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Selected Publications

Jonathan Barzilai, Pure Economics, FriesenPress, April 2022. Details

Jonathan Barzilai, On Neural Network Accuracy and Validation, in SIAM News, December 3, 2021. View

Jonathan Barzilai, A Note on Neural-Network Mini-Batches, in SIAM News, October 27, 2021. View

Jonathan Barzilai, On Neural-Network Training Algorithms, in Human-Machine Shared Contexts, William Lawless, Ranjeev Mittu, and Donald Sofge (Eds.), Elsevier, pp. 307—313, 2020. View

Jonathan Barzilai, "A Spectrum Algorithm and Optimization Notes," Pure and Applied Functional Analysis, Volume 3, Number 4, pp. 533–536, 2018. View

Jonathan Barzilai, A Linear-Equations Challenge, 2017. View

Jonathan Barzilai, Supply and Demand Equilibrium and Debreu’s Theory of Value, Pure Economics.

Jonathan Barzilai, Economic Theory’s Curves, Pure Economics.

Jonathan Barzilai, Demand, Barter, and Exchange, Pure Economics.

Jonathan Barzilai, A Unified Consumer Demand Theory, Pure Economics.

Jonathan Barzilai, And the Mathematics is Incorrect, SIAM News, March 2016. View
An unedited version here.

Jonathan Barzilai, Slutsky’s Mathematical Economics, Pure Economics.

Jonathan Barzilai, An Open Letter to the President of the Canadian Economics Association, March 2015. View

Jonathan Barzilai, A Note on Katzner's "Arbitrary Definitions," Technical Report, Dept. of Industrial Engineering, Dalhousie University, pp. 1–2, 2014. View

Jonathan Barzilai, An Open Letter to the President of the American Economic Association, September 2014. View

Jonathan Barzilai, "Demand Theory is Founded on Errors," Real-World Economic Review, No. 68, pp. 62–65, 21 August 2014.View

Jonathan Barzilai, Applicability of Mathematical Operations on Value Scales, pp. 1–6, 2013. View

Jonathan Barzilai, On Ordinal, Cardinal, and Expected Utility, pp. 1–6, 2011. Published as "Inapplicable Operations on Ordinal, Cardinal, and Expected Utility," Real-World Economic Review, No. 63, 25 March 2013. View

Jonathan Barzilai, "On Microeconomics Errors and Ordinal Group Decision Making, Pure Economics.

Jonathan Barzilai, The Challenge of Foundational Errors in Economic and Game Theory, pp. 1–3. A discussion paper, Lorentz Center workshop "Error in the Sciences," October 2011. View

Lex A. van Gunsteren, Economic Theory and the Reality Test, Lorentz Center workshop "Error in the Sciences," Leiden, October 2011. View

Jonathan Barzilai, Correcting the Mathematical Foundations of the Social & Economic Sciences, NSF White Paper, September 2010. View

Jonathan Barzilai, Von Neumann’s Error, CORS-SCRO Bulletin, Vol. 44 No. 4, pp. 23–24, November 2010. View

Jonathan Barzilai, "Preference Function Modeling: The Mathematical Foundations of Decision Theory," in Trends in Multiple Criteria Decision Analysis, Matthias Ehrgott, José Rui Figueira, and Salvatore Greco (Eds.), Springer, pp. 57–86, 2010. Pure Economics.

Jonathan Barzilai, Economic Theory Errors, pp. 1–5, 2009. View

Jonathan Barzilai, Ordinal Utility and Indifference Curves, Pure Economics.

Jonathan Barzilai, Game Theory Foundational Errors - Part IV, Technical Report, Dept. of Industrial Engineering, Dalhousie University, pp. 1–4, 2009. View

Jonathan Barzilai, Game Theory Foundational Errors - Part III, Technical Report, Dept. of Industrial Engineering, Dalhousie University, pp. 1–4, 2009. View

Jonathan Barzilai, "Avoiding MCDA Evaluation Pitfalls," in Real Time and Deliberative Decision Making, Igor Linkov, Elizabeth Ferguson, Victor S. Magar (Eds.), NATO Science for Peace and Security Series C - Environmental Security, Springer, pp. 349–353, 2008. View preprint

Jonathan Barzilai, Game Theory Foundational Errors - Part II, Technical Report, Dept. of Industrial Engineering, Dalhousie University, pp. 1–9, 2008. View

Jonathan Barzilai, Value of a Game, Notices of the American Mathematical Society, Vol. 55, No. 4, p. 446, April 2008. View

Jonathan Barzilai, On the Mathematical Foundations of Economic Theory, Technical Report, Dept. of Industrial Engineering, Dalhousie University, pp. 1–13, 2007. View

Jonathan Barzilai, Game Theory Foundational Errors and the Mathematical Foundations of Operations Research, CORS-SCRO Bulletin, Vol. 41, No. 4, pp. 42–43, November 2007. View

Jonathan Barzilai, Game Theory Foundational Errors - Part I, Technical Report, Dept. of Industrial Engineering, Dalhousie University, pp. 1–2, 2007. View

Jonathan Barzilai, A Game Theory Pitfall - 'The Value of a Game', CORS-SCRO Bulletin, Vol. 41, No. 3, p. 44, July 2007. View

Jonathan Barzilai, Pairwise Comparisons, in N.J. Salkind (Ed.), Encyclopedia of Measurement and Statistics, Sage Publications (Thousand Oaks, CA), Vol. II, pp. 726–727, 2007.

Jonathan Barzilai, On the Mathematical Modeling of Measurement, http://arxiv.org/, math.GM/0609555, pp. 1–4, 2006. View

Jonathan Barzilai, Preference Modeling in Engineering Design, in Decision Making in Engineering Design, K.E. Lewis, W. Chen and L.C. Schmidt (Eds.), ASME Press, pp. 43–47, 2006.

Jonathan Barzilai, Measurement and Preference Function Modeling, International Transactions in Operational Research, Vol. 12, pp. 173–183, 2005.

Jonathan Barzilai, Notes on Utility Theory, Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 1000–1005, 2004.

Jonathan Barzilai, Notes on the Analytic Hierarchy Process, Proceedings of the NSF Design and Manufacturing Research Conference, Tampa, Florida, pp. 1–6, 2001. View

Jonathan Barzilai, On the Decomposition of Value Functions, Operations Research Letters, Vol. 22, Nos. 4-5, pp. 159–170, 1998.

Jonathan Barzilai, Deriving Weights from Pairwise Comparison Matrices, Journal of the Operational Research Society, Vol. 48, No. 12, pp. 1226–1232, 1997.

Book: Pure Economics On Neural Network Accuracy and Validation On Neural Network Mini-Batches On Neural Network Training Algorithms Spectrum and Optimization Algorithms ChoiceRobot

The Foundations

Decision Theory Utility Theory

Software

Download Tetra Tetra Quickstart Guide Tetra Online Documentation

Algorithms

Numerical Mathematics

Video

An Elementary Demand Theory Error Ordinal Utility and Indifference Curves Von Neumann's Error Game Theory: Whose Values?