http://www.rationalresponders.com/plausibility_theory_paradox_resolution
rationalresponders.com
by Chaoslord2004

The concept of plausibility is not new. The concept dates back to the Ancient Greeks; the idea can be found in Aristotle’s Topica (Rescher, 1976, Preface). Plausible reasoning is used in evaluating hypothetical reasoning, scientific reasoning and even inductive reasoning. However, it will be argued that when applied to paradox resolution, it rests upon a fundamental misunderstanding of what a paradox is. It must be granted that the plausibility theory succeeds in providing us with a method for resolving a wide variety of paradoxes. However, in resolving the paradoxes, it over-looks the essential nature of paradoxes.
Contrary to Rescher’s theory of paradox resolution, paradoxes are not mere problems to be resolved, but rather important problems which challenge our basic intuitions of the world. In failing to appreciate the fundamental nature of paradox, one fails to appreciate what can be learned from paradoxes. Moreover, it will be demonstrated that plausibility theory suffers from serious counterintuitive consequences regarding truth and usefulness.

Motivation Behind Plausibility Theory

One of the driving forces behind plausibility theory is to provide us with a systematic way of resolving inconsistent sets. Take the contradictory set: [P, ~P]. If we assume classical logic, we know it tells us that one of these propositions must be rejected. However, we do not know which one must be rejected based purely on logic; pure logic alone cannot tell us which proposition to needs to be abandoned (Rescher, 1976, p.2).
Since logic fails to give us a definitive answer in the inconsistent case, something more is needed. Ergo, while logic tells us that if we want to restore consistency, we must abandon one of the above propositions, plausibility theory tells us which one of the propositions we ought to abandon. How plausibility theory works will be the focus of the following section.

The Logic Of Plausibility

As stated earlier, the function of plausibility theory is to provide one with a method for resolving cases in which we have accepted a set of inconsistent propositions. Another way to say it is that plausibility seeks to provide us with a systematic way to resolve cognitive dissonance (Rescher, 1974, p.1). For example, take the following set of propositions: [p Ú q, ~p, ~q]. Let us suppose that the propositions have the following plausibility breakdown: p Ú q = .7, ~p = .4, ~q = .5. According to plausibility theory, in order to restore consistency, we must abandon the proposition ~p, leaving us with the following set of propositions: [p Ú q, ~q].
In order to understand how plausibility theory works, we must know its cardinal maxim: In the inconsistent case, retain those propositions with the highest level of plausibility, and abandon the least plausible proposition (Rescher, 2001, p. 32). This, however, can only make sense after we have a firm grasp on exactly what “plausibility” is suppose to mean.
Nicholas Rescher (1974) states: “…plausibility is intended to reflect an index of what reasonable people would – and should – agree on, given the relevant information” (p. 5). In his most recent book on paradoxes, Rescher (2001) claims that, “Its precedence [with regards to a proposition] and priority ranking bears upon the systematic standing or status that we take a claim to occupy in the cognitive situation at hand” (p. 46). From the above information, it would seem that the theory of plausibility is merely based upon how certain we are regarding various propositions. For example, we generally think the axioms of number theory are more certain than the law of physics. While cognitive certainly is a major theme within plausibility theory, Rescher claims that he does not ground his theory of plausibility merely on how certain a proposition is within our cognitive web of beliefs.
Rescher also believes that there are objectively more plausible propositions than others. As stated earlier, we hold axioms of mathematics to be more certain than the laws of physics. The plausibility of the proposition goes up the closer it gets to (1). Rescher (2001) gives the following breakdown:
(1) Definitions, axioms of mathematics and logic, mathematical relations, and in the case of paradoxes, principles of the story. These are 100% certain and cannot be refuted
(2) The inductive sciences.
(3) Observations and experimental observations of life.
(4) Highly probable propositions regarding contingent fact.
(5) Reasonably warranted suppositions.
(6) Provisional and tentative conjectures.
(7) Speculative suppositions (p.50).
While this is how Rescher actually categorizes the hierarchy of plausibility, a better hierarchy can be given that is more clear and without doing damage to his overall idea. For example, it remains unclear as to how (5) and (6) differ in any significant way. Furthermore, does (2) refer to just the natural sciences, or the social sciences as well? Given what we know about plausibility theory thus far, here is a proposed revised hierarchy:
(1) Definitions, axioms of mathematics and logic, mathematical relations, and in the case of paradoxes, principles of the story. These are 100% certain and cannot be refuted
(2) Physical laws
(3) Scientific theories
(4) Conjectures
(5) Speculative suppositions.
The above hierarchy ought to be clear, only a minor elucidation is needed. When we say a conjecture, we mean that which we expect to be true, but as of yet, has remained unproven. For example, take Fermat‘s Last Theorem. Before it was proven, it was considered merely a conjecture within mathematics. We can also use the example of the continuum hypothesis as an example of a conjecture. It is unclear as to whether the continuum hypothesis is true or false.
The level of plausibility given to a proposition is also based upon the Rescher’s notion of “reliability.” We would apply Rescher’s idea of reliability when we are dealing with claims people make. For example, we would say that a physics professor is more reliable when it comes to matters of physics than a non-physicist. In the case of legal testimony, take two individuals who claim to have seen person x leaving the bank after it was robbed. Let us say that one of those individuals was inebriated at the time, whereas the other individual was not. We would say the individual who was not inebriated is more reliable than the individual who was inebriated.
One must also understand that plausibility theory and probability theory are distinct. The biggest difference between plausibility theory and probability theory is how they would handle the following set: [p, ~p]. Let us assume that we know that proposition p has probability of .8. Since p has probability of .8, we know that ~p must have a probability of .2. Hence, the probability of either p or ~p will either rise or fall depending upon the probability of the other proposition: this is a basic truth of probability theory. In plausibility theory, it is within the realm of possibility that both p and ~p could have the same value; thus, p could be .8, and ~p could be .8.

A Critique Of Using Plausibility Theory To Resolve Paradoxes

As stated earlier, resolving inconsistent sets, especially paradoxical sets, is at the very bedrock of plausibility theory. It will be granted that the logic of plausibility is not only a robust theory, but also internally consistent. Moreover, it will be granted that plausibility theory succeeds in giving us a method of resolving paradoxes. However, this method fails to appreciate not only the very nature of paradoxes themselves, but also collapses into a sort of incoherence. In order to show this, two paradoxes will first be considered: The Lottery Paradox and The Liar Paradox.

The Lottery Paradox

The Lottery Paradox (LP) is a paradox one runs into when working in epistemology. The Lottery Paradox challenges the common sense belief that fallible justifiability only requires high probability. The typical lottery paradox runs as follows: Suppose there is a fair lottery in which 1,000,000 tickets are sold. Moreover, suppose that only one ticket can be the winner. If we select any one ticket, we will see that the probability of that ticket being the winning ticket is .000001%. Since it is highly probable that this ticket will not win, and by assuming the traditional fallible justifiability, we know that the ticket we choose will not win. However, since our choice was random, and since the same probability would have applied to any ticket we selected, we can use the principle of universal generalization to apply our result to every single ticket. The immediate result that we get is that we know that every single ticket will not be the winning ticket. However, as part of the game, one ticket must win. Ergo, we get a contradiction: we know that one ticket will win, but we also know that no ticket will win.
Rescher (2001) concedes that his theory of paradox resolution does not apply in this case, since all the premises of the argument are equally plausible (p. 224). While Rescher is correct, this is not the main point of the paper.
Ever since Descartes proposed that knowledge demanded absolute certainty, there have been skeptical worries. Since infallible knowledge is slim, many epistemologists, both then and now, have been defending theories of fallible knowledge. Until the Lottery Paradox was formulated, it was generally held that high probability was sufficient for justifiability. Intuitively, this seems extremely plausible (excuse the pun). However, the Lottery Paradox demonstrates that high probability is not enough to warrant fallible knowledge. Furthermore, the Lottery Paradox can be formulated using the principle of mathematical induction. Thus, the Lottery Paradox challenges not only modern Epistemology, but also a principle of mathematics.
The Liar Paradox
Ever since the time of the Greeks, the Liar Paradox has been a proverbial thorn in the side of philosophy. In the Liar Paradox, we are asked to considered the following sentence L – L: “this sentence is false.” The question is posed, is (L) true? Assume that (L) is true. If (L) is true, then what it asserts is the case. (L) asserts of itself that it is false. Therefore, (L) is false. Assume that (L) is false. (L) says of itself that it is false. Therefore, (L) is true. From this we get the following biconditional: T(L) Û F(L).
The question naturally arises, how does plausibility theory handle the Liar Paradox? Rescher (2001) declares that: “…‘This sentence is false’ is semantically meaningless: neither truth nor falsity can be ascribed to it” (p. 43). Beyond this sentence, Rescher gives us no further analysis of why (L) is meaningless. To be fair, however, here are the following Liar presuppositions:
(1) (L) is a meaningful declarative sentence.
(2) (L) says of itself only that it is false.
(3) If (L) is meaningful declarative sentence, then it must be either true or false.
(4) Meaningful sentences can be self-referential.
Given what we know about plausibility theory, it is highly likely that Rescher would give the above propositions the following ranking (If he had chosen to rank them: (3) > [(4) (2)] > (1)#. Proposition (3) is a truth of classical logic. Since we can think of countless self-referential sentences that do no lead to absurdities, it seems plausible that (4) is not wrongheaded. In addition, since (2) seems equally as plausible as (4), it receives the same priority ranking as (4). We end up with (1) being the weakest link, for it is a mere supposition.
Regardless of which proposition one chooses to reject, there is an important insight this paradox gives us: that ether the nature of a proposition is not all that manifest, or bivalence is false. If Saul Kripke is correct, then propositions do not necessarily have to be either true or false; they can fall into the “gaps” of truth and falsity. If Graham Priest is correct, then we know that while the law of non-contradiction may be applied in most cases, it is not a necessary truth of logic. If Kripke is correct, we have learned something significant about the nature of truth and of propositions. If Priest is correct, then we have also learned something significant about the nature of truth and propositions. If Bertrand Russell and Alfred Tarski are correct, then we have learned that contrary to intuition, propositions cannot refer to themselves. Furthermore, if Tarski is correct, then we know that any artificial language which has it’s own truth predicate will be inconsistent. Once again, if they are correct we will have learned something significant about the nature of propositions and truth.

Critique of Rescher’s Hierarchy

Given Rescher’s hierarchy of plausibility, we can see that the following relation holds: (1) > (2) > (3) > (4) > (5). Starting with (5) we can see that a proposition gains plausibility the higher it is on the hierarchy. Thus, if (5) was given a plausibility ranking of .2, then it is a basic truth within plausibility theory that (4) must receive a minimum of a .21 ranking. When a proposition receives the ranking of (1) it is given a plausibility ranking of 1.0. Intuitively, the hierarchy seems reasonable. However, what justifies the hierarchy? The hierarchy can be justified in one of two ways: objective evidence external to the mind, or subjective evidence internal to the mind.
Assume for the sake of argument that the Rescherian Hierarchy can be justified in virtue of objective external evidence. If the hierarchy is justified in virtue of external objective evidence, then the propositions within logic and mathematics cannot be refuted. If they are given a ranking of 1.0, then it is logically impossible for the propositions within logic and mathematics to be false. Examining both modern logic and mathematics shows, however, that this is dubious. In order to show it is dubious, we must consider naïve set theory.
In the late 1800’s and early 1900’s, any collection of objects was thought to comprise a set. Before Russell’s paradox, naïve set theory was considered to be one of the most intuitively obvious theories within mathematics. Given the interpretation given to the Rescherian Hierarchy, naïve set theory receives a plausibility ranking of 1.0. However, we need only consult Russell’s paradox to see that naïve set theory is contradictory. Given the interpretation given, a counterintuitive result is that a proposition within mathematics or logic could be 100% plausible, but yet be demonstrably false. An even better example to illustrat this point is the Rule of Necessitation within Modal Logic.
The Rule of Necessitation (RN) within Modal Logic states that if one is able to prove a proposition from the axioms of Modal Logic, then one has also proven that the said proposition p is necessarily true. Hence, one can say that P is a necessary truth, if one can prove P from the axioms. However, this rule is only justified if the axioms of Modal Logic are true. However, if the axioms of Modal Logic are dubious, then saying that a proposition is necessarily true could very well only be a possible or contingent truth.
Assume for the sake of argument that the Rescherian Hierarchy is justified in virtue of its place within our cognitive web of beliefs. If this is the case, the hierarchy will differ from person to person; the hierarchy will even differ among logicians given the soundness of various logics. Given that Graham Priest is a Dialetheist, we can say with confidence that he would not put the Law of Non-Contradiction as having a cognitive status of 1.0. A logician who subscribes to 3-valued logic will explicitly reject the principle of bivalence, while a logician who accepts 2-valued logic will hold the principle of bivalence to be of 1.0. If this is what justifies the hierarchy, then it seems that the hierarchy collapses into mere subjective judgments.
Any way of justifying the hierarchy seems problematic as of now. However, the hierarchy is at the very bedrock of plausibility theory. Without the hierarchy as the foundation for plausibility theory, there is no coherent way of assigning plausibility rankings to propositions. If one cannot assign plausibility rankings to propositions in a coherent way, then plausibility theory collapses.
This criticism of plausibility theory is not an refutation of plausibility theory per say, but rather an informal demonstration that plausibility theory is problematic. Until these problems can be resolved, we must look upon any results plausibility theory produces with great dubiety.

What Paradoxes are “About”

On Rescher’s account of paradoxes, they are mere puzzles of the mind that cause cognitive dissonance. This can be seen most evidently with how Rescher defines what a paradox is. Rescher (2001) describes paradoxes as follows: “a paradox arises when a set of individually plausible propositions in collectively inconsistent” (p. 6). The only problem with this line of reasoning is that it implicitly assumes that plausibility is at the heart of paradoxes. However, this mistakes the effects a paradox might have on ones cognitive apparatus for the paradox itself.
In general, when we say a proposition is more plausible than another proposition we are making a judgment. We are saying “according to me, this proposition seems more reasonable.” Thus, according to Rescher’s definition of what a paradox is, it implicitly assumes that a sentient being is a necessary condition for paradoxes to arise. However, this is not the case.
One can easily imagine a possible world where no sentient beings exist, but the Lottery Paradox propositions are collected together in an inconsistent set. Hence, Rescher’s definition of what a paradox is needs a slight revision. A paradox is a set of propositions that seem to be individually plausible, but are nevertheless inconsistent. On the revised definition, a sentient mind is not necessary condition for a paradox to arise.
Once we eliminate the “human element” from paradoxes, the question remains, what are paradoxes about? The answer to this question will depend upon the type of paradox we are dealing with. For example, in the case of Russell’s Paradox, the paradox is about the flagrant usage of Frege’s Unrestricted Comprehension Principle. We can safely assume that Russell’s Paradox is not about cognitive dissonance. While it may have caused set theorists cognitive dissonance, Russell’s Paradox is not paradoxical in virtue of the cognitive dissonance the set theorists felt; even if the set theorists felt no cognitive dissonance, Russell’s Paradox would still be a paradox. It would be incoherent to think that the truth or falsity of a set of propositions is made true or false merely by a sentient mind cognizing it.
As stated earlier, when trying to resolve paradoxes, Rescher focuses on the cognitive status of the propositions of the paradoxes, rather than whether these propositions are actually fallacious. Thus, according to Rescher, the essential piece of paradox resolution is not in finding actually fallacious principles, but of merely trying to resolve cognitive dissonance. This approach should strike most people as very unsatisfying. It seems, at least prima facia, that when we try to resolve paradoxes we are not merely resolving cognitive dissonance, but that we have come to understand the fabric of reality in a much better way. Moreover, it seems that what a given paradox demonstrates is that something is fundamentally flawed with the way we understand the universe. This can be seen most evidently with the alleged paradoxes of infinity that plagued philosophers and mathematicians since antiquity.
Before Georg Cantor, the concept of “infinity” was generally thought of as a concept riddled with paradoxes. Galileo came up with a famous “paradox” that attempted to demonstrate the absurdity of the concept of infinity. Galileo observed that any infinite set could be put into a one-to-one correspondence with any one of its proper subsets. Hence, the even numbers could be put into a one-to-one correspondence with the natural numbers. It was precisely because of Galileo’s Paradox that lead Cantor to develop the theory of transfinite numbers. Thus, Galileo’s Paradox demonstrated a fundamental misunderstanding we had of infinity: contrary to intuition, there are different sizes’ of infinity. Galileo’s Paradox also demonstrated that we cannot understand the cardinality of infinite sets in the same way we understand the cardinality of finite sets.
If we had applied Rescher’s theory of paradox resolution, one of the greatest discoveries of mathematics might never have been discovered. A given proposition within Galileo’s Paradox would merely have been abandoned as “least plausible.” One of the implicit assumptions that gives Galileo’s Paradox it’s punch is that there is only one size of infinity. However, we know that not only is the above assumption is more than merely the least plausible of the paradox, but demonstrably false.

Truth and Plausibility

At the very bedrock of using plausibility theory to resolve paradoxes is that we are not making claims about what is true or false. Hence, when we abandon a proposition within the context of a paradox, we are not claiming that the said proposition is false; rather, we are making the claim that within the context of a paradox, a given proposition is “least plausible.” If by employing plausibility theory one is not making a claim about the truth or falsity of a proposition, then what are we really accomplishing? To see that plausibility theory is absurd, consider mathematical models that mathematicians construct. The combined efforts of Kurt Gödel and Paul Cohen demonstrated that within Zermelo-Fraenkel Set Theory (ZFC) the continuum hypothesis (CH) was independent of its axioms. Therefore, it would be consistent to either accept or deny the continuum hypothesis.
Given the results of Gödel and Cohen, set theorists have developed mathematical models within set theory based on either the acceptance or denial of the (CH). If we accept (ZFC), then one of the models developed will accurately map the mathematical universe. It is debatable as to which model actually represents the way the mathematical universe is. However, there can be little doubt that set theorists working on the (CH) are trying to figure out which model is true. While the models do not make any claims about what is true, set theorists constructed them with the hope of one day discovering which one is in fact true. The goal of set theorists is to discover what is true, even if they must construct useless models.
Unlike mathematical models, the goal of plausibility theory is not an attempt to get at what is true. While many mathematical models are inevitably useless, the goal is clear: while many of these models cannot be true, we hope that one of them is true. If truth is not the goal of plausibility theory, then what is?
Usefulness and Plausibility
If plausibility theory is not a method for accessing what is true, then what is its usefulness? This question can best be answered by comparing the method of plausibility theory to the method of science. The methodology of science is useful in virtue of its providing us with a way of knowing the empirical world. Hence, we know the scientific method is useful because it simply is the best method one has for knowing the truth or falsity of the propositions about the empirical world. Plausibility theory is cannot be useful in the same way that the scientific method is useful; science claims that certain propositions are true, while others false, whereas plausibility theory makes no such claim. If plausibility theory is not useful in virtue of it providing us with a method of knowing a given set of propositions, then in virtue of what is it useful?
Plausibility theory is useful in virtue of it’s ability to resolve cognitive dissonance, as stated earlier. It must be conceded that plausibility theory succeeds in resolving cognitive dissonance (to a degree). If eliminating cognitive dissonance is the way to resolve paradoxes, a much simpler idea can be given to serve this function: ignore the paradox. When a paradox arises, one can simply choose not to think about it; one can simply kick the paradox under the rug, so to speak. There seems to be no reason why one should favor Rescher’s method over simply ignoring the paradox.

Conclusion

While plausibility theory provides one with a method for resolving many paradoxes, it has been shown to rest upon a faulty diagnosis of what a paradox is. Moreover, how it resolves a paradoxes leaves one feeling unsatisfied. In addition, the way propositions are ranked suffers from serious problems. Perhaps plausibility theory’s greatest drawback is its claim to not deal with what is true or false. Given that plausibility theory is problematic, one should reject it as a viable theory of paradox resolution.

Work Cited

Rescher, Nicholas (2001) Paradoxes. Illinois: Open Court.

Rescher, Nicholas (1961) “Plausible Implication”, Analysis 21(6): 128-135.

Rescher, Nicholas (1976) Plausible Reasoning. Amsterdam: Van Gorcum, Assen

“In the high school halls, in the shopping malls, conform or be cast out” ~ Rush, from Subdivisions

http://www.strategy-business.com/article/04204?gko=70d6e
strategy-business.com
by Tim Laseter and Matthias Hild

Investors and executives are spending an awful lot of time these days analyzing the “bet the company” decisions that corporate leadership teams increasingly are called upon to make. Some are obviously, colossally bad — for example, the bankrupting decision by the late dot-com Webvan to run up an $830 million cumulative loss by building facilities three times larger than needed to meet the market demand. Other big bets turn out spectacularly well. In the mid-1980s, theorizing that Japanese competition would commoditize his main business, Andy Grove, then chairman of Intel, decided to fundamentally shift the company from memory chips to microprocessors, a risky strategy that, as it turned out, positioned Intel to become the dominant player it is today.

But a company’s fate doesn’t hinge only on the big strategic bets of the top brass. More commonly, it depends upon the myriad day-to-day decisions of managers at multiple levels. Do we invest in a new manufacturing technology? What price should we accept for a long-range contract with a major customer? Do we introduce a new product in a new market segment? If enough of these routine decisions go awry — and they easily can — a company will eventually falter. Managers, although rational, still possess the human biases, frailties, and emotions that can cloud effective decision making.

To counteract the hazard of human error in risk assessment and decision making, businesses for decades have employed rigorous analytical techniques (such as decision trees, simulation models, and probabilistic reasoning) drawn from a discipline known as decision analysis. Yet, despite several decades of exposure to these techniques, human intuition and emotion still upend the best-laid plans of CEOs.

Defenders of existing methods of decision analysis argue for better training to overcome these weaknesses. But rather than fight human behavior, decision analysis can em-brace intuition. Plausibility Theory is a promising new approach that accepts the rationality of intuitive decision making and offers business leaders a path forward.

The analytic underpinnings — as well as the weaknesses — of conventional decision analysis lie in Bayesian statistics, named for Thomas Bayes, an 18th-century English Presbyterian minister who developed rules for weighing the likelihood of different events and their expected outcomes. In the 1960s, Harvard Business School Professor Howard Raiffa popularized the application of Bayesian analysis in a business context. Managers influenced by Bayesian theory make decisions based on a rigorous calculation of the probabilities of all the possible outcomes. By weighting the value of each outcome by the probability and summing the totals, Bayesian analysis calculates an “expected value” for any given decision. The technique teaches managers to accept decisions with positive expected values and avoid those with negative ones.

The Gambling Instinct
Unfortunately, making decisions on the basis of an expected value is not very intuitive for most people. Consider a coin toss. You are offered a bet by which you’ll receive $100,000 if the coin lands on heads, but you must pay $50,000 if it lands on tails. Although the expected value of this bet is a positive $25,000 ([50% x $100,000] – [50% x $50,000]), few people would rush to take the wager. The potential downside — losing $50,000 — is simply too great.

However, many decision makers who would reject the high-stakes gamble on the single flip of a coin might accept a situation that redefines the gamble, based upon the results of 100 flips of the same coin. Although the expected value of each individual flip remains $25,000, the chance of a major loss is now extremely low.

Even those with limited mathematical training recognize that the acceptance of 100 independent coin tosses lowers risk; it’s the logic that underlies diversified stock portfolios. But despite the appeal of portfolio betting, Bayesian decision analysis faults the intuition behind it as the “fallacy of large numbers,” since the single bet always has the same expected value of $25,000, whether it is part of a portfolio or not. Paul Samuelson, the 1970 Nobel laureate in economics, showed that even though our intuition tells us to reject the one-shot bet and to accept the portfolio of bets, it is logically inconsistent to do so.

Despite the mathematical proof defending the logic of expected value, in the real world, when hearts and minds do battle, the heart — one’s fears and hopes — often prevails. Our gut instinct knows that focusing on the average result may work in the long run, but as individuals we are more concerned about the specific case: How much can we lose? What’s the likelihood of a bad result occurring?

Plausibility Theory replaces the Bayesian expected-value calculation with a risk threshold that is more comfortable for most people. Although developed only in the last five years, it shows great promise as a way to drive rigorous decision analysis while focusing on the real priority of most decision makers: downside risk. This new theory still examines the range of possible outcomes but focuses on the probability of hitting a threshold point — such as a net loss — relative to an acceptable risk.

For example, using Plausibility Theory to analyze the coin-tossing bet would yield different conclusions about the appropriateness of the one-time bet versus the portfolio of 100 bets. A conservative decision maker might set as a risk threshold no more than a 1 percent chance of losing money. Using the calculus of Plausibility Theory, the gamble on a single coin toss — which presents a 50 percent chance of losing $50,000 — would be rejected. But the gamble of flipping the coin 100 times would be acceptable because the probability of a loss would be well under the risk threshold.

Unknowable Risks
The use of a risk threshold also resolves another conundrum associated with Bayesian statistics: the problem of unknowable risk. Most business decisions involve a mix of knowable and unknowable risks. Knowable risks involve predictable odds. For example, Capital One Financial Corporation in Richmond, Va., amasses data on millions of customers, which allows the company to predict precisely the probability that a customer with a certain demographic profile will default on his or her credit card debt. Uncertainty over whether a particular customer will default remains, but the odds of default are understood well enough that the company can set interest rates high enough to profit. With enough data, such decisions are like the roulette wheel at a casino. Any one customer may win or lose, but “the house” will definitely come out ahead in the long run.

In contrast, unknowable risks cannot be defined with predictable odds. When Capital One first experimented with an auto loan business, it had no historical data to predict the behavior of this new type of customer. Bayesian decision analysis defines a probability for such unknowable risks by inference from the choices made by the decision maker. This approach, however, can also lead to nonintuitive results.

Consider another hypothetical gamble (a bit more complicated than a coin toss, but necessary to illustrate the point, so please bear with us). It’s based on randomly drawing a ball from an urn containing three balls. You have been assured the urn contains one red ball. All you know about the other two balls is that they are either blue or yellow: The urn could contain one red plus two blue balls; or it could have one red plus two yellow balls; or it could contain one red, one blue, and one yellow ball. The knowledge that there is one red ball provides an example of “knowable risk.” The uncertain mix of blue and yellow balls represents “unknowable risk.”

You are given the option to receive a payout of $1,500 based upon the color of one ball drawn randomly from the urn. You can pick red or blue — not yellow — as your winning color. A strict Bayesian view treats the two choices as equal, given the lack of information about the blue balls. But, since it is possible that the urn contains no blue balls, most people will choose red, for it offers the known probability of one chance in three of winning.

If you are then offered another gamble from an identical urn, your choices can easily appear, to a Bayesian, even more irrational. Suppose you are offered $750 if either one of a pair of selected colors — blue/yellow or red/yellow — is drawn. In this scenario, the choices are again between a known and unknown risk. Although you don’t know the mix of blue and yellow, you do know that only one ball is red. So the first option of selecting the pair of blue and yellow as your winning colors produces the “known” probability, a two-thirds chance of winning. The second option, choosing red and yellow, returns us to the “unknown,” because we don’t know how many yellow balls are in the urn: There could be zero, one, or two, and each scenario would produce a very different probability of winning.

So, most people choose the first option because it offers a precisely quantifiable, known probability of two-thirds versus an unknown probability.

Bayesians are troubled by this behavior. If you chose red in the first gamble, it suggests you believe that it is more likely that the urn contains two yellow balls than two blue balls. But, if this is true, you should then prefer the combination of red and yellow in the second bet. From a Bayesian point of view, you are behaving inconsistently based on the contradictory probabilities implicit in your decisions.

Plausibility Theory finds no fault with these intuitive choices. We are rationally choosing knowable risks over unknowable risks because they allow us to examine our decision against a risk threshold.

Back to Business
Analogous gambles occur regularly in companies whenever unknowable risks with no historical precedents drive the profitability of a business strategy. Go back to the Webvan story. According to a February 2001 report in the Wall Street Journal, a venture capitalist told Webvan’s founder, retailing entrepreneur Louis Borders, “Louis, I think this is going to be a billion-dollar company.” Mr. Borders replied, “Naw, it’s going to be $10 billion. Or zero.”

In a sense, the colloquy is like the urn example, for it underscores the limited value of treating all decisions with a common metric of “expected value” presumably equally relevant to any “rational player.” Mr. Borders and the venture capitalist each had different risk thresholds that made them willing to take the bet on the unknown. A successful and wealthy entrepreneur, Mr. Borders implicitly understood that he was making a one-off gamble on an unknowable risk with potentially extreme outcomes. The venture capitalist’s willingness to wager was based on his ownership of a portfolio of risky businesses, wherein a few winners more than justify the majority of startups that bomb. Unfortunately, the thousands of individual investors caught up in the hype surrounding Webvan’s public offering clearly had far lower risk thresholds than either Mr. Borders or the venture capitalist, but most failed to appreciate the unknowable nature of the risks in Webvan. A more explicit recognition of their individual risk thresholds could have saved many naive investors from squandering their nest eggs.

Establishing a risk threshold helps to define downside risks. The financial-services industry, for instance, has begun to embrace a rigorous analysis of downside risk rather than a simple examination of expected value. Using historical data, regulators can assess the amount of money that a bank stands to lose with a probability of some threshold percentage over a specified period of time. The Basel Committee on Banking Supervision recently set forth detailed guide-lines for the calculation of a risk-threshold limit called “value-at-risk,” to determine a bank’s required minimum capital holdings (www.bis.org). These capital adequacy rules are proposed for the Basel II Accord.

Although an explicit calculation of downside risk is still rare outside the field of financial services, the concept could clearly be applied more broadly. Consider a business looking to build a plant in China. The managers might analyze the decision by comparing the cost of the investment to the risk of complete failure. The analysis would examine a range of scenarios — for example, a rapid growth in consumer affluence coupled with favorable exchange rates, versus continued poverty-level existence for the vast majority of citizens coupled with protectionist government tariffs. Although the “expected value” across all of the scenarios may be large because of some very high returns in the most favorable scenarios, the “downside risk” of the worst scenarios may be beyond the risk threshold for the company.

Changing Paradigms
Rigorous application of Plausibility Theory’s new math could change the way many strategic decisions are made. No longer forced to choose between their gut instincts and “rational” analysis, managers can now apply rigorous analysis in a far more instinctive way. Plausibility Theory embraces rather than challenges the rationality of intuitive decision making. Its use of risk thresholds offers an approach to decision analysis that is much easier for managers to accept than the Bayesian expected value. Plausibility Theory offers a comprehensive set of consistent rules for decision making. It draws upon the hypothesis-testing logic of classical statistical methodology while avoiding some of the “paradoxes” created by the Bayesian method.

Further work remains to be done, of course, before the new theory can be established in the world of statistical analysis. The current Bayesian paradigms draw upon more than a century of testing and refinement by several generations of mathematicians, whereas the basic logic of Plausibility Theory has emerged only in the last five years. Nonetheless, many signs within the world of business suggest that the time is ripe for a fundamental rethinking of our definitions of “rational” thought.

The greatest resistance to this new theory as a method for strategic decision making may come from within the community of academics, economists, and statisticians committed to the Bayesian view. As one senior scholar commented, “I hope I die before this takes over. I’ve invested too much effort learning the traditional model to switch at this point.” But businesspeople tend to follow a more practical approach: If it works, use it.

Reprint No. 04204

Author Profiles:
Tim Laseter (lasetert@darden.virginia.edu) is the author of Balanced Sourcing: Cooperation and Competition in Supplier Relationships (Jossey-Bass, 1998) and serves on the operations faculty at the Darden Graduate School of Business Administration at the University of Virginia. Formerly a vice president with Booz Allen Hamilton, he has 20 years of experience in supply chain management and operations strategy.

http://www.manyworlds.com/exploreCO.aspx?coid=CO620413313091
manyworlds.com
by Matthias Hild, Tim  Laseterstrategy+business

A new form of decision analysis is helping executives reevaluate risk management.
You have to make a difficult decision involving risk. You could use a thoroughly rational approach to risk evaluation and accept its results—no matter how terrifying and unintuitive, or you can go with your gut in a way rejected as “irrational” by accepted forms of decision analysis. Unfortunately, now you can see that not only do you have to decide, you also have to decide how to decide. Tim Laseter and Matthias Hild explain a relatively new approach to decision analysis that appears to resolve this painful choice: Plausibility Theory.

In the space of four pages, Laseter and Hild effectively convey the essentials of Plausibility Theory and how it differs from standard decision analysis based strictly on Bayesian probability theory. That standard approach counteracts errors in risk assessment and decision making by using tools such as decision trees, simulation models, and probabilistic reasoning. Although these techniques have been available (and heavily promoted) for five decades, decisions typically remain at the mercy of intuition and emotion. The solution might lie in trying harder or more cleverly to overcome these human weaknesses. On the other hand, as advocates of Plausibility Theory argue, we can stop fighting inherent forms of human behavior and find a way to embrace intuition while retaining a comprehensive set of consistent rules founded on statistical methodology.

The problem with the traditional Bayesian approach is that it relies on an expected-value calculation that produces sometimes highly unintuitive or unacceptable results. Plausibility Theory does away with expected-value calculation, in favor of focusing on downside risk. By taking managers’ risk thresholds seriously, the new approach is more psychologically realistic. It also resolves the problem of unknowable risk that arises frequently, such as when a company enters a market with no historical data on which to base decisions.

As the authors note, Plausibility Theory plausibly challenges the reasonableness of treating all decisions with a common metric of “expected value” presumably equally relevant to any “rational player. Even if the “expected value” across all possible outcomes may be large due to a few high pay-off outcomes, the worst scenarios may embody a degree of “downside risk” beyond the risk threshold of a company. One concern that might arise about Plausibility Theory focuses precisely on its pandering to downside risk. As Peter Drucker wrote this same month, the most effective leaders focus on opportunities rather than risks. It is not yet clear whether Plausibility Theory necessarily conflicts with a growth orientation, but it is a factor worth considering.