During the summer break of 2006/7, I spent some time working on the famous Two-Envelope Paradox. I embarked on this project after reading the WIKIPEDIA entry on this topic.
In my humble opinion the version currently (4:37AM, January 20, 2007 ) available there is terribly wrong.
So you might be interested in reading my article
The Two-Envelopes Paradox: A Primer for Dummies on this topic. There are some interesting results there.
in fact, you might be interested in my work on decision-making under severe uncertainty:
Recent Articles, Working Papers, Notes
Also, see my complete list of articles
- Caserta, M., Voss, S., Sniedovich, M. (2009) Applying the corridor method to a blocks relocation problem, OR Spectrum in press.
- Sniedovich M.(2009) A Critique of Info-Gap Robustness Model. In: Martorell et al. (eds), Safety, Reliability and Risk Analysis: Theory, Methods and Applications, pp. 2071-2079, Taylor and Francis Group, London.
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- Sniedovich M.(2009) A Classical Decision Theoretic Perspective on Worst-Case Analysis, Working Paper No. MS-03-09, Department of Mathematics and Statistics, The University of Melbourne, (PDF File)
- Caserta, M., Voss, S., Sniedovich, M. (2008) The corridor method - A general solution concept with application to the blocks relocation problem. In: A. Bruzzone, F. Longo, Y. Merkuriev, G. Mirabelli and M.A. Piera (eds.), 11th International Workshop on Harbour, Maritime and Multimodal Logistics Modeling and Simulation, DIPTEM, Genova, 89-94.
- Sniedovich, M. (2008) FAQS about Info-Gap Decision Theory, Working Paper No. MS-12-08, Department of Mathematics and Statistics, The University of Melbourne, (PDF File)
- Sniedovich, M. (2008) A Call for the Reassessment of the Use and Promotion of Info-Gap Decision Theory in Australia (PDF File)
- Sniedovich, M. (2008) Info-Gap decision theory and the small applied world of environmental decision-making, Working Paper No. MS-11-08
This is a response to comments made by Mark Burgman on my criticism of Info-Gap (PDF file
- Sniedovich, M. (2008) A call for the reassessment of Info-Gap decision theory, Decision Point, 24, 10.
- Sniedovich, M. (2008) From Shakespeare to Wald: modeling wors-case analysis in the face of severe uncertainty, Decision Point, 22, 8-9.
- Sniedovich, M. (2008) Wald's Maximin model: a treasure in disguise!, Journal of Risk Finance, 9(3), 287-291.
- Sniedovich, M. (2008) Anatomy of a Misguided Maximin formulation of Info-Gap's Robustness Model (PDF File)
In this paper I explain, again, the misconceptions that Info-Gap proponents seem to have regarding the relationship between Info-Gap's robustness model and Wald's Maximin model.
- Sniedovich. M. (2008) The Mighty Maximin! (PDF File)
This paper is dedicated to the modeling aspects of Maximin and robust optimization.
- Sniedovich, M. (2007) The art and science of modeling decision-making under severe uncertainty, Decision Making in Manufacturing and Services, 1-2, 111-136. (PDF File)
- Sniedovich, M. (2007) Crystal-Clear Answers to Two FAQs about Info-Gap (PDF File)
In this paper I examine the two fundamental flaws in Info-Gap decision theory, and the flawed attempts to shrug off my criticism of Info-Gap decision theory.
- My reply (PDF File)
This is an exciting development!
- Ben-Haim's response confirms my assessment of Info-Gap. It is clear that Info-Gap is fundamentally flawed and therefore unsuitable for decision-making under severe uncertainty.
- Ben-Haim is not familiar with the fundamental concept point estimate. He does not realize that a function can be a point estimate of another function.
So when you read my papers make sure that you do not misinterpret the notion point estimate. The phrase "A is a point estimate of B" simply means that A is an element of the same topological space that B belongs to. Thus, if B is say a probability density function and A is a point estimate of B, then A is a probability density function belonging to the same (assumed) set (family) of probability density functions.
Ben-Haim mistakenly assumes that a point estimate is a point in a Euclidean space and therefore a point estimate cannot be say a function. This is incredible!
- A formal proof that Info-Gap is Wald's Maximin Principle in disguise. (December 31, 2006)
This is a very short article entitled Eureka! Info-Gap is Worst Case (maximin) in Disguise! (PDF File)
It shows that Info-Gap is not a new theory but rather a simple instance of Wald's famous Maximin Principle dating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context of Game Theory (1928).
- A proof that Info-Gap's uncertainty model is fundamentally flawed. (December 31, 2006)
This is a very short article entitled The Fundamental Flaw in Info-Gap's Uncertainty Model (PDF File)
It shows that because Info-Gap deploys a single point estimate under severe uncertainty, there is no reason to believe that the solutions it generates are likely to be robust.
- A math-free explanation of the flaw in Info-Gap. ( December 31, 2006)
This is a very short article entitled The GAP in Info-Gap (PDF File)
It is a math-free version of the paper above. Read it if you are allergic to math.
- A long essay entitled What's Wrong with Info-Gap? An Operations Research Perspective (PDF File)
This is a paper that I presented at the ASOR Recent Advances in Operations Research (PDF File)
Recent Lectures, Seminars, Presentations
If your organization is promoting Info-Gap, I suggest that you invite me for a seminar at your place. I promise to deliver a lively, informative, entertaining and convincing presentation explaining why it is not a good idea to use — let alone promote — Info-Gap as a decision-making tool.
Here is a list of relevant lectures/seminars on this topic that I gave in the last two years.
- A Critique of Info-Gap Decision theory: From Voodoo Decision-Making to Voodoo Economics(PDF File)
(Recent Advances in OR, RMIT, Melbourne, Australia, November 25, 2009)
- Robust decision-making in the face of severe uncertainty(PDF File)
(GRIPS, Tokyo, Japan, October 16, 2009)
- Decision-making in the face of severe uncertainty(PDF File)
(KORDS'09 Conference, Vilnius, Lithuania, September 30 -- OCtober 3, 2009)
- Modeling robustness against severe uncertainty (PDF File)
(SOR'09 Conference, Nova Gorica, Slovenia, September 23-25, 2009)
- How do you recognize a Voodoo decision theory?(PDF File)
(School of Mathematical and Geospatial Sciences, RMIT, June 26, 2009).
- Black Swans, Modern Nostradamuses, Voodoo Decision Theories, Info-Gaps, and the Science of Decision-Making in the Face of Severe Uncertainty (PDF File)
(Department of Econometrics and Business Statistics, Monash University, May 8, 2009).
- The Rise and Rise of Voodoo Decision Theory.
ASOR Recent Advances, Deakin University, November 26, 2008. This presentation was based on the pages on my website (voodoo.moshe-online.com).
- Responsible Decision-Making in the face of Severe Uncertainty (PDF File)
(Singapore Management University, Singapore, September 29, 2008)
- A Critique of Info-Gap's Robustness Model (PDF File)
(ESREL/SRA 2008 Conference, Valencia, Spain, September 22-25, 2008)
- Robust Decision-Making in the Face of Severe Uncertainty (PDF File)
(Technion, Haifa, Israel, September 15, 2008)
- The Art and Science of Robust Decision-Making (PDF File)
(AIRO 2008 Conference, Ischia, Italy, September 8-11, 2008 )
- The Fundamental Flaws in Info-Gap Decision Theory (PDF File)
(CSIRO, Canberra, July 9, 2008 )
- Responsible Decision-Making in the Face of Severe Uncertainty (PDF File)
(OR Conference, ADFA, Canberra, July 7-8, 2008 )
- Responsible Decision-Making in the Face of Severe Uncertainty (PDF File)
(University of Sydney Seminar, May 16, 2008 )
- Decision-Making Under Severe Uncertainty: An Australian, Operational Research Perspective (PDF File)
(ASOR National Conference, Melbourne, December 3-5, 2007 )
- A Critique of Info-Gap (PDF File)
(SRA 2007 Conference, Hobart, August 20, 2007)
- What exactly is wrong with Info-Gap? A Decision Theoretic Perspective (PDF File)
(MS Colloquium, University of Melbourne, August 1, 2007)
- A Formal Look at Info-Gap Theory (PDF File)
(ORSUM Seminar , University of Melbourne, May 21, 2007)
- The Art and Science of Decision-Making Under Severe Uncertainty (PDF File)
(ACERA seminar, University of Melbourne, May 4, 2007)
- What exactly is Info-Gap? An OR perspective. (PDF File)
ASOR Recent Advances in Operations Research mini-conference (December 1, 2006, Melbourne, Australia).