Open Journal Systems

COMPARABILITY, DECISION THEORY AND THE AHP

Sibs von Solms

Abstract


Saaty (2011) briefly discusses the three basic laws of Aristotelian logic and suggests a fourth, which he calls the Law of Comparisons.  He argues that comparison is both relevant and essential to the other three laws and, in fact, precedes them.  This view - comparativism - is however, not without criticism.  Here we present a more comprehensive discussion of various problems regarding comparability, focusing on three aspects; (i) the problem of a proper scale; (ii) the problem of a proper aggregation of conflicting criteria and (iii) the debate whether values are subjective or objective.  The debate regarding incomparability is varied and intense making a perfunctory or uncritical acceptance of comparativism wrong.  However, Saatian Comparativism will be shown to be a solution to the major issues raised by incomparativists.  Two conclusions are reached; (i) Saaty’s (2011) view is confirmed and (ii) the work of Saaty is not reflected in the incomparability or incommensurability literature and this debate stands to be enriched by seriously considering Saatian Comparativism.


Keywords


Analytic Hierarchy Process; Covering Value; Incomparability; Incommensurability; Value Realism.

Full Text:

PDF

References


Acton, G.S. (2003). What is good about Rasch measurement? Rasch Measurement Transactions, 16(4), 902-903.

Aldred, J. (2002). Cost-benefit analysis, incommensurability and rough equality. Environmental Values, 11(1), 27-47. doi: 10.3197/096327102129340966

Aldred, J. (2006). Incommensurability and monetary valuation. Land Economics, 82(2), 141-16.

Anderson, E. (1997). Practical reason and incommensurable goods. In Chang, R. (Ed), Incommensurability, incomparability and practical reason. Cambridge, MA: Harvard University Press.

Arneson, RJ. (1999). Human flourishing versus desire satisfaction. Social Philosophy and Policy, 16(1), 113-142.

Arneson, RJ. (2010). Good, period. Analysis, 70(4), 731-744. doi: 10.1093/analys/anq019

Arrow, KJ. (1951). Social choice and individual values. New York, NY: John Wiley & Sons.

Arrow, KJ & Raynaud, H. (1986). Social choice and multicriterion decision-making. Cambridge, MA: MIT Press.

Barrett, PT. (2003). Beyond psychometrics: Measurement non-quantitative structure and applied numerics. Journal of Managerial Psychology, 18(5), 421-439. doi: 10.1108/02683940310484026

Bisdorff, R. (2004). Concordant outranking with multiple criteria of ordinal significance. 4OR, 2(4), 293-308. doi: 10.1007/s10288-004-0053-7

Boot, M. (2007). Incommensurability, incomplete comparability and the scales of justice. DPhil Dissertation; Balliol College, Oxford, UK: University of Oxford.

Boot, M. (2009). Parity, incomparability and rationally justified choice. Philosophical Studies, 146 (1), 75-92. doi: 10.1007/s11098-008-9245-x

Bouyssou, D. (2001). Outranking methods. In Floudas, C.A. & Pardalos, P.M. (Eds), Encyclopedia of optimization. London, UK: Kluwer Academic Publishers.

Bouyssou, D., Marchant, T., Pirlot, M., et al. (2000). Evaluation and decision model: A critical perspective. Dordrecht, The Netherlands: Kluwer Academic Publishers.

Bowden, B & Swartz, N., (2004). Truth. The internet encyclopedia of philosophy. on-line at http://www.iep.utm.edu/t/truth.htm

Bradley, B. (2014). Objective theories of well-being. In Eggleston, B. & Miller, D.E. (Eds), The Cambridge companion to utilitarianism. Cambridge, UK : Cambridge University Press.

Brans, J-P. & Mareschal, B. (2005). PROMETHEE methods. In Figueira, J. Greco, & Ehrgott, M. (Eds), Multiple Criteria Decision Analysis: State of the art surveys. New York, NY: Springer Science & Business Media Inc.

Broome, J. (1997). Is incommensurability vagueness? In Chang, R (Ed), Incommensurability, incomparability and practical reason. Cambridge, MA: Harvard University Press.

Broome, J. (2000). Incommensurable values. In Crisp, R. & Hooker, B. (Eds); Well-being and morality: Essays in honour of James Griffin. Oxford, UK: Clarendon Press.

Chang, R.E. (1997). Introduction. In Chang, R.E. (Ed), Incommensurability, incomparability and practical reason. Cambridge, MA: Harvard University Press.

Chang, R.E. (1998). Comparison and the justification of choice. University of Pennsylvania Law Review, 146(5), 1569-1598.

Chang, R.E. (2001). Against constitutive incommensurability or buying and selling friends. Philosophical Issues, 11(1), 33-60. doi: 10.1111/0029-4624.35.s1.2

Chang, R.E. (2002a). The possibility of parity. Ethics, 112(4), 659-688. doi: 10.1086/339673

Chang, R.E. (2002b). Making comparisons count. London, UK: Routledge.

Chang, R.E. (2004a). All things considered. Philosophical Perspectives, 18(1), 1-22.

Chang, R.E. (2004b). Putting together morality and well-being. In Baumann, P. & Betzler, M. (Eds), Practical conflicts. Cambridge, UK: Cambridge University Press.

Chang, R.E. (2004c). Can desires provide reasons for action? In Wallace, R.J., Pettit, P., Scheffler, S. & Smith, M. (Eds), Reasons and value: Themes from the philosophy of Joseph Raz. Oxford, UK: Oxford University Press.

Chang, R.E. (2012). Value pluralism. In Wright, J.D. (Ed), International encyclopedia of the social and behavioral sciences, 2nd Edition. Oxford, UK: Elsevier Publishers.

Chang, R.E. (2013). Incommensurability (and incomparability). In LaFollette, H. (Ed); International encyclopedia of ethics. Hoboken, NJ: Blackwell-Wiley.

Checkland, P.B. & Scholes, J. (1990). Soft systems methodology in action. Chichester, UK: John Wiley & Sons.

Coello Coello, C.A. (2000). Handling preferences in evolutionary multiobjective optimization: A survey. 2000 Congress on Evolutionary Computation, 30-27. Piscataway, NJ; IEEE Service Center.

Crisp, Rb (2013)b Well-being; In Zalta, E.N. (Ed); The Stanford encyclopedia of philosophy. on-Line at http://plato.stanford.edu/archives/sum2013/entries/well-being

da Silva, VA. (2011). Comparing the incommensurable: Constitutional principles, balancing and rational decision. Oxford Journal of Legal Studies, 31(2), 273-301. doi: 10.1093/ojls/gqr004

Dembczyński, K., Kotlowski, W. & Slowiński, R. (2007). Ordinal classification with decision rules. In Raś, Z.W., Tsumoto, S. & Zighed, D. (Eds), Proceedings of the 3rd International Workshop, Mining Complex Data; Warsaw, Poland.

Dorsey, D. (2012). Intrinsic value and the supervenience principle. Philosophical Studies, 157(2), 267-285. doi: 10.1007/s11098-010-9636-7

Edmundson, W.A. (2009). Pluralism, intransitivity, incoherence. In White, M.D. (Ed), Theoretical foundations of law and economics. Cambridge, UK: Cambridge University Press.

Ellis, S. (2008). The main argument for value incommensurability (and why it fails). Southern Journal of Philosophy, 46(1), 27-43. doi: 10.1111/j.2041-6962.2008.tb00068.x

Ellis, S. (2012). Prioritizing multiple objectives: Feeling our way. Working Paper; Department of Philosophy, Norman, OK: University of Oklahoma. available On-Line at www.ou.edu/ouphil/faculty/ellis/Prioritizing.pdf

Eriksson, L., (2003). Completeness and incomparability: Limits of RCT. Annual Meeting of the American Political Science Association, Philadelphia, PA. on-line at www.allacademic.com/meta/p62882_index.html

Forman, E.H. & Peniwati, K. (1998). Aggregating individual judgments and priorities with the Analytic Hierarchy Process. European Journal of Operational Research, 108(1), 165-169.

Forman, E.H. & Selly M.A. (2001). Decision by objectives: How to confine others that you are right. Singapore: World Scientific Publications.

Geldermann, J., Spengler, T. & Rentz, O. (2000). Fuzzy outranking for environmental assessment: case study: Iron and steel making industry. Fuzzy Sets and Systems, 115(1), 45-65. doi:10.1016/S0165-0114(99)00021-4

Gert, J. (2004). Value and parity. Ethics, 114(3), 492-510.

Gowdy, J. & Erickson, J.D. (2005). The approach of ecological economics. Cambridge Journal of Economics, 29(2), 207-222. doi: 10.1093/cje/bei033

Greco, S., Matarazzo, B. & Slowiński, R. (2005). Decision rule approach. In Figueira, J., Greco, S. & Ehrgott, M. (Eds), Multiple Criteria Decision Analysis: State of the art surveys. New York, NY: Springer Science & Business Media Inc.

Griffin, J. (1997). Incommensurability: What’s the problem?. In Chang, R. (Ed), Incommensurability, incomparability, and practical reason. 35 Cambridge, MA: Harvard University Press.

Grimm, S.R. (2003). Is incommensurability a problem for practical reason? Paper Presented at Columbia/NYU Graduate Conference in Philosophy, New York, NY: New York University.

Grimm, S.R. (2007). Easy cases and value incommensurability. Ratio, 20(1), 26-44. doi: 10.1111/j.1467-9329.2007.00344.x

Harris, G.W. (2001). Value vagueness, zones of incomparability and tragedy. American Philosophical Quarterly, 38(2), 155-176.

Heathwood, C. (2014). Subjective theories of well-being. In Eggleston, B. & Miller, D.E. (Eds), The Cambridge companion to utilitarianism. Cambridge, UK: Cambridge University Press.

Hsieh, N-H.; (2005a). Equality, clumpiness and incomparability. Utilitas, 17(2), 180-204. doi: http://dx.doi.org/10.1017/S0953820805001512

Hsieh, N-H. (2005b). Value maximization, incomparability and managerial choice. 3rd Biennial Global Conference on Business Ethics. Santa Clara, CA: Santa Clara University.

Hsieh, N-H. (2007). Incommensurable values. In Zalta, E.N. (Ed), The Stanford encyclopedia of philosophy; on-line at http://plato.stanford.edu/entries/value-incommensurable

Hurley, S.L. (1985). Supervenience and the possibility of coherence, Mind, 94(376), 501-525. doi:10.1093/mind/XCIV.376.501

Hurley, S.L. (1989). Natural reasons, personality and polity. New York, NY: Oxford University Press.

Jackson, M.C. (2003). Systems thinking: Creative holism for managers. Chichester, UK: John Wiley & Sons.

Kekes, J. (1992). Pluralism and conflict in morality. Journal of Value Inquiry, 26(1), 37-50. doi: 10.1007/BF00136589

Kelly, C. (2008). The impossibility of incommensurable values. Philosophical Studies, 137(3), 369-382. doi: 10.1007/s11098-006-0005-5

Klocksiem, J. (2010). In defense of the trichotomy thesis. Acta Analytica, 25(3), 317-327. doi: 10.1007/s12136-009-0067-z

Kornhauser, L.A. (1998). No best answer?, University of Pennsylvania Law Review, 146(5), 1599-1637.

Laitenin, A. (2008). Strong evaluation without moral sources. Berlin, Germany: Walter de Gruyter GmbH & Co.

List, C. (2013). Social choice theory. In Zalta, E.N. (Ed), The Stanford encyclopedia of philosophy. on-line at http://plato.stanford.edu/archives/win2013/entries/social-choice

Luban, D. (2001). Value pluralism and rational choice, Georgetown University Law Center Working Paper No 264335, Washington, DC: Georgetown University.

Martinez-Alier, J. Munda, G. & O’Neill, J. (1998). Weak comparability of values as a foundation for ecological economics. Ecological Economics, 26(3), 277-286.

Mason, E. (2011). Value pluralism. In Zalta, E.N. (Ed); The Stanford encyclopedia of philosophy, published on-line at http://plato.stanford.edu/entries/value-pluralism

Mather, H.S. (2002). Law-making and incommensurability. McGill Law Journal, 47(2), 345-388.

May, K.O. (1954). Intransitivity, utility and the aggregation of preference patterns. Econometrica, 22(1), 1-13.

Michell, J. (1997). Quantitative science and the definition of measurement in psychology. British Journal of Psychology, 88(3), 355-383.

Michell, J. (2003). The quantitative imperative - Positivism, naive realism and the place of qualitative methods in psychology. Theory and Psychology, 13(1), 5-31.doi: 10.1177/0959354303013001758

Michell, J. (2008). Is psychometrics pathological science?, Measurement, 6(1-2), 7-24. doi: 10.1080/15366360802035489

Mingers, J.C. (2008). Management knowledge and knowledge management: Realism and forms of truth. Knowledge Management Research & Practice, 6(1), 62-76. doi: 10.1057/palgrave.kmrp.8500161

Munda, G. (2004). Social Multi-Criteria Evaluation (SMCE): Methodological foundations and operational consequences. European Journal of Operational Research, 158(3), 662-677. doi:10.1016/S0377-2217(03)00369-2

Munda, G. (2012). Choosing aggregation rules for composite indicators. Social Indicators Research, 109(3), 337-354. doi:10.1007/s11205-011-9911-9

Munda, G. Nijkamp, P. & Rietveld, P. (1994). Qualitative multicriteria evaluation for environmental management, Ecological Economics 10(2), 97-112. doi: 10.1016/0921-8009(94)90002-7

Murphy, M.C. (1999). The simple desire-fulfillment theory. Nous, 33(2), 247–272.

Nooteboom, B. (1984). Intransitive preferences in retailing. Services Industries Journal, 4(1), 82-92.

Okapal, J.M. (2007). Comparative choice without comprehensive factors. 104th Annual Meeting of the American Philosophical Association, Chicago, IL Central Division.

Okapal, J.M. (2010). Problematic arguments for comprehensive values. Florida Philosophical Review, 10(1), 43-74.

O’Neill, J. (1997). Value pluralism, incommensurability and institutions. In Foster, J. (Ed), Valuing nature? Ethics, economics and the environment. London, UK: Routledge.

Pildes, R.H. & Anderson, E.S. (1990). Slinging arrows at democracy: Social Choice Theory, value pluralism and democratic politics. Columbia Law Review, 90(8), 2121-2214.

Qizilbash, M. (2000). Comparability of values, rough equality and vagueness: Griffin and Broome on incommensurability. Utilitas, 12(2), 223-240.

Qizilbash, M. (2005). The mere addition paradox, incompleteness and vagueness, Conference on Broome’s Weighing Lives. London School of Economics; University of London.

Rabinowicz, W. (2008). Value relations. Theoria, 74(1), 18-49. doi: 10.1111/j.1755-2567.2008.00008.x

Railton, P. (1986). Moral realism. Philosophical Review, 95(2), 163-207. doi: 10.2307/2185589

Rauschmayer, F. (2001). Philosophical aspects of incommensurability and incomparability, Informatica, 12(1), 119-132.

Raz, J. (1986). The morality of freedom. Oxford, UK: Clarendon Press.

Raz, J. (1997). Incommensurability and agency. In Chang, R.E. (Ed), Incommensurability, incomparability and practical reason. Cambridge, MA: Harvard University Press.

Rescher, N. (1973). The coherence theory of truth. Oxford, UK: Clarendon Press.

Richardson, H.S. (1994). Practical reasoning about final ends. Cambridge, UK: Cambridge University Press.

Rorty, R. (1991). Objectivity, relativism and truth: Philosophical papers. Cambridge, UK: Cambridge University Press.

Rosati, C.S. (1995). Persons, perspectives and full information accounts of the good. Ethics, 105(1), 296-325. doi: 10.1086/293702

Roy, B. & Vincke, P. (1984). Relational systems of preference with one or more pseudo-criteria: Some new concepts and results. Management Science, 30(11), 1323-1335. http://dx.doi.org/10.1287/mnsc.30.11.1323

Saaty, T.L. (2000). Fundamentals of decision making and priority theory with the Analytic Hierarchy Process. Pittsburgh, PA: RWS Publications.

Saaty, T.L. (2001). Decision-making with dependence and feedback: The Analytic Network Process; 2nd Edition. Pittsburgh, PA: RWS Publications.

Saaty, T.L. (2010). Principia mathematica decernendi: Mathematical principles of decision-making. Pittsburgh, PA: RWS Publications.

Saaty, T.L. (2011). The serious omission of comparisons in Aristotle’s laws of thought. International Journal of the Analytic Hierarchy Process, 3(2), 180-181. doi: http://dx.doi.org/10.13033/ijahp.v3i2.124

Saaty, T.L. (2013). On the measurement of intangibles: A principal eigenvector approach to relative measurement derived from paired comparisons. Notices of the American Mathematical Society, 60(2), 192-208.

Saaty, T.L. & Peniwati, K. (2008). Group decision making: Drawing out and reconciling differences. Pittsburgh, PA: RWS Publications.

Saaty, T.L. & Sagir, M. (2009). Extending the measurement of tangibles to intangibles, International Journal of Information Technology and Decision Making, 8(1), 7-27. doi: 10.1155/2012/873710

Saaty, T.L. & Vargas, L.G. (2005). The possibility of group welfare functions. International Journal of Information Technology & Decision Making, 4(2), 167-176. doi:10.1007/s00355-011-0541-6

Saaty, T.L. & Vargas, L.G. (2009). Decision-making with the Analytic Network Process: Economical, political, social and technological applications with benefits, opportunities, cost and risks, 2nd Edition; New York, NY: Springer Science & Business Media.

Saaty, T.L. & Vargas, L.G. (2012). Models, methods, concepts and applications of the Analytic Hierarchy Process, 2nd Edition. New York, NY: Springer Science & Business Media.

Sen, A.K. (1995). Rationality and social choice. American Economic Review, 85(1), 1-24.

Seung, T.K. & Bonevac, D. (1992). Plural values and indeterminate rankings. Ethics, 102(4), 799-813.

Simpson, L. (1996). Do decision makers know what they prefer?: MAVT and ELECTRE II. Journal of the Operational Research Society, 47(7), 919-929.

Sunstein, C.R. (1997). Incommensurability and kinds of valuation: Some applications in law. In Chang, R.E. (Ed), Incommensurability, incomparability and practical reason. Cambridge, MA: Harvard University Press.

Thomson, J.J. (1997). The right and the good. Journal of Philosophy 94(6), 273-298. doi: jphil199794637

Tiberius, V. (2008). The reflective life: Living wisely with our limits. Oxford, UK: Oxford University Press.

Vargas, L.G. (1994). Comparison of three multicriteria decision making methodologies: The Analytic Hierarchy Process, Multiattribute Utility Theory and Outranking Methods, Proceedings of the 3rd International Symposium on the Analytic Hierarchy Process, Washington, DC.

Vincke, P. (2000). {P,Q,I,J} – Preference Structures. In Fodor, J. De Baets, B. & Perny, P. (Eds), Preference and decisions under incomplete knowledge. New York, NY: Physica-Verlag.

von Mises, L. (1998). Human sction: A treatise on rconomics, Scholar’s Edition. Auburn, AL: Ludwig von Mises Institute.

von Solms, S.H. (2009). Homogeneity and choice aggregation in the Analytic Hierarchy Process. Proceedings 10th International Symposium on the Analytic Hierarchy Process, Pittsburgh, PA: University of Pittsburgh.

von Solms, S.H. (2011). Validity of the AHP/ANP: Comparing apples and oranges, International Journal of the Analytic Hierarchy Process, 3(1), 2-27. doi: http://dx.doi.org/10.13033/ijahp.v3i1.60

von Solms, S.H. (2013). The fiction of a factual approach to decision-making. Proceedings 12th International Symposium on the Analytic Hierarchy Process, Kuala Lumpur, Malaysia.

von Solms, S.H. & Peniwati, K. (2001). To agree or not to agree, that is the question: Choice aggregation in the AHP. Proceedings 6th International Symposium on the Analytic Hierarchy Process, Bern, Switzerland.

Wasserman, R. (2004). Indeterminacy, ignorance and the possibility of parity. Philosophical Perspectives, 14(1), 391-403.




DOI: http://dx.doi.org/10.13033/ijahp.v7i3.313