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The Business Lawyer article: Belated Comment




Re: Ronald David Greenberg, The Lawyer's Use of Quantitative Analysis in Settlement Negotiations, 38 Bus. Law. 1557 (1983) ["Greenberg, 38 Bus. Law 1557 (1983)"]. Click here for more information on article.  Click here for publications citing article.   Click here for information on settlement out of court versus litigation.

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Comment: Greenberg, 38 Bus. Law 1557 (1983) focuses on the attorney's role in advising clients of the prospects of a successful outcome in a case for damages in court. According to Holmes, in The Path of the Law (10 Harvard Law Review 457 (1897), one object of lawyers is to advise clients by engaging in "prediction, the prediction of the incidence of the public force through the instrumentality of the courts." Greenberg, 38 Bus. Law 1557 (1983 at page 1557, Introduction, first full paragraph, last sentence.

The article emphasizes that courts may award to an injured party damages measured by the present worth of the injured party's future earnings, rent, or other income lost (e.g., in cases re personal injury, wrongful death, real property, contract, taxation, and bankruptcy). The article undertakes an evaluation of settlement out of court versus trial in court. Id. at 1559, at first full paragraph, first two sentences ["main purpose of this article is to suggest that in some circumstances the application by lawyers of quantitative analysis using concepts of probability and present value is not a radical departure from accepted legal analysis. The tools of probability and present value, which combine into the concept of expected present value, have long been applied by courts in the law of damages in a variety of contexts to determine compensation to successful plaintiffs"].

See also  Ronald David Greenberg, Quantitative Aspects of Legal Analysis, 1976 Ins. L.J. 589 (1976) ["Greenberg,, 1976 Ins. L.J. 589 (1976)"] at page 590, second full paragraph, third sentence ["law is replete with examples of the use of interest, present, value, and expected value in grappling with this kind of uncertainty in the law of damages" referring to uncertainty as discussed by Bertrand Russell, in his A History of Western Philosophy (1945) at page 663 in commenting on Hume's Treatise on Human Nature, part of the treatise "Of Knowledge and Probability," that Hume does not mean mathematical theory of probability (such as in chances in throwing dice) but instead "uncertain knowledge" of the future and "unobserved portions of the past and present," which includes "everything except, on the one hand, direct observation, and , on the other, logic and mathematics"]; at page 589, fn. 2 [re "utility"] and fn. 3 [re "opportunity cost"].

A Belated Comment:


Earlier articles in error: The preamble to Victor, The Proper Use of Decision Analysis to Assist Litigation Strategy, 40 Bus. Law 617 (1985) ["Victor, 40 Bus. Law 617 (1985)"] contains the following remarks: "Unfortunately, the last few years have also seen a number of articles that incompletely or incorrectly describe decision analysis" [at fn. 1 and accompanying text]; "This article attempts to correct some of the misconceptions they might have created" [next sentence]; "The earlier articles have all trivialized the purpose of using decision analysis" [first sentence after preamble]. The following articles are listed (in fn. 1): Peterson, New Tools for Reducing Civil Litigation Expenses (1983); Bodily, When Should You Go to Court?, 59 Harv. Bus. Rev. 103 (May-June 1981); Greenberg, The Lawyer's Use of Quantitative Analysis in Settlement Negotiations, 38 Bus. Law. 1557 (1983); Nagel, Applying Decision Science to the Practice of Law, 30 Prac. Law. 13 (Apr. 15, 1984) [at fn. 1].

As to, e.g., Peterson (at fn. 5 [ preceding discussion should make it clear that Peterson has seen too few good decision analysis]; Nagel (at fn. 10) [allowing for probability ranges will only promote fuzzy thinking; same criticism can be leveled against breakeven or "threshold" analysis, especially the two- and three-way versions suggested by Nagel]. As to Greenberg, 38 Bus. Law 1557 (1983), comparative views on selected issues are highlighted below with italics in crimson.

For an excerpt of Victor, 40 Bus. Law. 617 (1985), click here. For more information on Mr. Victor, click here (Google™ search results).For more information on his company, Litigation Risk Analysis, Inc. (which provides consulting on Litigation Risk Analysis™),  click here.


Best guess v. range: Victor, Bus. Law 617 (1985) continues, e.g., "The second problem with some of the previous articles is their lack of understanding of probabilities. Probabilities are nothing more than the quantitative expression of a lawyer's professional best guess. Lawyers make best guesses all the time. In fact, that is one of he principal reasons they are retained in the first place--to counsel the client as to the value of the lawsuit. Few lawyers could stay in business if they refused to give opinions" [at page 625, second full paragraph].

Victor, Bus. Law 617 (1985) continues, e.g., "Once one appreciatess that probabilities are simply a less ambiguous way to express subjective judgments, one should realize how inappropriate it is to talk about a range of probabilities, as Greenberg did [at fn. 9 and accompanying text]; "At any one point in time, there is only one probability that best reflects a single attorney's judgment" [at page 626, first sentence of first full paragraph]; "It is utter nonsense for a lawyer to have a range of probabilities on winning a lawsuit. Imagine telling a client that the overall chances of winning a lawsuit (all legal and factual uncertainties considered) are "about even" (50%), and then in the next breath saying "but this case is almost a sure winner" (90%)!" [at page 626, third asnd fourth sentences of second full paragraph].

Cf., e.g., Greenberg, 38 Bus. Law 1557 (1983) at page 1578, at paragraph one, sentence one ["above range of damage awards reflects an optimistic scenario, a pessimistic scenario, and a most likely scenario on the damages issue"]; at fn. 48 [citing Vagts' example of client's receiving an offer to settle for $40,000, if lawyer advises client to accept offer; in effect, the lawyer is advising that the expected value "figure is no more than $40,000"]; at fn. 55 [citing analysis of Grayson in Victor Brudney and Marvin A. Chirelstein, Corporate Finance (3rd ed. 1987) [Brudney and Chirelstein] at pages 52-53 that a"probability distribution, in its simplest form, could consist of only a few estimates, one popular form consists of three figures: the optimistic, most likely, and pessimistic," or the "high, low, or best guess" estimates"; proper to ask forecaster to give estimates of "entire range of figures that might occur--entire probability distribution, now more information available for decision maker]; Dennis E Logue, Handbook of Modern Finance (1984) (Kerry D. Vandell (chap. 33 Real Estate Finance)) at pages 55-56 [sensitivity analysis [sic] attempts to test the degree of uncertainty in various parameters, usually carried out by varying the values of the input variables in the model and observing the effect on output; usually, the analyst’s judgment is used to select optimistic, most probable, and pessimistic values for each parameter].


Most realistic v. range:  Victor, Bus. Law 617 (1985) contains the statement: "Besides sounding foolish on its face, there are other problems with Professor Greenberg's suggestion that counsel use a range of probabilities. Why would a client want anything other than the attorney's most realistic assessment?" [at page 626, first two sentences of third full paragraph]. Cf. Greenberg, 38 Bus. Law. 1557 (1983) at page 1578, paragraph one, sentence four ["client should appreciate that counsel is giving the most realistic evaluation possible"].


Subjective probability; different persons may differ:  Cf., e.g.,Grayson, The Use of Statistical Techniques in Capital Budgeting, Financial Research and Management Decisions (Robichek ed. 1967) at pages 98-107, reproduced in Brudney and Chirelstein at pages 52 -56 [personalistic or subjective view as probability of a single event without involving repeatability in long run; no probability is unknown to person making the prediction; he can determine probability by interrogating himself; in real life no truly objective probabilities exist; all probabilities are subjective; if large amounts of historical or past data exist, these should be considered and will strongly influence the subjective assignment of the probability of future event; research has shown the two decision makers with roughly the same objective data or past experience will assign to the future roughly the same subjective probability if they believe the future will be similar to the past,but if one forecaster believes in a structural change, or has reliable information on a change, he may alter or discard past data in making his subjective probability assignment]. Samuel B. Richmond, Operations Research for Management Decisions (1968) [Richmond] (some other person might classify these subjective probabilities differently; it is not to be expected that two given persons will agree on the exact subjective probability value that should be assigned to a particular phenomenon; the interpretation that should characterize their subjective probabilities is possible to define; imagine a ”perfect” roulette wheel with its circumference divided into 10 equal, equally-likely sectors, 7 of which labeled “success” and 3 of which labeled “not-success;” or imagine a wheel having only 3 divisions, 2 of which are “success”; the mathematical methods, rules and procedures for manipulating and computing probability values are the same, regardless of the original source of the original probability values and the interpretation persons may wish to assign to them).
Cf. also, e.g.Eugene L. Grant and W. Grant Ireson, Principles of Engineering Economy (4th ed. 1960) at fn. 8, page 267, Ch. 13 [many modern writers on statistical decision theory and operations research advocate use of probabilities obtained through intuition in cases where no data available to estimate relative frequencies in long run; for clear exposition of case for use of such “personal probabilities” in decision making, see Robert Schlaifer, Probability and Statistics for Business Decisions (1959)]; Frederick Mosteller, Rober E. K. Rourke, Georg B. Thomas, Jr., Probability and Statistics - Official Textbook for Continental Classroom (1961) at 2-3 [two extreme positions on probability (and many in between) are objective and personalistic; personalist regards probability as measure of personal belief and believes that different reasonable individuals may differ in their degrees of belief, even when offered the same evidence, and so their personal probabilities may differ; when the amount of data is large, each usually gets similar answers; last word is never said on these matters; new schools of thought arise]; Mark L. Berenson and David M. Levine, Basis Business Statistics: Concepts and Applications (4th ed. 1989) at 177-178 [subjective probability refers to the chance of occurrence assigned to an event by a particular individual and may be quite different from the subjective probability assigned by another individual; assignment of subjective probabilities to various events usually based upon a combination of an individual’s past experience, personal opinion, and analysis of particular situation]; Robert Schlaifer, Probability and Statistics for Business Decisions (1959) [re, e.g., Bayesian analysis, subjective knowledge, decision trees]; Leonard J. Savage,The Foundations of Statistics (2d rev. ed. 1972) at pages 27-67 [persons may differ on decisions by assigning different utility functions or different beliefs on probabilities of outcomes]and Leonard J. Savage, excerpt of address at The International Congress of Mathematicians, Edinburgh (14 August to 21 August 1958) [contrary to what the word 'subjective' seems to connote to many, the theory is not mysterious or particularly not operational; it gives, a few of us believe, a consistent, workable, and unifying analysis for all problems about the interpretation of the theory of probability, a much contested subject; it unifies the treatment of uncertainties, measuring them all by probabilities and emphasizing that they depend not only on patterns of information but on the opinions of individual persons].

Pretrial strategy:  Victor, Bus. Law 617 (1985) also adds [at page 627, first full paragraph] that "a role for using computers (or calculators) to perform 'sensitivity analysis' clearly exists: varying probabilities and recalculating the settlement("expected value") can provide insights valuable for planning pretrial strategy." Cf. Greenberg, 38 Bus. Law. 1557 (1983) at page 1585, text accompanying fn. 138 [competent use of the computer in developing decision trees may save time and yield more accurate and consistent results] and Greenberg,, 1976 Ins. L.J. 589 (1976) at page 603 [legal analysis benefits from "greater innovation in the use of mathematics and the computer on many legal matters"].  Cf. also Greenberg, 38 Bus. Law 1557 (1983) at page 1579, third full paragraph [the "lawyer could also reassess the value of the case from time to time as the case developed" [first sentence], and "the lawyer might wish to reassess the expected present value of the case from time to time before trial, during trial, and on appeal if an appeal is made" [third sentence].

More precise disciplined decisions:  Victor, Bus. Law 617 (1985) adds further that decision analysis "[w]hen properly used , this technique imposes discipline on counsel forcing them to think as carefully and systematically as possible about the evidence and legal issues that are important to their case." Victor, Bus. Law 617 (1985), at page 617, preamble, second sentence. It adds that "pretrial planning is impossible with all the simple decision trees that merely begin with win or lose" and "can be performed only following the construction of a richer decision tree that includes both influencing factors and ultimate issues". Victor, Bus. Law 617 (1985), at page 627, fourth full paragraph. It concludes that "when properly used, decision analysis can be a great supplement to the intelligent attorney". [Id. at page 628].

Cf. Greenberg, 38 Bus. Law. 1557 (1983) at 1559, first full paragraph, first full paragraph, third and fourth sentences ["thesis of this article [is] that an expected present value analysis should be used by lawyers" and that "in dispute resolution [it] will enable lawyers to give better counsel to their clients, especially business clients" on questions of settlement versus judgments on the merits]; at page 1585, second full paragraph, fifth sentence ["lawyer will be forced to think more precisely about each aspect of case, and thus his judgment about the whole case will be more acute"]; at sixth sentence ["will give the financially minded client a meaningful vantage point from which to judge settlement proposals"].


Subjective probability; unique events; relative frequency: See, e.g., Milton H. Spencer and Louis Siegelman, Managerial Economics: Decision Making and Forward Planning (revised ed. 1964) at pages 9-14, 29-31 [dispersion; range; standard deviation]; William J. Baumol, Economic Theory and Operation Analysis (second ed. 1965) [Baumol] at pages 550-558, 571 et seq.; Ivan S. Sokolnikoff and Elizabeth S. Sokolnikoff, Higher Mathematics for Engineers and Physicists (2nd ed. 1941) at pages 492-523, 525-560. Cf. Murray R. Spiegel, Theory and Problems of Statistics (1961) at page 305 [In forecasting, to estimate the trend many possible methods can be used]; H. T. Hayslett, Jr., Statistics Made Simple (1968) at page 35 [Certain sort of imprecision is intolerable in mathematics; part of the imprecision is due to the fact that the probability of unique event is being discussed, and part of it comes from discussing an event for which there is more than one point of view; these difficulties can be avoided if we restrict our discussion of probability to events which are outcomes of experiments that can be repeated, and if we deal with idealized situations]; Iver E.Bradley and John B. South, Introductory Statistics for Business Economics (1981) [Bradley and South] at page 73 [one is not completely free in the assignment of probability to events; probabilities assigned to the events must be rational (e.g., assigning a probability of 1.5 or -.5 is irrational].

See also, e.g., David S. Moore and George P. McCabe, Introduction to the Practice of Statistics (1989) at pages 309-310 [mathematical probability is an idealization based on imagining what would happen to the relative frequencies in an indefinitely long series of trials; long-term relative frequency is not the only intuitive interpretation of probability; observing many outcomes is only one source of personal opinion about the chance that the next toss will produce a head; the mathematics of probability makes more sense if you keep in mind long-term relative frequency or personal assessment of chance; we will therefore concentrate on the relative frequency interpretation of probability]; Neil E. Harlan, Charles J. Christenson, Richard F. Vancil, Managerial Economics: Text and Cases (1962) at pages 200, 202-204 [even when a decision maker lacks a firm quantitative base, in the form of relative frequencies, for assigning probabilities to events, he may have a certain amount of qualitative experience that enables him to make such judgments as “event A is more likely than event B"; to “measure” probability judgments, we need some sort of “yardstick” against which to match up events; use of the yardstick urn as a hypothetical frame of reference will be helpful in developing one’s intuition about probability estimates; two ways in which probabilities could be assigned to events are: (1) by using observed relative frequencies or (2) by reducing judgments about likelihoods of events to a numerical basis; simulation (Monte Carlo) methods of estimating probabilities may be appropriate in certain processes that are feasible to manipulate experimentally and that can be used as a model for the real process of interest]; Robert Schlaifer, Probability and Statistics for Business Decisions. An Introduction to Managerial Economics under Uncertainty (1959) [practical examination of subjective probability and utility]; Howard Raiffa and Robert Schlaifer, Applied Statistical Decision Theory (1961); John W. Pratt, Howard Raiffa, Robert Schlaifer, Introduction to Statistical Decision Theory (1995) [examines subjective decision approach and objective (classical) approach].


Best estimate; probable error in empirical experiments:  See, e.g., Esbach: Handbook of Engineering Fundamentals (2d ed. 1952) at Section 2, Mathematics, Article 23, Statistical Design of Experiments, at page 2-32 [to get valid conclusions from an experiment, need proper control of other variables besides those being investigated and sufficiently large and random samples]; Article 24, Precision of Measurements, Observations and Errors, at page 2-33 [in a large number of measurements random errors are as often negative as positive and have little effect on the arithmetic mean; all other errors are systematic and if due to the same cause, affect the mean in the same sense and give it a definite bias; if all systematic errors are eliminated, possible to consider sample of individual repeated measurements of a quantity with a view to securing the "best" estimate of the mean value m and assessing degree of reproducibility that has been attained; final result expressed in the form E ± L, where E is the best estimate of m, L is the characteristic limit of variation associated with a certain risk not merely E, but entire result E ± L is the value measured]; Precision of Measurements, The Normal Distribution, pages 2-33 to 2-38 [e.g., Relative Frequency of Errors (error distribution curve with precision index that measures the concentration of observations about their mean); Probability (the fraction P of the total number of errors whose values lie between x = -a and x = a on error distribution curve Probable Error (results of measurements sometimes expressed in the form E ± r, where r of single observation (E ± r, where r is the probable error of a single observation and is defined as the number that the actual error may with equal probability be greater or less than))]; Conditions of Applicability [observations made with equal care and skill, individual deviations are small in most cases, assuming a normal error distribution curve; if number of observations n in a sample is small, the estimate of the standard deviation (σ) of the possible infinity of observations with a mean m is itself subject to considerable error (e.g., probable error calculations are quite legitimate, e.g., for n > 100; and for n < 30, a rough estimate can be obtained from the fact that a percentage of cases lying outside the range, m ± kσ, is < 100k-2.for k > 1 and is non-parametric(independent of the nature of the distribution assumed))].

Precision:  For a view of precision (or lack of precision) in, e.g., engineering on the calculation of factors of safety in structural design, see, e.g., Kent's Mechanical Engineers' Handbook: Design and Production Volume (12th ed. 1950) at Section 8, Strength of Materials, page 8-06 [although no definite rules can be given, if a factor of safety is to be used, the following circumstances, among others, should be taken into account in its selection: ultimate strength of material known within narrow limits, as for structural steel for which tests of samples have been made, load is entirely a steady one of known amount, and no reason to fear deterioration of metal by corrosion, lowest factor is 3; strength of material or amount of load, or both, uncertain, factor should be increased by an allowance sufficient to cover amount of uncertainty; strains are complex and of uncertain amount, such as those in the crankshaft of a reversing engine, very high factor is necessary, possibly even as high as 40; property loss caused by failure of the part may be large or if loss of life may result, as in a derrick hoisting materials over crowded street, factor should be large].

Risk; utility function:
The decision maker must try to ascertain whether a client is "risk neutral"(Victor, Bus. Law 617 (1985) at fn. 6), risk averse, or of opposite inclination. This assessment will necessitate an inquiry into a client's marginal utility to estimate the expected utility function applicable.On the relevance of marginal utility and opportunity cost in these matters, see, e.g.,Greenberg, 1976 Ins. L.J. 589 (1976) at page 589, fn. 2 [marginal utility: re person's accumulation of wealth, each successive unit of wealth tends to less appreciated (as accumulated wealth increases, marginal utility of the additional wealth decreases]; at page 590, fn.3 [opportunity cost]; and at page 590, fn. 5 [citing Neil E. Harlan, Charles J. Christenson, Richard F. Vancil, Managerial Economics: Text and Cases (1962) at pages 187-217 re expected monetary value; expected utility; attitude toward risk]. See also, e.g.,Brudney and Chirelstein at pages 58-65 [utility; risk aversion; dispersion]; Bradley and South at pages 483; 500-508 [utility; expected monetary value]; Richmond at pages 530-531[utility function]; Baumol at pages 518-520 [expected utilities v. expected (actuarial) value]. For more information on: risk aversion (and its opposite), click here; opportunity cost, here.

Basic goals:  One of the goals in
Greenberg, 38 Bus. Law. 1557 (1983) and Greenberg, 1976 Ins. L.J. 589 (1976) was to cite examples of present value and expected present value to encourage lawyers to use decision tree analysis in advising clients on settlement. See, e.g.,Greenberg, 38 Bus. Law. 1557 (1983) at fn. 100 and accompanying text; Greenberg,, 1976 Ins. L.J. 589 (1976) at fn. 78 and accompanying text. Both articles focus on basic concepts with which most lawyers may be somewhat unfamiliar: present value, probability (objective and subjective), expected present value, its application to legal contexts (e.g., law of torts, product liability, personal injury, contracts, property, taxation, and bankruptcy), and the use of decision tree analysis in the law.

A more basic goal in both The Business Lawyer article and The Insurance Law Journal article was to introduce lawyers to this decision tool to persuade them of, and interest them in, its usefulness. Most lawyers are usually not comfortable with quantitative analysis. Thus Greenberg, 38 Bus. Law. 1557 (1983) treaded softly on possible complexities of a decision tree whereas in The Insurance Law Journal, Greenberg, 1976 Ins. L.J. 589 (1976), a complex case for a client was reduced to a hypothetical containing a fairly complex decision tree. The hypothetical in The Insurance Law Journal article was derived from litigation involving a large multinational corporation, which litigation was the subject of a legal memo to the senior litigator on the case in which expected present value decision tree analysis (probably an uncommon topic among lawyers at the time) was introduced. See Greenberg,, 1976 Ins. L.J. 589 (1976) at pages 601-603, 605-607.


General comments:  The above authorities suggest that in the realm of subjective probabilities applicable to out-of-court settlements (and other situations) a decision maker may find persuasive analyses that in some situations extend beyond a one best estimate or guess, a one best answer, or a similar criterion. (What if, e.g., an antitrust case had market definition issues with overtones of conscious parallelism and other complicating factors over which counsel for the party seeking a possible settlement, as well as the courts, regulators, and legislators that have weighed in on these issues (in the past or currently, or both), in the United States and abroad, could, and do,reasonably irreconcilably, differ, on various aspects (long-term or short-term, or both) of the case? Add to the mix: economists, executives, corporations, politicians, and others, having an intellectual interest or possibly financial or political interests in the outcome of the case, to stir up the pot further.)


More information on above authorities:  For more information on: Mark A. Peterson, click here and here; Samuel E. Bodily, here; Stuart S. Nasgel, here; Samuel B. Richmond, here; Victor Brudney, here; Marvin A. Chirelstein, here, C. Jackson Grayson, here; Eugene L. Grant, here; W. Grant Ireson, here; Frederick Mosteller, here; Robert E. K. Rourke, here; George B. Thomas, Jr., here and here; Mark L. Berenson, here; David M. Levine, here; Dennis E. Logue, here;Kerry D. Vandell, here; William J. Baumol, here; Ivan S. Sokolnikoff,here; Elizabeth S. Sokolnikoff, here; Howard Raiffa, here; John W. Pratt, here and here; Robert Schlaifer, here; Milton H.Spencer, here; Louis Siegelman, here; H. T. Hayslett, Jr.,  here; Murray R. Spiegel, here and here; Neil E. Harlan, here and here; Charles J. Christenson, here; Richard F. Vancil, here; Leonard J. Savage, here and here.