Causal Analytics for Applied Risk Analysis Louis Anthony Cox, Jr


Part 5 Risk Management: Insights from Prescriptive, Learning, and Collaborative Analytics



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Part 5
Risk Management: Insights from Prescriptive, Learning, and Collaborative Analytics

Chapter 12

Improving Individual, Group, and Organizational Decisions: Overcoming Learning-Aversion in Evaluating and Managing Uncertain Risks
The descriptive, causal, predictive, and evaluation analytics illustrated in Chapters 3-11 are largely about risk assessment. That is, they are about quantifying how large risks are now; predicting how much smaller they would become if costly interventions were undertaken (e.g., shifting pigs from closed to open production or further reducing air pollution levels); and evaluating how effective past interventions have been and how well current systems that help to monitor and control potential risks are performing. Such analytics help to inform decision-makers about current risks and the probable effectiveness and tradeoffs among objectives created by proposed risk management actions. This chapter and those that follow turn to prescriptive risk management issues: deciding what to do next and learning how to better achieve desired goals. This chapter reviews principles of benefit-cost analysis and practical psychological pitfalls that make it difficult for individuals, groups, and organizations to learn optimally from experience. It proposes possible ways to overcome these obstacles, drawing on insights from learning analytics and adaptive optimization from Chapter 2. Chapter 13 offers advice on how to help move organizations toward effective risk management practices by recognizing and rejecting common excuses that inhibit excellent collective risk management decision-making and by taking advantage of opportunities to learn and collaborate in sensing, interpreting, and responding to warning signs. Chapter 14 considers how regulatory and judicial institutions can work together to promote improved societal risk management and to advance the public interest by assuring that sound causal analytics, manipulative causation, and valid causal inferences, are made the basis for regulatory interventions. Chapter 15, which concludes this book, brings together and extends these prescriptive threads by considering philosophical, game-theoretic, and economic models for how to make risk management decisions with consequences that span multiple generations.
Introduction

Risk management decisions and learning should make good use of information from descriptive, causal, predictive, evaluation, and learning analytics, but it is often not easy to do so. Decision biases distort perceptions and cost-benefit evaluations of uncertain risks and the value of reducing them, leading to risk management policy decisions with predictably high retrospective regret. Well-documented psychological heuristics and biases used in decision-making encourage a phenomenon that we will call learning-aversion: sub-optimal learning and premature decision-making in the face of high uncertainty about the costs, risks, and benefits of proposed changes. Narrow framing, overconfidence, confirmation bias, optimism bias, ambiguity aversion, and hyperbolic discounting of the immediate costs and delayed benefits of learning (Kahneman, 2011) all contribute to deficient individual and group learning, avoidance of information-seeking, under-estimation of the value of further information, and hence needlessly inaccurate risk-cost-benefit estimates and sub-optimal risk management decisions. In practice, such biases can create predictable regret in selection of potential risk-reducing regulations. 



The reinforcement learning and adaptive optimization method surveyed in Chapter 1 suggest principles that can help to improve decisions by more effectively balancing exploration (deliberate experimentation and uncertainty reduction) and exploitation (taking actions to maximize the sum of expected immediate reward, expected discounted future reward, and value of information). This chapter discusses how these and related ideas might be used to understand and overcome learning-aversion and implement low-regret learning strategies, using regulation of air pollutants with uncertain health effects as an example.
Benefit-Cost Analysis
For most of the past century, economists have sought to apply methods of benefit-cost analysis (BCA) (Portney, 2008) to help policy makers identify which proposed regulations, public projects, and policy changes best serve the public interest. BCA provides methods to evaluate quantitatively, in dollar terms, the total economic costs and benefits of proposed changes. In versions commonly used by regulators and analysts, BCA prescribes that decisions be made to maximize the expected net present value (NPV) of resulting time streams of net benefits (i.e., monetized benefits minus costs), with delayed and uncertain impacts being appropriately discounted to yield a net present value for each option being evaluated (e.g., Treasury Board of Canada Secretariat, 1998). Similarly, in law-and-economics analyses of negligence torts, the Learned Hand Rule prescribes a duty to take care to prevent or reduce risk if the cost of doing so is less than the expected benefit (Grossman et al., 2006). In regulatory BCA, benefits are typically measured as the greatest amounts that people who want the changes would be willing to pay (WTP) to obtain them. Costs are measured by the smallest amounts that people who oppose the changes would be willing to accept (WTA) as full compensation for them (Portney, 2008). Recommending alternatives with the greatest expected NPV helps to adjudicate the competing interests of those who favor and those who oppose a proposed change.
Example:  A Simple BCA Justification for Banning Coal Burning
Recall from Chapter the 2002 study in the Lancet suggesting that a relatively simple public health intervention, banning burning of coal in Dublin County, Ireland, created substantial health benefits (Clancy et al., 2002). The study concluded that “Reductions in respiratory and cardiovascular death rates in Dublin suggest that control of particulate air pollution could substantially diminish daily death....Our findings suggest that control of particulate air pollution in Dublin led to an immediate reduction in cardiovascular and respiratory deaths.” In a press release, one of the authors explained that "The results could not be more clear, reducing particulate air pollution reduces the number of respiratory and cardiovascular related deaths immediately" (Harvard School of Public Health, 2002). Citing these estimated benefits, policy makers extended the bans more widely, reasoning that “Research has indicated that the smoky coal ban introduced in Dublin in 1990 resulted in up to 350 fewer deaths…per year.  It has clearly been effective in reducing air pollution with proven benefits for human health and our environment... ” (Department of the Environment Community and Local Government, 2012).

As a simple example to illustrate BCA ideas and principles, suppose that “350 fewer deaths per year” is well-defined, with each such postponed death being valued at $1M for purposes of BCA. (Technically, what actually changes is presumably the ages at which deaths occur, rather than the number of deaths per year. In steady state, the deaths postponed from this year to next year would be exactly offset by the number of deaths postponed from last year to this year, so the number of deaths per year would actually remain unchanged (and on average equal to the number of births per year, since each birth eventually generates one death), even though everyone now lives a year longer. However, for purposes of illustration, we will assume that total benefits of $350M per year from increased longevity is a realistic estimate of the benefits in question.) Assume that extending the coal-burning ban to a wider area is estimated to double the effect of the original ban, creating another “350 fewer deaths per year.” Also for simplicity, suppose that that the total costs of the proposed extended coal ban are estimated as $100M per year (e.g., from diminished coal producer and consumer surpluses, increased costs of gas and electricity as these are substituted for coal burning, unsatisfied demand for more heat at an affordable price in the winter, etc.) For purposes of illustration, only these costs and benefits will be considered. Since total estimated benefits from extending the ban greatly exceed total estimated costs, creating a total net benefit per year from extending the ban that is estimated to be $350M - $100M = $250M per year, the BCA recommendation would be to extend the ban. Even if the estimated cost were doubled or the estimated benefit were halved (but not both), the estimated net benefit would still be positive. Such sensitivity analysis is often used to check whether policy recommendations are robust to plausible uncertainties, as they appear to be here. (This example is continued below.)


Arguably, seeking to maximize net social benefit in this fashion promotes a society in which everyone expects to gain from public decisions on average and over time, even though not everyone will gain from every decision. Hence, BCA offers a possible approach to collective choice that appears to meet minimal standards for justice (it might be favored by everyone from an initial position behind Rawls’s veil of ignorance) and economic efficiency (those who favor an adopted change gain more from it than those who oppose it lose). At first glance, BCA appears to have developed a decision-making recipe that circumvents the daunting impossibility theorems of collective choice theorists (e.g., Hylland and Zeckhauser 1979; Mueller 2003; Man and Takayama, 2013; Nehring 2007; Othman and Sandholm, 2009), which imply that no satisfactory way exists in general to use individual preferences to guide economically efficient social choices while protecting other desirable properties (such as voluntary participation and budget balance). For that is precisely what BCA seeks to do.

However, this chapter argues that, whatever its conceptual strengths and limitations might be for homo economicus, or purely rational economic man, BCA for real-world regulations or projects with risky outcomes often leads to predictably regrettable collective choices in practice (and does not really succeed in bypassing impossibility results in principle). More useful recommendations can be developed by seeking to minimize expected rational regret, rather than to maximize expected NPV, especially when probabilities for different costs and benefits are unknown or uncertain. This criterion, explained further later, is also better suited to the needs of real decision-makers with realistically imperfect information about the costs and benefits of proposed changes than is the principle of maximizing expected NPV.


Example (Cont.):  A BCA Justification for Banning Coal Burning May Be Regrettable

 

In the Dublin study, the original researchers’ conclusion that “The results could not be more clear, reducing particulate air pollution reduces the number of respiratory and cardiovascular related deaths immediately” (Harvard School of Public Health, 2002)” was later questioned by methodologists, who noted that the study lacked key elements, such as a control group, needed to draw valid causal conclusions. Wittmaack, 2007 pointed out that mortality rates were already declining long before the ban, and occurred in other parts of Europe and Ireland not affected by it, and concluded that “Serious epidemics and pronounced trends feign excess mortality previously attributed to heavy black-smoke exposure.” Similarly, Pelucchi et al., 2009 noted that “However, during the same period, mortality declined in several other European countries. Thus, a causal link between the decline in mortality and the ban of coal sales cannot be established.” As of 2012, when the ban was extended to additional areas and towns, there was thus some reason to question whether the original health benefits estimates were credible, or whether they might be simply an artifact of poor statistical methodology. However, the question was primarily of interest to methodologists, and played no significant role in policy-making, which assumed that the original health benefits estimates were at least approximately correct (DECLG, 2012).



Such discrete uncertainties (e.g., will proposed interventions actually cause their intended and projected consequences?) cannot be resolved by simple BCA sensitivity analyses that vary inputs over ranges around the best point estimates of their values. They require confronting the discrete possibility that the true benefits might be zero, or extremely different from the estimated levels (here, around $350M/yr.), due to flaws in the underlying assumptions of the BCA. How best to incorporate such discrete uncertainties into BCA has long been a challenge and topic of controversy among BCA scholars (Graham,1981). It is no easy task to assess and justify specific probabilities for them, and any such probability would be based on information and assumptions that others might disagree with. Thus, the question arises of how to do BCA when there are substantial uncertainties about the underlying premises, modeling assumptions, and policy-relevant conclusions of the cost and benefits models (here, for health risk reductions) being used.

If the original data are available for reanalysis, then methodological issues and challenges can be openly surfaced and discussed, and whether the original BCA conclusions and recommendations change when different methodological choices can be examined. For air pollution studies, original data are not always made available to other investigators. In the case of the Dublin study, however, the Health Effects Institute (HEI) funded the original investigators to re-do their analysis, taking into account methodological considerations such as the need to compare declines in mortality inside and outside the areas affected by the ban. The main result (HEI, 2013) was that, “…In contrast to the earlier study, there appeared to be no reductions in total mortality or in mortality from other causes, including cardiovascular disease, that could be attributed to any of the bans. That is, after correcting for background trends, similar reductions were seen in ban and non-ban areas. The study by Dockery and colleagues shows that accounting for background trends in mortality can be crucial, since the earlier Dublin study appears likely to have overestimated the effects of the 1990 coal ban on mortality rates from diseases that were already declining for other reasons.” Thus, when uncertainty about benefits from a coal ban was finally reduced by further investigation in 2013, it turned out that the originally projected health benefits that had seemed to provide a strong BCA rationale for coal-burning bans were no longer supported. The decision to extend the bans might be considered regrettable, if, in hindsight, the true benefits of doing so turned out to be less than the true costs.

A striking feature of this example is that the analysis done in 2013, comparing reductions in mortality risks from before to after the ban across areas affected and not affected by the ban, could have been done just as easily in 2002 as in 2013. However, there was no felt need to do so. The investigators and the recipients of the analysis believed that the correct interpretation was at hand and was obviously correct (“could not be more clear”), justifying prompt action (the ban) intended to protect the public interest, and making further investigation both unnecessary and undesirable.

The following sections suggest that this pattern is no accident. Rather, there is a strong tendency, which we refer to as learning aversion, to stop BCA calculations and data collection prematurely (Russo and Schoemaker, 1989). Confident recommendations for action may be based on BCA estimates in which the sign of estimated net benefits could easily be reversed by further data or analysis. Sensitivity or uncertainty analyses and additional information may be presented that bolster confidence in results (e.g., by showing that even if the best estimates of costs and benefits are changed by some factor, the recommendations do not change) while doing little to highlight fundamental remaining uncertainties about whether the key premises of the BCA calculations are correct (e.g., that banning coal burning measurably reduces all-cause and cardiovascular mortality risks). In short, rather than, or in addition to, “analysis-paralysis,” the reverse problem of making high-stakes decisions prematurely, when more information having high decision-analytic value-of-information (VOI) is readily available, is also a threat to effective use of BCA. This behavior is unsurprising in light of findings from behavioral economics on how people respond to uncertainties (especially “ambiguous” ones that cannot easily be quantified via known probabilities). Once recognized, it is easily avoided, e.g., by shifting the driving metaphor for BCA away from maximizing expected net benefits based on present information, and toward minimizing later regrets (Russo and Schoemaker, 1989).


The remainder of this chapter is structured as follows. The next section discusses common aspirations and motivations for BCA and discusses its promise and limitations for improving collective choices in societies of homo economicus. Then we discuss key features of purely rational individual decision-making and some impossibility results from collective choice theory for purely rational agents. Turning to how real people make decisions, including many “predictably irrational” ones (Ariely, 2009), we argue that a web of well-documented decision heuristics and biases calls into question the usual normative prescriptive use of elicited or inferred WTP and WTA amounts in many practical applications. Both WTP and WTA amounts are sensitive to details of framing, context, perceptions of fairness and rights, feelings about social obligations and entitlements, and other factors that depart from the simplified economic models (e.g., quasi-linear preferences with additively separable costs and benefits) envisioned in the usual foundations of BCA. Psychological phenomena such as ambiguity aversion (reluctance to bet on unknown or highly uncertain subjective probabilities) imply several forms of what we will call learning aversion, i.e., refusal to use available information to improve decision-making. Simple examples illustrate mechanisms of learning-aversion for organizations as well as individuals. In following the prescriptions of BCA, real people and organizations (whether individuals, companies, regulatory agencies, or legislators and policy-makers) typically spend too much to get too little, for a variety of reasons rooted in decision psychology and political theory. We not only systematically over-estimate the prospective value (net benefit) of projects with uncertain outcomes (as in the planning fallacy (Kahneman and Tversky, 1979)), but we also typically fail to test and learn enough about the likely consequences of alternative courses of action before acting (Russo and Schoemaker, 1989). Hence we make collective bets on social programs and regulations that are excessively risky, in the sense that their benefits do not necessarily, or with high probability, outweigh their costs. We also usually fail to study and learn enough after acting to optimally improve decision-making models and assumptions over time. In effect, our policy-making and regulatory institutions are often learning-averse, with a strong bias toward premature action and insufficient prospective investigation of alternatives or retrospective learning and evaluation of decisions and outcomes (Russo and Schoemaker, 1989). They show a revealed preference for acting as if we already have sufficient information to identify the best course of action with confidence now, even if available information is actually inadequate to do so, and even if a careful decision analysis (based on value-of-information analysis for maximizing expected utility) would prescribe postponing a choice.

The last part of the chaper considers how to do better. For deciding which alternative action to take next (from among those being considered, e.g., to pass or not to pass a proposed new regulation), the BCA prescription “Choose the alternative that maximizes expected NPV” is often less good than the advice from other rules, such as: “Choose the alternative that minimizes expected rational regret,” or “Do not choose yet, but continue to learn from small-scale trials before making a final choice for large-scale deployment.” Results from machine learning and psychology suggest that seeking to minimize regret can be a highly adaptive strategy for uncertain environments in which relevant probabilities of decision outcomes are initially unknown – that is, environments where ambiguity-aversion is likely to be especially important in decision-making. The chapter concludes with comments on the prospects for using regret minimization as an alternative to expected NPV maximization as a foundation for more practical and valuable BCA.


Aspirations and Benefits of BCA
To improve the rationality and effectiveness of collective choices, such as whether to implement a costly regulation or to undertake a costly public works project, economic benefit-cost analysis (BCA) attempts to calculate and compare the total cost of each alternative being considered to the total benefit that it would produce. If an alternative’s costs clearly exceed its benefits, it can be rejected outright.  Conversely, it can be considered further for possible adoption if its benefits exceed its costs, and if no other feasible alternative would create a clearly preferable distribution of costs and benefits.  Even if costs and benefits are uncertain, one can seek to implement only those alternative(s) that produce preferred probability distributions of net benefits (e.g., distributions that are not stochastically dominated by the distributions from other choices). Thus, BCA seeks to inject rationality, objectivity, and optimization into public discourses about what to do with limited resources.

BCA comparisons are admittedly complicated by the need to make trade-offs over time, under uncertainty, and across individuals and groups, especially when those who bear most of the costs of an intervention do not receive most of its benefits.  Despite these difficulties, a welcome element of common sense and benign rationality seem to infuse basic BCA prescriptions, such as Don’t take actions whose costs are expected to exceed their benefits; or Take actions to produce the greatest achievable net benefits.  People may argue about how best to quantify costs and benefits, including how to evaluate opportunity costs, delayed or uncertain rewards, real options, and existence values. They may disagree about how best to characterize uncertainties – e.g., what information, models, and assumptions should be used in estimating the probabilities of different possible outcomes. But the key concept of submitting proposed courses of action to the relatively objective-seeming tests of quantitative BCA comparisons, rather than letting pure politics or other processes drive public decisions about expensive actions, has appealed powerfully to many scholars and some policy makers over the past half century.  

It is easy to understand why.  Without such guidance, collective decisions – even those taken under a free, democratic rule of law – may harm all involved, as factional interests and narrow focusing on incremental changes take precedence over more dispassionate and comprehensive calculations for identifying which subsets of changes are most likely to truly serve the public interest.

 

Example:  Majority rule without BCA can yield predictably regrettable collective choices

 

Table 12.1 shows five proposed changes that a small society, consisting of individuals 1-3 (“players,” in game theory terminology) is considering adopting. The proposed changes, labeled A-E, are shown in the rows, of the table. These might represent proposed regulatory acts, investment projects, initiatives, mandates, etc. The table presents resulting changes in annual incomes for player if each measure is adopted, measured in convenient units, such as thousands of dollars per year.  (For simplicity, the impacts of the different measures are assumed to be independent of each other.) For example, project A, if implemented would cost player 1 three units of income (perhaps in the form of a tax on player 1’s business or activities), and would produce benefits valued at one unit of income for each of players 2 and 3.  Thus, its costs are narrowly concentrated but its benefits are widely distributed. Conversely, project D would impose a tax, or other loss of income, of one unit of income on each of players 2 and 3, but would produce three units of income for player 1.  E is the status quo.



 

Table 12.1.  A hypothetical example of changes in annual incomes (e.g., in thousands of dollars) for each of three people from each of five alternatives



Proposed change

Player 1’s income change

Player 2’s income change

Player 3’s income change

A

-3

1

1

B

1

-3

1

C

1

1

-3

D

3

-1

-1

E

0

0

0

 

 

If the collective choice process used in this small society is direct majority rule, with each participant voting for or against each proposed change, A-E, then which proposed changes will be approved?  Assuming that each voter seeks to maximize his own income (or minimize his own loss), measures A-C will be adopted, since a majority (two out of three) of the players prefer each of these to the status quo.  Summing the changes in incomes for all three of the adopted measures A-C shows that each player would receive a net loss of 1 unit of income from these three adopted collective decisions. Thus, applying simple majority rule to each proposed change A-E creates a predictably regrettable outcome: it is clear that changes A-C will be adopted (the outcome is predictable) and it is clear that this will make all voters worse off than they would have been had they instead rejected the changes and maintained the status quo (the adopted changes are, in this sense, jointly regrettable).


The problem illustrated here is familiar: each voter is willing to have “society” (as embodied in the collective choice process) spend other people’s money to increase his own benefit.  Yet, when each faction (a coalition, or subset of players, such as players 2 and 3, for change A) has the political power to adopt a measure that achieves gain for all its members at the expense of its non-members, the portfolio of alternatives that end up being adopted harms everyone, in the sense that everyone would have preferred the status quo. Political theorists have recognized this possibility for centuries; it loomed large in Federalist Paper Number 10, and in concerns about tyranny of the majority. 
BCA seeks to remedy this ill by subjecting each alternative to a cost-benefit test. A familiar example is the potential compensation test: Do the gainers gain more than the losers lose?  Would those who prefer adoption of a proposed alternative still prefer it if they had to fully compensate those who preferred the status quo? (This question makes sense under the usual assumptions of quasi-linear preferences (utility can be expressed as benefits minus costs) and if utility is assumed to be transferable and proportional to money. Although these assumptions, in turn, may be difficult to defend, they suffice to illustrate some key points about strengths and limitations of BCA even under such idealized conditions.) Alternatives A-C in Table 12.1 fail this test, but alternative D – which would not be selected by majority rule – passes. For example, if a tax of one income unit taken from each of individuals 2 and 3 allows individual 1 to gain a benefit (such as socially subsidized healthcare) evaluated as equivalent to three income units, it might be deemed an alternative worth considering further, since individual 1 could (at least in principle) pay one unit of income to each of individuals 2 and 3 and still be better off (by one income unit) than before the change.  BCA practitioners often apply such tests for potential Pareto improvements to determine whether a proposed change is worth making (Feldman, 2004).

Of course, taking from some to benefit others, especially if potential compensation remains only a theoretical possibility, raises questions about rights and justice (e.g., is enforced wealth transfer a form of theft? Would individuals voluntarily choose to adopt procedures that maximize estimated net social benefits, if they made the choice from behind the veil of ignorance in Rawls’s initial position?) Moreover, it is well known that potential compensation criteria can lead to inconsistencies when a proposed alternative to the status quo increases one good, e.g., clean air, but reduces another, e.g., per-capita income. (Those who prefer a change in the status quo might still do so if they had to fully compensate those who prefer it; and yet those who prefer the status quo might still do so if they had to fully compensate those who do not (Feldman, 2004).)   Thus, potential compensation tests are by no means free of conceptual and practical difficulties. Nonetheless, the idea that a proposed change should not be adopted unless its benefit (defined as the sum of willingness-to-pay (WTP) amounts from those who want it) exceeds its cost (defined as the sum of willingness-to-accept (WTA) amounts needed to fully compensate those who don’t) provides a plausible and much-cited screen for eliminating undesirable proposals (Portney, 2008).



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