Professor Bruce Bueno de Mesquita claims that he developed a method that can -- against all odds -- yield reliable predictions of future events, for example the future of Iran. In his words:
" ... It can predict complex negotiations or situations involving coercion, that is in essence everything that has to do with politics, much of what has to do with business ..."
Consider the political developments that are unfolding now (February 28, 2011) in the Middle East and North Africa and Nassim Taleb's famous observation:
Experts and "Empty Suits"
The inability to predict outliers implies the inability to predict the course of history, given the share of these events in the dynamics of events. But we act as though we are able to predict historical events, or, even worse, as if we are able to change the course of history. We produce 30-year projections of social security deficits and oil prices without realizing that we cannot even predict these for next summer --- our cumulative prediction errors for political and economic events are so monstrous that every time I look at the empirical record I have to pinch myself to verify that I am not dreaming. What is surprising is not the magnitude of our forecast errors, but absence of awareness of it.
Taleb (2007, p. xx)
Does Bueno de Mesquita actually claim that his mathematical model can (reliably) predict the occurrence of Black Swans of the type that we now observe in the Middle East and North Africa?
Given then Bueno de Mesquita's apparent lack of concern about the effect of Black Swans, it should be interesting to hear what Nassim Taleb thinks about this matter.
In any case, on this page I provide a compilation of publications that criticize Bueno de Mesquita's theories. I also provide some supplementary material and links.
If you are here for the sole purpose of reading my assessment of Bueno de Mesquita's 2004 (now very famous) prediction of Ayatollah Khomeini's successor, then I suggest that you take this direct route.
In any case.
The following specific prediction is timely but ... wrong.
In February 2011 Bueno de Mesquita predicted that the unrest in the Arab world will not spread to such places as Saudia Arabia and ... Libya. Yes, Libya. Watch and listen carefully to the segment starting at 1:51 min into the interview:
I quote:
" ... So it is unlikely to spread to those parts of the Middle East that have substantial oil wealth such as Saudia Arabia Libya and so forth ... "
The explanation is interesing but evidently ... wrong.
This is a new, exciting website dedicated to a long term project whose aim is to contain the spread of voodoo-decision theories in Australia and the UK.
You might also be interested in reading the following presentation:
One need hardly point out that the mathematical modeling of socio-political-economic systems and processes is an extremely difficult task. As many academics/analysts/consultants would no doubt testify, modeling even small-scale real-world problems with prima facie well-defined attributes, goals, and so on, can present such difficulties that formulating a precise mathematical model that faithfully captures all the problem's nuances may defeat even the most experienced analysts/modelers.
Yet ... according to Bueno de Mesquita (For example, his Feb 7, 2009 Ted.TV talk), not only does he possess a remarkable ability to model socio-political/economic systems, the method that he has developed
can predict complex negotiations or situations involving coercion, that is in essence everything that has to do with politics, much of what has to do with business, but sorry, if you're looking to speculate in the stock market, I don't predict stock markets -- OK, it's not going up any time really soon. But I'm not engaged in doing that. I'm not engaged in predicting random number generators, I actually get phone calls from people who want to know what lottery numbers are going to win. I don't have a clue.
One thing is certain. Bueno de Mesquita is right to exclude the stock market from this effort. For as we all know, his prediction "OK, it's not going up any time really soon" turned out to be wrong, very wrong. The DJIA Index started climbing in the first week of March 2009, a month after the lecture. Here is the picture now (January 7, 2012):
Bueno de Mesquita's method is grounded on the assumption that people are basically rational beings:
Now who is rational? A lot of people are worried about what is rationality about? People are rational. Mother Theresa, she was rational. Terrorists, they're rational. Pretty much everybody is rational. I think there are only two exceptions that I'm aware of -- two-year-olds, they are not rational, they have very fickle preferences, they switch what they think all the time, and schizophrenics are probably not rational, but pretty much everybody else is rational. That is, they are just trying to do what they think is in their own best interest.
But isn't this precisely where all the trouble lies? Even if we play down the evidence that people do not always behave rationally (especially under stress), the fundamental difficulty of methods based on this conception of rational behavior is the accurate modeling of :"what is in their best interest"?!
Is it surprising then that Bueno de Mesquita's contentions regarding his models' capabilities to yield concrete results, in predicting precise outcomes of conflict situations, have provoked such criticism?
However, before I proceed to list some of the arguments criticizing Beuno de Mesquita's method -- discussed in articles published in refereed journals -- here is an [edited] comment on his Feb 7, 2009 Ted.TV talk:
Charles Harpole
Nov 30 2009:
Bruce' Bueno's mumbo jumbo is [...]. If you give me the same info he has, I will equal or beat his math. The reason is that human nature is simply not always rational. I thought everyone knew that. And, that no one can look into another's head with accuracy as he claims.
My accurate prediction: by 2026, China will surpass usa as a world economic power and will create a new international money to replace the Dollar... and make it stick. Go chew on that one and I used the most powerful non-rational and also human understanding power of all........ my brain. [...]
Ignoring the uncalled for explitives and crass language, this comment does highlight the basic dificulty that "... no one can look into another's head with accuracy ..." to construct a model that will predict with accuracy their behavior ... not even high-ranking politicians assisted by the most able experts in deicison-making ...
Also, Bueno de Mesquita's theory is based on expected utility theory. It is highly questionable whether this theory is a proper tool for the analysis of the behaviour of complex socieconomic systems that are subject to severe uncertainty.
And readers who are conviced that we behave rationally (most of the time) may wish to read Dan Ariely's books on this interesting topic. Here is the publisher's book description for Predictably Irrational:
Why do our headaches persist after we take a one-cent aspirin but disappear when we take a fifty-cent aspirin? Why do we splurge on a lavish meal but cut coupons to save twenty-five cents on a can of soup?
When it comes to making decisions in our lives, we think we're making smart, rational choices. But are we?
In this newly revised and expanded edition of the groundbreaking New York Times bestseller, Dan Ariely refutes the common assumption that we behave in fundamentally rational ways. From drinking coffee to losing weight, from buying a car to choosing a romantic partner, we consistently overpay, underestimate, and procrastinate. Yet these misguided behaviors are neither random nor senseless. They're systematic and predictable—making us predictably irrational.
To give the reader some insight into one of Bueno de Mesquita's predictions --- now being hailed as an illustration of the true power of his predcition models --- I consider the following interesting episode.
Consider Bueno de Mesquita's 1984 prediction of the Ayatollah Khomeini's successor. The 2007 version of the story is as follows:
His first foray into forecasting controversy took place in 1984, when he published an article in PS, the flagship journal of the American Political Science Association, predicting who would succeed Iran’s ruling Ayatollah Khomeini upon his death. He had developed a rudimentary forecasting model that was different from anything anyone had seen before in that it was not designed around one particular foreign-policy problem, but could be applied to any international conflict. "It was the first attempt at a general mathematical model of international conflict," he says. His model predicted that upon Khomeini’s death, an ayatollah named Hojatolislam Khamenei and an obscure junior cleric named Akbar Hashemi Rafsanjani would emerge to lead the country together. At the time, Rafsanjani was so little known that his name had yet to appear in the New York Times.
Even more improbably, Khomeini had already designated his successor, and it was neither Ayatollah Khamenei nor Rafsanjani. Khomeini's stature among Iran’s ruling clerics made it inconceivable that they would defy their leader’s choice. At the APSA meeting subsequent to the article’s publication, Bueno de Mesquita was roundly denounced as a quack by the Iran experts --- a charlatan peddling voodoo mathematics. "They said I was an idiot, basically. They said my work was evil, offensive, that it should be suppressed," he recalls. "It was a very difficult time in my career." Five years later, when Khomeini died, lo and behold, Iran’s fractious ruling clerics chose Ayatollah Khamenei and Hashemi Rafsanjani to jointly lead the country. At the next APSA meeting, the man who had been Bueno de Mesquita’s most vocal detractor raised his hand and publicly apologized to him.
The only conclusion that can be drawn from these statements is clear:
Against all odds, and contrary to Expert opinions, Bueno de Mesquita's model correctly predicted that an obscure junior cleric would succeed Ayatollah Khomeini.
And this is how this predcition is cited in a refereed paper in a prestigious journal:
The rise to power of Hasheimi Rafsanjani in Iran was predicted in an article published in 1984 at a time when Rafsanjani was widely viewed as an unimportant figure, and the Ayatollah Khomeini had officially designated Ayatollah Montezeri as his successor.
James Lee Ray and Bruce Russett
The Future as Arbiter of Theoretical Controversies: Predictions, Explanations and the End of the Cold War. British Journal of Political Science, Vol. 26, No. 4 (Oct., 1996), pp. 441-470.
The quote is from page 449.
However, if like me, statements such as these strike you as too good to be true! you would do the obvious: investigate this matter a little further.
The key to resolving this issue is to find out: how "obscure" was the obscure junior cleric Hasheimi Rafsanjani at the time Bueno de Mesquita made this prediction (1984)?
I therefore thank Professor Patrick O'Neil (Department of Politics and Government,
University of Puget Sound, Tacoma WA) for drawing my attention to this article (emphasis added):
KHOMEINI'S GRIP APPEARS AT ITS TIGHTEST
By R.W. APPLE Jr. Special to the New York Times (The New York Times)
Foreign Desk, November 21, 1982, Sunday
Late City Final Edition, Section 1, Page 1, Column 2, 1444 words
The Islamic Government led by Ayatollah Ruhollah Khomeini appears to have fastened its grip more firmly on this country of 38 million people than at any time since the revolution that overthrew Shah Mohammed Riza Pahlevi almost four years ago.
....
....
....
None of this is likely to change much while Ayatollah Khomeini lives, in the view of diplomats in Teheran. But he is 83 years old, his health is frail, and the search for a successor has begun. A committee to decide will be elected on Dec.10, but most politicians here seem to assume that a triumvirate will emerge to run the country after he dies. It would include Hojatolislam Rafsanjani, who is regarded as the most able politician; President Khamenei, and Ayatollah Hussein Ali Montazeri, the Imam's designated heir, who is considered intellectually weak and insufficiently sophisticated by many politicians.
In brief then, according to the New York Times (1982), not only was Rafsanjani not an "obscure junior cleric" at the time, he was regarded as "the most able politician" and was assumed, by most politicians in Iran, to be in the triumvirate that will emerge to run the country after Khomeini's death.
And the surprising thing is that to find this vital piece of information in the political science literature, all you have to do is to read ... Bueno de Mesquita's 1984 article where this prediction was made:
Forecasting Policy Decisions: An Expected Utility Approach to Post-Khomeini Iran American Political Science Review, 17(2), 226-236, 1984.
Indeed, in this paper you would find the following information (emphasis is mine):
Table 1 lists the groups identified by several Iranian experts as the key figures who will influence decisions on the issues in question. Estimates of the "overall influence" of each group, normalized to sum to 100, are also listed in Table 1.
Bueno de Mesquita (1984, p. 231)
So here is the content of Table 1.
Group
Overall Influence
Afghan Refugees (AFG)
0.5
Tudeh Party (TUD)
0.6
Kurds (KUR)
2.3
Turkoman (TUR)
0.3
Baluchis (BAL)
0.6
Royalists (ROY)
0.2
Bazaaris (BAZ)
5.6
Middle Class Rural Peasants (MCR)
0.9
Lower Class Rural Peasants (LCR)
4.5
Urban Middle Class (UMC)
1.1
Urban Poor (UP)
4.5
Technocrats (TEC)
0.6
Junior Clerics -- Rafsanjani (JC)
11.3
President Khamenei (PRE)
10.7
Prime Minister Musavi-Khamenei (PM)
9.0
Tehran Militant Clerics (TMC)
3.4
Qum Clerics (QUM)
4.5
Supreme Court (SC)
4.5
Ayatollah Montezari (MON)
0.1
Revolutionary Guards (REV)
12.4
Committees/Cabinet (COM)
11.8
Council of Guardians (CG)
9.0
Ayatollah Golpayegani (GOL)
0.6
Ayatollah Shariat Madari (SHA)
0.6
Ayatollah Sherazi (SHE)
0
Ayatollah Tabot Tabai (TAB)
0
Soviet Union (SOV)
0.6
Surprisingly, the table does not list the groups/individuals in a decreasing order of the "Overall Influence" index. In fact, it is totally unclear what criterion, if any, was used by Bueno de Mesquita to determine the order in which the groups/individuals were listed in this table.
So, to make sense of the information contained in the table, here is the same information re-arranged in a decreasing order of "Overall Influence" index of the groups/individuals:
Group
Overall Influence
1
Revolutionary Guards (REV)
12.4
2
Committees/Cabinet (COM)
11.8
3
Junior Clerics -- Rafsanjani (JC)
11.3
←
4
President Khamenei (PRE)
10.7
5
Prime Minister Musavi-Khamenei (PM)
9.0
6
Council of Guardians (CG)
9.0
7
Bazaaris (BAZ)
5.6
8
Lower Class Rural Peasants (LCR)
4.5
9
Urban Poor (UP)
4.5
10
Qum Clerics (QUM)
4.5
11
Supreme Court (SC)
4.5
12
Tehran Militant Clerics (TMC)
3.4
13
Kurds (KUR)
2.3
14
Urban Middle Class (UMC)
1.1
15
Middle Class Rural Peasants (MCR)
0.9
16
Tudeh Party (TUD)
0.6
17
Baluchis (BAL)
0.6
18
Technocrats (TEC)
0.6
19
Ayatollah Golpayegani (GOL)
0.6
20
Ayatollah Shariat Madari (SHA)
0.6
21
Soviet Union (SOV)
0.6
22
Afghan Refugees (AFG)
0.5
23
Turkoman (TUR)
0.3
24
Royalists (ROY)
0.2
25
Ayatollah Montezari (MON)
0.1
←
26
Ayatollah Sherazi (SHE)
0
27
Ayatollah Tabot Tabai (TAB)
0
So, how "obscure" was the obscure junior cleric Hasheimi Rafsanjani at the time Bueno de Mesquita made this prediction (1984)?
According to the Iranian experts that Bueno de Mesquita consulted in 1984 to compile the information contained in Table 1, far from being obscure this junior cleric was in fact, the highest ranking individual --- other than groups --- listed in the table. Ranked even higher than President Khamenei!!!!
The question is then: If Hasheimi Rafsanjani was indeed so "obsucre" in 1984, how is it that at the time the Iranian experts gave this "obscure" cleric such high ranking in the table?
Of course, Hasheimi Rafsanjani may have been unknown to the New York Times in 1984, but this is beside the point. Because, according to the Iranian Experts and Bueno de Mesquita's other statements in his (1984) paper, Hasheimi Rafsanjani was extremely influencial in 1984. In fact, more influential than President Khamenei!!!!
And how about the person designated by Ayatollah Khomeini to be his successor? Where is he on the list?
This was Ayatollah Montezari, whose weight in the "Overall Influence" table --- according to the Iranian experts --- was 0.1. So what is the wonder that he was not chosen as the successor?
In short, contrary to the stories now circulating in the media (and in professional journals), Bueno de Mesquita's 1984 prediction did not contradict the views of Iranian experts that he consulted. It is therefore unclear why other Iran experts should have roundly denounced him in 1984 as a quack, a charlatan peddling voodoo mathematics, an idiot whose work was evil, offensive, that should be suppressed.
What is more, in his 1984 paper, Bueno de Mesquita did not give even the sligthest indication that the prediction was in any way "surprising" nor that it contradicted the views of the Iranian experts that he consulted at that time.
And yet, some 23 years later, in 2007, Bueno de Mesquita was telling his interviewers that despite Hasheimi Rafsanjani's great obscurity in 1984 it was his model that predicted that this "obscure junior cleric" would be the successor!
In short, the story that Bueno de Mesquita is telling us in 2010 is clearly inconsistent with his analysis in the 1984 article.
Remark
The most interesting statement in Beueno de Mesquita's (1984) paper is this:
The above political forecast is, of course, predicated on the assumption that Khomeini will leave the scene soon enough so that the preferences and power of the various groups will remain as it was specified in this analysis.
Bueno de Mesquita (1984, p. 233)
So basically what Bueno de Mesquita is telling us is that the quality of the predictions of his model is only as good as the quality of the data provided by the experts.
In any case, regarding the reference to the timing of Khomeini leaving the scene, if you don't see the irony here, ask yourself: isn't severe uncertainty the real issue in forecasting future political developments? How does Bueno de Mesquita theory deal with severe uncertainty, then?
As Yogi Berra said, Prediction is very hard, especially about the future!
And if you are a Game Theory enthusiast, note that there is no mention of Game Theory in Bueno de Mesquita (1984) article. It is stated clearly in the paper that the prediction model is based on Expected Utility Theory. In fact, the title of the paper is:
Forecasting Policy Decisions: An Expected Utility Approach to Post-Khomeini Iran
To give you an idea of the kind of "formal" criticism that Bueno de Mesquita's theory has provoked, here is a short list of articles published in refereed journals.
A comment regarding Bueno de Mesquita's (1981) claims concerning the contribution of his theory to the state of the art and the empirical evidence supporting its validity:
These are strong claims, and they merit careful scrutiny. Unfortunately, I do not believe they are fully justified. In the first part of this article, I will argue that Bueno de Mesquita's theory cannot be derived from his assumptions. In the second part, I will examine the operational version of his theory, which is the one that was actually tested. I will argue that it can be more plausibly interpreted as a version of a theory he professes to discredit rather than the theory he professes to deduce from his own assumptions. I will also argue that the empirical evidence offered provides less impressive confirmation even of the theory actually tested than Bueno de Mesquita claims.
Wagner (1984, p. 408)
From the Conclusions section:
Contrary to appearances, therefore, The War Trap provides no evidence, one way or the other, on the question of whether theories of individual rational choice can explain foreign policy decisions. Moreover, when one considers how Bueno de Mesquita's analysis would have to be modified to avoid the criticisms made above, it is apparent that it would not be easy to devise as straightforward a test this hypothesis as the book professes to provide.
There are several problems with the conceptualizations that Bueno de Mesquita employs. First, he drastically reduces the scope of his concepts' meaning, thereby vitiating their significance. Second, his concepts turn out to be too ambiguous or problematic for rigorous inquiry. Finally, Bueno de Mesquita makes assumptions that are unjustified and inconsistent.
Majeski and Sylvan (1984, p. 317)
From the discussion so far, it should be apparent that the theory put forward in The War Trap is badly flawed in both conceptualization and measurement. For this reason, the empirical analyses in Chapter 5 must be taken with more than a grain of salt. We therefore restrict ourselves to a brief look at Bueno de Mesquita's empirical tests.
Majeski and Sylvan (1984, p. 338)
The Conclusions section is particularly harsh:
It is always easier to criticize than to propose constructive alternatives. For reasons of space the latter are omitted. However, from the above analysis, it is clear that such an alternative would include more realistic theory, subtler and more complex measurement, and "softer" and more micro-level empirical tests. The precise form of such changes is, of course, an open research question; we remain convinced, however, that movement in this direction is a necessity if future research on war initiation is to yield valid and useful results. Unfortunately, the research design of The War Trap rules out any such movement, and pursuing it further would be counterproductive.
This article attempts to evaluate the claims of Bruce Bueno De Mesquita in The War Trap to have provided a deductive, expected utility theory of war initiation in the light of various criticisms that have been levied against him. The criticisms concern both the status of the model as a rational choice model and the evidence adduced in its support. It is suggested that the interpretation of the concept used in the theory as expected utility is both unnecessary and misleading, while the strong claim of the theory to provide necessary conditions for war initiation is refuted, not confirmed, by the evidence presented. However, a weaker, but still important claim may well be true, though only a part of the evidence presented is appropriate to support it. The assertion that the theory is a step forward in a Lakatosian Research Program, in that it explains more than its predecessors, is viewed skeptically.
The last paragraph of the article reads as follows:
This article is not an attack on rational choice models in general or
expected utility models in particular. On the contrary, the formal
depiction of the international system as the consequence of goal-seeking
behavior is very effective as is shown, for example, in the literature that
stems in one way or another from the theory of games (in this I differ
strongly from Kong). Bueno de Mesquita claims to have made a major
advance in pushing forward this research program. Whatever the merits
of this claim in relation to his later work on other issues (for example,
Bueno de Mesquita et al., 1985), and I think they have some, they do not
apply to the theory discussed in this article.
Such are our authors' forecasts. The acid tests of these predictions, of course, lie in the answers to a series of questions: Are these predictions clear? Are they testable? Do they accord with outside evidence? Do they accord with the authors' own supporting documentation? Does that documentation exist, or is it, at least, presented? And ultimately, are the forecasts correct?
Unfortunately, the book falls short on every one of these counts, The trouble begins early on, as the authors present their four general points about the 1984 Declaration. Point Three states that, for both British and Chinese, Hong Kong's stability until 1997 was an important goal. Perhaps so, but this statement is a description of ends and not a prediction of means. Point Two indicates that Chinese and British interests were different - a thought that, again, is scarcely a prediction; and the same is true of Point Four, which alludes to Britain's supposed "impotence". Only Point One is really a forecast, since it tells us that Hong Kong's sovereignty will be transferred to China. The authors fail, however, to define "sovereignty," a critical failure, as we can see if we turn to the specific forecasts for the Joint Declaration.
Thompson (1987. p. 188)
The last ten lines of the paper reads as follows:
But whatever the shortcomings of China scholars, the authors' approach is also lacking. By their own admission (p. 13), they select the information demanded by their model and even, it seems possible, invent their facts - at least, they give us no way of checking their facts. In short, they let their method determine their "evidence." But that process is argument by tautology and so has little or nothing to do with the real world. And that is precisely the problem. The authors, and others who would apply mathematical models to Chinese studies, have yet to demonstrate that their approach is not tautological.
This is one of the most detailed and comprehensive technical analysis of The War Trap. Some quotes:
Internal Conceptual Problems. There are two major kinds of internal conceptual problems that plague Bueno de Mesquita's expected utility theory. The first of these — use of vague and ambiguous concepts — has already been discussed in relation to his work by other authors. Majeski and Sylvan (1984), for example, emphasize the "reductionism" and ambiguity of such concepts as utility, national foreign policy, possible opponents of potential war initiators and the like. They argue that these concepts, as used by Bueno de Mesquita in The War Trap are ambiguous and that the scope of their meanings are reduced in actual use. Luterbacher (1984) argues that by only taking into account what third parties might or might not do, Bueno de Mesquita's conceptualization of risk taking is too restrictive and does not capture most of what we mean by this concept.
Simowitz and Price (1990, p. 445)
We have identified the theory's solved empirical problems, as well as theoretical predictions that were either unsupported by the data or were faced with refuting instances. While agreeing with Bueno de Mesquita that refutations do not falsify his theory, we have argued that he needs to treat these anomalous cases as if they were theoretical refutations and at some point attempt to modify his theory to eliminate them. We also agreed that an appraisal of his theory requires Bueno de Mesquita to compare his theoretical predictions and the predictions of rival theories. We found, however, that due to inferential errors in his deductions, his comparisons were seriously flawed. Consequently, we are unable to choose between Bueno de Mesquita's theory and rival theories of conflict on the basis of which one has solved more empirical problems. We are nevertheless able to provide an overall evaluation of Bueno de Mesquita's theory in light of our review of the theory's solved empirical problems and unresolved conceptual and anomalous problems.
Simowitz and Price (1990, p. 454)
By adopting Laudan's criteria for theoretical progress, we were led to identify invalid inferences in Bueno de Mesquita's theory, as well as to examine all derivations of the theory confronted with refutations. Just as importantly, we were provided a framework for assessing a wide range of diverse criticisms directed at this theory. By helping us to weigh the strengths and weaknesses of Bueno de Mesquita's work, Laudan's framework led us to recommend pursuing Bueno de Mesquita's theory in spite of its obvious flaws. Whether or not one agrees with this recommendation, however, the fact that Laudan's theory of scientific progress was so helpful in evaluating Bueno de Mesquita's work and the wide range of criticism it has provoked indicates that Laudan's criteria has broad applicability to social science theories.
Simowitz and Price (1990, p. 457)
We additionally believe that Bueno de Mesquita has misrepresented the balance of power theory in his presentation of the hypotheses. Specifically, the balance of power theory incorporates both power and alignments as sufficient conditions for war; but Bueno de Mesquita, in his tests of balance of power and alliances, tests the individual impact of each of these variables on war Initiation. Wagner (1984) makes a similar point.
Simowitz and Price (1990, Note 13, p. 458)
Commentary on this criticism can be found in
James D. Morrow, Barry L. Price, Roslyn Simowitz
Conceptual Problems in Theorizing About International Conflict
The American Political Science Review, Vol. 85, No. 3 (Sep., 1991), pp. 923-940.
The criticism is technical in nature in that it exposes an obvious error in the mathematical analysis of the proposed model. The important point here is that this error demolishes the foundation of the proposed model.
In "Capabilities, Perception, and Escalation," Bueno de Mesquita, Morrow, and Zorick (1997) model the evolution of disputes between nations as a game of two-sided incomplete information and test empirically their theoretical results. Their main conclusion is that the relationship between the ex ante probability of a crisis escalating to armed conflict and the countries' observable military capabilities is not monotonic; in particular, this probability is initially decreasing and then increasing. In other words, the ex ante probability of an escalation to armed conflict is at a minimum when power, measured by observable military capabilities, is balanced. Although these findings are supported by the data, the analysis of the equilibria contains a mistake that invalidates some of the statements.
This note explains the nature of the mistake and discusses how the conclusions change once the correct equilibria are considered. I find that the relationship between the observed military capabilities and the probability of armed conflict given a crisis is constant and equal to one. Therefore, observable military capabilities have no role in explaining differences in the evolution of crises, and we are left with no explanations for the empirical findings of Bueno de Mesquita, Morrow, and Zorick
Molinari (2000, p. 425 )
Bueno de Mesquita, Morrow, and Zorick acknowledge the error in their article.
Other pointers
An interesting criticism of expected utility theory, rational choice theory, and game theory in the framework of comparative politics can be found in
Gerardo L. Munck
Game Theory and Comparative Politics: New Perspectives and Old Concerns
World Politics, Vol. 53, No. 2 (Jan., 2001), pp. 173-204.
An example of a more recent (February 2010) criticism can be found at the website the Foregin Policy Magazine.
Given that Bueno de Mesquita's method is used by organizations such as the CIA to predict the outcome of wars and conflicts, it is in the public interest to know how "good"/"bad" the predictions generated by his models are.
The important point to note in this regard, and as emphasized by de Mesquita himself, the application of his prediction models hangs on the information (expert knowledge) supplied by experts on the subject matter.
Intelligence analysis, like other complex tasks, demands considerable expertise. It requires individuals who can recognize patterns in large data sets, solve complex problems, and make predictions about future behavior or events. To perform these tasks successfully, analysts must dedicate a considerable number of years to researching specific topics, processes, and geographic regions.
Paradoxically, it is the specificity of expertise that makes expert forecasts unreliable. While experts outperform novices and machines in pattern recognition and problem solving, expert predictions of future behavior or events are seldom as accurate as simple actuarial tables. In part, this is due to cognitive biases and processing-time constraints. In part, it is due to the nature of expertise itself and the process by which one becomes an expert.
Rob Johnston
Integrating Methodologists into Teams of Substantive Experts
Reducing Analytic Error
Studies in Intelligence Volume 47, Number 1, 2003.
One imagines that the above statement is based on the vast experience gained at the CIA from a wide-ranging interaction with internal/external experts.
Therefore, the claim that extensive tests conducted by the CIA show that Bueno de Mesquita's prediction models were accurate 90% of the time, is impressive. Indeed, in a sense, it contradicts the CIA assessment regarding the performance of experts in the messy business of forecasting.
If you are familiar with publications providing evidence substantiating this claim, please send me the details and I shall post them here. The main reference I have to this claim is
Feder, Stanley A.
Annual Review of Political Science
5:111-25, 2002
and references cited therein.
On the other hand, the extensive empirical tests reported on in
D. Scott Bennett and Allan C. Stam
The Behavioral Origins of War
University of Michigan Press, 2004
According to a recent article in the New Scientist's opinion section about Bueno De Mesquita's model (March 17, 2010):
"The old model --- essentially a sophisticated version of the one I used in 1979 --- was accurate 90 per cent of the time," he says. "This new model blows the old one out of the water in terms of the result and the accuracy of the path leading up to the outcome." In February he presented a paper at a meeting of the International Studies Association detailing the difference in performance between the two models.
Now, if the old model was accurate 90 per cent of the time, and "This new model blows the old one out of the water" then surely, to put across the huge difference between them, it would not be too far-fetched to put the accuracy level of the model that blows the old one out of the water in the high 90.
In other words it would not be too far-fetched to ascribe the model an accuracy rate of say 97.3423% of the time.
Of course, even a success rate of 90 percent should give one pause as it seems to put the model squarely in the too good to be true! category.
Still, my aim in putting this matter somewhat "provocatively" is to point out that these assertions do not give rise merely to squabbles about figures about the model's success rate. But to remind the reader that these assertions go to the more basic question of the model's purported capabilities to predict with great precision the outcomes of complex situations that are subject to severe uncertainty. One need not be an expert (statistician, decision theorist, game theory maven etc.) in this field to be more than a bit skeptical not only about the model's rate of success but about its very ability to perform that which it is claimed to be able to accomplish.... Because one of the strongest impressions one has, reading de Mesquita's publications, is that the situations that he is concerned with seem to be impervious to the unexpected, the surprising, the highly unpredictable or to what Nassim Taleb calls Black Swans.
So I raise again the following point: give Bueno de Mesquita's apparent lack of concern about the affect of Black Swans, it should be interesting to hear what Nassim Taleb thinks about this matter, recalling that:
Experts and "Empty Suits"
The inability to predict outliers implies the inability to predict the course of history, given the share of these events in the dynamics of events. But we act as though we are able to predict historical events, or, even worse, as if we are able to change the course of history. We produce 30-year projections of social security deficits and oil prices without realizing that we cannot even predict these for next summer --- our cumulative prediction errors for political and economic events are so monstrous that every time I look at the empirical record I have to pinch myself to verify that I am not dreaming. What is surprising is not the magnitude of our forecast errors, but absence of awareness of it.
Taleb (2007, p. xx)
But, all that de Bueno de Mesquita requires to predict the results of complicated conflicts that are subject to severe uncertainty, and to thereby engineer the future, is ... game theory and his new model!
In a recent (February 2009) TED lecture Bueno de Mesquita made the contention that the number of possible interactions between n individuals is n factorial, namely n!. He showed a graphic example with n=5 individuals and the ten links between them (6:00 minute into the lecture):
n=5 individuals
n=5 individuals with 10 links
So far so good.
Then, out of the blue, he went on to claim that there are n! possible interactions between these 5 individuals:
n=5 individuals, 10 links. How many interactions?
Clearly, this does not add up. However, as this point was eventually taken up and discussed at some length on the internet (eg. see Abu muqawama and TED), I shall not elaborate on it any further except to note the following.
The number of links between n individuals is "n choose 2" = n!/(2!(n-2)!). See for example the following comment at Abu muqawama:
Apparently Bueno de Mesquita was asked to clarify his assertion that the number of interactions is n!. Unfortunately, the explanation is as confusing as the original statement, if not more so. A clip from Abu muqawama:
In fact, the 'logic' is not "very simple" at all. For, it is hardly clear what kind of "interactions" Bueno de Mesquita has in mind. For instance, consider this (Abu muqawama):
More generally, it is easy to envisage a definition of "interaction" that will yield more than n! possible "interactions" between n individuals. To repeat then: what kind of "interactions" enter into Bueno de Mesquita's analysis of the future of Iran?
The fact is that Bueno de Mesquita should have no problem at all to give us an edifying account of the type of interactions that form part of his analysis because, given that 4!=24, it is rather simple to enumerate all such interactions for n=4.
As things stand then, this claim is manifestly false (unless unbeknownst to us, Bueno de Mesquita is making certain assumptions about the problem). The inference is then that Bueno de Mesquita would do well to provide a clear explanation to resolve this question.
For, wouldn't it be ironic if it turns out that Bueno de Mesquita is in error on such a simple, yet important, matter!
Remark (September 5, 2010):
I have checked Bueno de Mesquita's explanation of the "n!" in his latest book (The Predictioneer's Game, 2010, pp. 51-52). It is crystal clear that he is wrong. So I can definitely say that this is indeed ironic! I do hope that he will fix this bug in the second edition of the book and his ... lectures.
Not only professionals specializing in "decision under uncertainty", but also the proverbial "man in the street", take it for granted that the ability to accurately predict future events is one of the most onerous challenges facing humankind — especially persons in authority, persons responsible for the management of business or economic organizations etc.
Who, according to Good Magazine, specializes in predicting future events — at least in the area of international conflicts.
The claim is that this distinguished political scientist can actually predict the outcome of any international conflcit!
To do this Prof. Bueno de Mesquita does not use a Crystal Ball, but a thoroughly scientific method which he claims, is based in a branch of applied mathematics called Game Theory.
" ... Bruce Bueno de Mesquita is a political scientist, professor at New York University, and senior fellow at the Hoover Institution. He specializes in international relations, foreign policy, and nation building. He is also one of the authors of the selectorate theory.
He has founded a company, Mesquita & Roundell, that specializes in making political and foreign-policy forecasts using a computer model based on game theory and rational choice theory. He is also the director of New York University's Alexander Hamilton Center for Political Economy.
He was featured as the primary subject in the documentary on the History Channel in December 2008. The show, titled Next Nostradamus, details how the scientist is using computer algorithms to predict future world events ..."
Here is an interview with Prof. Bueno de Mesquita (with Riz Khan - The art and science of prediction - 09 Jan 08):
Apparently, all you need to accomplish this is a computer, expert-knowledge on Iran, and game theory!
Some of the predictions attributed to Prof. Bueno de Mesquita are:
The second Palestinian Intifada and the death of the Mideast peace process, two years before this came to pass.
The succession of the Russian leader Leonid Brezhnev by Yuri Andropov, who at the time was not even considered a contender.
The voting out of office of Daniel Ortega and the Sandanistas in Nicaragua, two years before this happened.
The harsh crack down on dissidents by China's hardliners four months before the Tiananmen Square incident.
France's hairs-breadth passage of the European Union's Maastricht Treaty.
The exact implementation of the 1998 Good Friday Agreement between Britain and the IRA.
China's reclaiming of Hong Kong and the exact manner the handover would take place, 12 years before it happened.
Impressive, isn't it!
As might be expected, these and similar claims by Prof. Bueno de Mesquita have sparked a vigorous debate not only in the professional journals but also on the WWW. Interested readers can consult this material to see for themselves, whether Bueno de Mesquita's claims attest to a major scientific breakthrough or ... voodoo mathematics.
Also, in addition to consulting this material you may want to have a look at a short video clip by Matt Brawn (right) which, he compiled in response to a short note entitled This man can actually predict the future!.
Of particular interest is, of course, the "success" rate of the Prof. Bueno de Mesquita's predictions: over 90% — yes over ninty percent!
Here is Trevor Black's common sense reaction to this claim:
I am a little skeptical about anyone who claims to have a 90% success rate. I just don't buy it. Especially when they say that they can explain away a lot of the other 10%.
If you come to me and tell me you have a model that gets it right 60% or 70% of the time, I may listen. Skeptically, but I will listen. 90% and I start to smell something.
All I wish to add here is that Prof. Bueno de Mesquita (left) makes his predictions under conditions of "severe uncertainty" which of course render them hugely vulnerable to what Prof. Naseem Taleb (right) dubs the Black Swan phenomenon.
Hence, the very proposition that such predictions can be made at all, let alone be reliable, is diametrically opposed to Nassim Taleb's categorical rejection of any such position. For his thesis is that Black Swans are totally outside the purview of mathematical treatment, especially by models that are based on expected utility theory and rational choice theory.
Even more interesting is the fact that Nassim Taleb (right) and Bueno de Mesquita (left) are staff members of the same academic institution, namely New York University. So, all that's left to say is: Go figure!
As indicated above, the debate over Bueno de Mesquita's theories is not new. It has been ongoing, in the relevant academic literature, at least since the publication of his book The War Trap (1981).
Of course, there are other New Nostradamuses around.
According to the Associated Press, the latest (2009, Mar 4, 4:39 AM EST) news from Russia about the future of the USA is that
" ... President Barack Obama will order martial law this year, the U.S. will split into six rump-states before 2011, and Russia and China will become the backbones of a new world order ..."
Apparently this prediction was made by Igor Panarin (right), Dean of the Russian Foreign Ministry diplomatic academy and a regular on Russia's state-controlled TV channels (see full AP news report).
Regarding the future of Russia,
"You don't sound too hopeful".
"Hopeful? Please, I am Russian. I live in a land of mad hopes, long queues, lies and humiliations. They say about Russia we never had a happy present, only a cruel past and a quite amazing future ..."
Malcolm Bradbury
To the Hermitage (2000, p. 347)
We should therefore be reminded of J K Galbraith's (1908-2006) poignant observation:
There are two classes of forecasters: those who don't know and those who don't know they don't know.
And in the same vein,
The future is just what we invent in the present to put an order over the past.
Malcolm Bradbury
Doctor Criminale (1992, p. 328)
So, we shall have to wait and see.
And how about this more recent piece by Heath Gilmore and Brian Robins in the Sydney Morning Herald (March 27, 2009):
"... COUPLES wondering if the love will last could find out if theirs is a match made in heaven by subjecting themselves to a mathematical test.
A professor at Oxford University and his team have perfected a model whereby they can calculate whether the relationship will succeed.
In a study of 700 couples, Professor James Murray, a maths expert, predicted the divorce rate with 94 per cent accuracy.
His calculations were based on 15-minute conversations between couples who were asked to sit opposite each other in a room on their own and talk about a contentious issue, such as money, sex or relations with their in-laws.
Professor Murray and his colleagues recorded the conversations and awarded each husband and wife positive or negative points depending on what was said. ..."
Such interviews should perhaps be made mandatory for all couples registering their marriage.
More details on the mathematics of marriage can be found in The Mathematics of Marriage: Dynamic Nonlinear Models by J.M. Gottman, J.D. Murray, C. Swanson, R. Tyson, and K.R. Swanson (MIT Press, Cambridge, MA, 2002.)
I fear though -- in view of my experience of the past 40 years - that the danger is that the huge success of the Black Swan will inspire a new wave of voodoo decision theories, purportedly capable of ... "domesticating" black swans and preempting the discovery of ... purple swans!
We shall have to wait and see.
For those who have "been in hiding" I should note that Taleb has become quite a celebrity. According to the Prudent Investor Newsletters (Tuesday, June 3, 2008):
Mr. Taleb charges about $60,000 per speaking engagement and does about 30 presentations a year to "to bankers, economists, traders, even to Nasa, the US Fire Administration and the Department of Homeland Security" according to Timesonline’s Bryan Appleyard.
He recently got $4million as advance payment for his next much awaited book.
Earned $35-$40 MILLION on a huge Black Swan event-on the biggest stockmarket crash in modern history-Black Monday, October 19,1987.
So, if you haven’t heard him in person you can easily find on the WWW numerous videos of his interviews.
Here is a link to a very short (2:45 min) clip, recorded by Taleb himself, apparently at Heathrow Airport, of 10 tips on how to deal with Black Swans, and life in general.
Scepticism is effortful and costly. It is better to be sceptical about matters of large consequences, and be imperfect, foolish and human in the small and the aesthetic.
Go to parties. You can't even start to know what you may find on the envelope of serendipity. If you suffer from agoraphobia, send colleagues.
It's not a good idea to take a forecast from someone wearing a tie. If possible, tease people who take themselves and their knowledge too seriously.
Wear your best for your execution and stand dignified. Your last recourse against randomness is how you act -- if you can't control outcomes, you can control the elegance of your behaviour. You will always have the last word.
Don't disturb complicated systems that have been around for a very long time. We don't understand their logic. Don't pollute the planet. Leave it the way we found it, regardless of scientific 'evidence'.
Learn to fail with pride -- and do so fast and cleanly. Maximise trial and error -- by mastering the error part.
Avoid losers. If you hear someone use the words 'impossible', 'never', 'too difficult' too often, drop him or her from your social network. Never take 'no' for an answer (conversely, take most 'yeses' as 'most probably').
Don't read newspapers for the news (just for the gossip and, of course, profiles of authors). The best filter to know if the news matters is if you hear it in cafes, restaurants ... or (again) parties.
Hard work will get you a professorship or a BMW. You need both work and luck for a Booker, a Nobel or a private jet.
Answer e-mails from junior people before more senior ones. Junior people have further to go and tend to remember who slighted them.
It is interesting to juxtapose Prof. Taleb’s thesis in The Black Swan that severe uncertainty makes (reliable) prediction in the Socio/economic/political spheres impossible, with the polar position taken by his colleague, Prof. Bruce Bueno de Mesquita, who actually specializes in predicting the future.
One thing for sure: Sooner or later info-gap scholars will find a simple reliable recipe for handling Black Swans!
If you are taking it for granted that the quest for a magic formula capable of transforming severe lack of knowledge / information into substantial knowledge was abandoned with the Enlightenment, I have news for you!
Apparently, against all scientific odds, Info-Gap scholars were successful in imputing likelihood and chanceto results generated by a non-probabilistic model that is completely devoid of any notion of likelihood!
Recall that Info-Gap decision theory prides itself on being non-probabilistic and likelihood-free. Yet, Info-gap scholars -- the Father of Info-Gap included -- now claim that Info-Gap's robustness model is capable of identifying decisions that are most likely to satisfy a given performance requirement.
Consider for instance the following quotes (emphasis is mine):
Information-gap (henceforth termed 'info-gap') theory was invented to assist decision-making when there are substantial knowledge gaps and when probabilistic models of uncertainty are unreliable (Ben-Haim 2006). In general terms, info-gap theory seeks decisions that are most likely to achieve a minimally acceptable (satisfactory) outcome in the face of uncertainty, termed robust satisficing. It provides a platform for comprehensive sensitivity analysis relevant to a decision.
Burgman, Wintle, Thompson, Moilanen, Runge, and Ben-Haim (2008, p. 8). Reconciling uncertain costs and benefits in Bayes nets for invasive species management ACERA Endorsed Core Material: Final Report, Project 0601 - 0611, July 2008.
(PDF file, Downloaded on March 21, 2009)
However, if they are uncertain about this model and wish to minimize the chance of unacceptably large costs, they can calculate the robust–optimal number of surveys with eqn 5.
Tracy M. Rout, Colin J. Thompson, and Michael A. McCarthy (2009, p. 785)
Robust decisions for declaring eradication of invasive species
Journal of Applied Ecology 46, 782–786.
This is a major scientific breakthrough!
For, until now we have been warned repeatedly by Info-Gap scholars that no likelihood must be attributed to results generated by Info-Gap decision models. Indeed, we have been advised that this would be deceptive and even dangerous (emphasis is mine):
However, unlike in a probabilistic analysis, r has no connotation of likelihood. We have no rigorous basis for evaluating how likely failure may be; we simply lack the information, and to make a judgment would be deceptive and could be dangerous. There may definitely be a likelihood of failure associated with any given radial tolerance. However, the available information does not allow one to assess this likelihood with any reasonable accuracy.
Ben-Haim (1994, p. 152)
Convex models of uncertainty: applications and implications Erkenntnis, 4, 139-156.
This point is also made crystal clear in the second edition of the Info-Gap book (emphasis is mine):
In info-gap set models of uncertainty we concentrate on cluster-thinking rather than on recurrence or likelihood. Given a particular quantum of information, we ask: what is the cloud of possibilities consistent with this information? How does this cloud shrink, expand and shift as our information changes? What is the gap between what is known and what could be known. We have no recurrence information, and we can make no heuristic or lexical judgments of likelihood.
Ben-Haim (2006, p. 18) Info-Gap Decision Theory: Decisions Under Severe uncertainty
Academic Press.
So the question is: have Info-gap scholars managed to accomplish a major feat in the area of decision-making under severe uncertainty?
Of course the answer is that this new claims (Burgman et al. 2008, Rout et al. 2009) are not due to a breakthrough in decision-making under severe uncertainty, but rather to a serious misrepresentation of Info-gap’s robustness model, culminating in a thoroughly incorrect representation of the results.
My view on these episode -- based as it is on numerous discussions with Info-Gap scholars over the past five years -- is that these new claims are simply -- but not surprisingly -- ... Freudian slips.
The point is that -- see my FAQs about Info-Gap -- without imputing some sort of "likelihood" to Info-Gap's decision model, Info-Gap decision theory is, and cannot escape being, a voodoo decision theory.
So, all that these Freudian slips manage to do is to extend the already existing error -- an alternative that some Info-Gap scholars seem to prefer to an admission to a mistake.
It is interesting to note, though, that some Info-Gap scholars have taken note of my criticism of Info-Gap's robustness analysis to the effect that they now introduce an assumption that explicitly imputes "likelihood" to Info-Gap's uncertainty model. For instance, consider this (emphasis is mine):
An assumption remains that values of u become increasingly unlikely as they diverge from û.
Hall, J. and Harvey, H. (2009, p. 2)
Decision making under severe uncertainty for flood risk management: a case study of info-gap robustness analysis. Eighth International Conference on Hydroinformatics
(January 12-16, 2009, Concepcion, Chile)
(PDF file)
Although this attempt at a quick-fix fails to fix the problem (see FAQ # 78), it does attest to a recognition that without such an assumption, conducting an analysis of the kind prescribed by Info-Gap's robustness model is utterly senseless.
One can only wonder then: how long will it take other Info-Gap scholars such as Burgman et al. (2008) and Rout et al. (2009) to reach this unavoidable conclusion?
Only time will tell (March 21, 2009).
Postscript:
The good news is that I am extremely pleased that, apparently for the first time, an official Government commissioned report takes notice of my criticism of Info-Gap decision theory.
More important: I hope that senior academics promoting this theory in Australia and elsewhere will reconsider their position, especially insofar as supervising PhD students on this subject.
More recently, Info-Gap approaches that purport to be non-probabilistic in nature developed by Ben-Haim (2006) have been applied to flood risk management by Hall and Harvey (2009). Sniedovich (2007) is critical of such approaches as they adopt a single description of the future and assume alternative futures become increasingly unlikely as they diverge from this initial description. The method therefore assumes that the most likely future system state is known a priori. Given that the system state is subject to severe uncertainty, an approach that relies on this assumption as its basis appears paradoxical, and this is strongly questioned by Sniedovich (2007).
Mervyn Bramley, Ben Gouldby, Anthony Hurford, Jaap-Jeroen Flikweert
Marta Roca Collell, Paul Sayers, Jonathan Simm, Michael Wallis
Delivering Benefits Through Evidence
PAMS (Performance-based Asset Management System) Phase 2 Outcome Summary Report (PDF File)
Project: SC040018/R1
Environment Agency -- December 2009
Department for Environment Food and Rural Affairs
UK
The diplomatic language of the report cannot veil the obvious fact: Info-Gap decision theory is a voodoo theory!
But, .... if the flaws are so obvious, how is it that senior academics continue to promote this paradoxical, voodoo theory?
Sniedovich, M. (2012) Fooled by local robustness, Risk Analysis, Early View.
Sniedovich, M. (2012) Black swans, new Nostradamuses, voodoo decision theories and the science of decision-making in the face of severe uncertainty, International Transactions in Operational Research, 19(1-2), 253-281 (Available free of charge)
Sniedovich, M. (2011) A classic decision theoretic perspective on worst-case analysis, Applications of Mathematics, 56(5), 499-509.
Sniedovich, M. (2011) Dynamic programming: introductory concepts, in Wiley Encyclopedia of Operations Research and Management Science (EORMS), Wiley.
Caserta, M., Voss, S., Sniedovich, M. (2011) Applying the corridor method to a blocks relocation problem, OR Spectrum, 33(4), 815-929, 2011.
Sniedovich, M. (2011) Dynamic Programming: Foundations and Principles, Second Edition, Taylor & Francis.
Sniedovich, M. (2010) A bird's view of Info-Gap decision theory, Journal of Risk Finance, 11(3), 268-283.
Sniedovich M. (2009) Modeling of robustness against severe uncertainty, pp. 33- 42, Proceedings of the 10th International Symposium on Operational Research, SOR'09, Nova Gorica, Slovenia, September 23-25, 2009.
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) 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) .
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.
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.
Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.
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According to the 
The good news is that I am extremely pleased that, apparently for the first time, an official Government commissioned report takes notice of my criticism of Info-Gap decision theory.
More recently, Info-Gap approaches that purport to be non-probabilistic in nature developed by Ben-Haim (2006) have been applied to flood risk management by Hall and Harvey (2009). Sniedovich (2007) is critical of such approaches as they adopt a single description of the future and assume alternative futures become increasingly unlikely as they diverge from this initial description. The method therefore assumes that the most likely future system state is known a priori. Given that the system state is subject to severe uncertainty, an approach that relies on this assumption as its basis appears paradoxical, and this is strongly questioned by Sniedovich (2007).
