage, J. (2005). Studies in Legal Logic. Dordrecht: Springer.
Jestaedt, M. (2012). The Doctrine of Balancing – Its Strengths and Its Weaknesses. En M. Klatt (ed.), Institutionalized Reason. The Jurisprudence of Robert Alexy (pp. 152-171). Oxford: Oxford University Press.
Klatt, M. y Meister, M. (2012). The Constitutional Structure of Proportionality. Oxford: Oxford University Press.
Klatt, M. y Schmidt, J. (2012). Epistemic Discretion in Constitutional Law. International Journal of Constitutional Law, 10, 69-105.
Kumm, M. (2012). Alexy´s Theory of Constitutional Rights and the Problem of Judicial Review. En M. Klatt (ed.), Institutionalized Reason. The Jurisprudence of Robert Alexy (pp. 201-217). Oxford: Oxford University Press.
Lindhal, L. (2009). On Robert Alexy´s Weight Formula for Weighing and Balancing. En J. A. Raposo, J. Lopes Alves, P. de Sousa Mendes, A. Silva Dias, y L. Duarte D’Almeida (eds.), Liber Amicorum de José de Sousa e Brito: em comemoraçao do 70.° aniversário; estudos de direito e filosofia (pp. 355-376). Coimbra: Almedina.
Mendonca, D. (2006). Los Derechos en Juego, Conflicto y Balance de Derechos. Madrid: Tecnos.
Moreso, J. J. (2007). Alexy y la Aritmetica de la Ponderacion. En R. Garcia Manrique (de.), Derechos Sociales y Ponderación (pp. 223-247). Madrid: Fundacion Coloquio Juridico Europeu.
Petersen, N. (2017). Proportionality and Judicial System. Cambridge: Cambridge University Press.
Poscher, R. (2020). Resuscitation of a Phantom? On Robert Alexy’s Latest Attempt to Save His Concept of Principle. Ratio Juris, 33(2), 134-149.
Ratti, G. y Rodriguez, J. (2022). Estructura y Coherencia de los Sistemas Jurídicos. Madrid: Marcial Pons.
Rivers, J. (2012). Constitutional Rights and Statutory Interpretation. En M. Klatt (ed.), Institutionalized Reason. The Jurisprudence of Robert Alexy (pp. 248-273). Oxford: Oxford University Press.
Rivers, J. (2007). Proportionality, Discretion and the Second Law of Balancing. En G. Pavlakos (ed.), Law, Rights and Discourse: The Legal Philosophy of Robert Alexy. (pp. 167-188). Londres: Hart Publishing.
Sampaio, J. S. (2023). Ponderaçao e Proporcionalidade. II. Coimbra: Almedina.
Sartor, G. (2018). A Quantitative Approach to Proportionality. En G. Bongiovanni, G Postema y otros (eds.), Handbook of Legal Reasoning and Argumentation (pp. 613-635). Dordrecht: Springer.
Sartor, G. (2013). The Logic of Proportionality: Reasoning with Non-Numerical Magnitudes. German Law Journal, 14(8),1419-1456.
Sartor, G. (2010). Doing Justice to Rights and Values: Teleological Reasoning and Proportionality. Artificial Intelligence and Law, 14, 175- 215.
Sieckmann, J. (2012). The Logic of Autonomy. Oxford: Hart Publishing.
Sieckmann, J. (2010). Balancing, Optimisation, and Alexy´s “Weight Formula”. En J. Sieckmann (ed.), Legal Reasoning: the Methods of Balancing (pp. 101-118). Stuttgart: Franz Steiner Verlag.
Tsakyrakis, S. (2009). Proportionality: An Assault on Human Rights? International Journal of Constitutional Law, 7(3), 468–493.
Tushnet, M. (2008). Weak Courts, Strong Rights. Princeton: Princeton University Press.
Young, K. (2010). A Tipology of Economic and Social Rights Adjudication: Exploring the Catalytic Function of Judicial Review. International Journal of Constitutional Law, 8, 385-420.
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