Benefits of a Multi-Objective Approach
Over and over again, Riddington, Beck and Cowie (2004) are bedevilled by differing perspectives on the value of preventing an injury or fatality. The authors themselves admit that acceptance of COBA by the government and long years of reliance by the then-railway monopoly on decision-tree analysis have outweighed the oftentimes-subjective stands of other stakeholders such as the community at large and potential or actual victims. And yet, multi-objective approaches better accommodate decision-making under low risk and high-uncertainty.
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Coming to grips with assumptions, pursuing the goal of benefits exceeding costs, determining objectives, and even doing a risk analysis at all are apt to be matters that defy consensus even when discussions involve solely the well-informed and well-intentioned.
Multi-objective approaches may be better suited to evaluating train safety when complemented by subjective probability assessments (SPA). Particularly when uncertainty about attribute levels is high, SPA enables construction of a probability distribution of attributes and overall risk.
Another applicable subset might be the ‘von Neumann-Morgenstern utility’ which works if a decision-maker, say, is indifferent among three objectives such as maximised safety versus high-speed mass transit versus more affordable fares.
Two Approaches to Valuing Human Life
The estimate of future earnings discounted by consumer, inflation is based on the concept of a person as human capital. Disadvantages to relying on the net present value (NPV) of a future earnings stream include the possibility that the presumed inflation rate will be superseded by hyperinflationary shocks, as has happened often enough in the last thirty-five years since OPEC discovered how easily it could bend the world to its will. Second, future cash flows can be nonlinear, as exemplified by promotion or an entrepreneurial venture that reaches a critical mass of market acceptance. Most of all, however, is the ineffable emotional and developmental crippling that a fatality always visits on a family or clan. This can never be monetised.
Past valuation practice is not without its shortcomings, too. In a global context, the lower cost of living in less-developed nations leads to the disturbing notion that a life lost in Nigeria is worth less than one in the UK. Past practice is also no guide to geopolitical factors and the advance of science and technology. For example, the public had been lulled into complacency by the excellent safety record of the airline passenger business. Today, no amount of investment in airport and in-flight security is considered excessive to prevent one more occurrence of the Twin Towers disaster. Similarly, the debate about the increasing marginal cost of health care for citizens of the UK and US is taking place at all only because at least some regulators and society at large admit that the lives of the elderly have only marginal utility. Down that slippery slope lies euthanasia and abandonment, a throwback to the primitive societies that civilized man had thought ill-informed.
Monte Carlo Simulation
Procedurally, one constructs a simulation model for railway fatalities by first allowing for the annual probability of a rail transport accident occurring, which is given as a one-in-five chance each year. To simulate the level of fatalities, by definition unpredictable and random, we employ as a lookup table the fatality equivalents (FE’s) reported by Riddington, Beck, and Cowie (2004) from historical records provided by British Railways, Atkins, and the AEA.
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Table 1: Partial Representation of Model: First Ten Years
Each time an accident occurs, the model then accounts for the range of minor to catastrophic types that might result by relying on generated random numbers to represent random fatality rates but only when an accident occurs. Note that the construct “fatality equivalents” count death as 1, a major injury (e.g. a lost limb) as “merely” 0.1, and a minor injury (e.g. a head bump, a laceration) as 0.005 ‘equivalent fatality.’
By repeating this procedure over very long runs – the equivalent of 2,500 years in this case – the procedure known as Monte Carlo modeling represents probable rates of injury and death that are close to being realistic for an event that is essentially random and predictable. Doing so is based on the rationale that a fluke occurrence of, say, more than one accident a year evens out toward ‘normal’ odds over lengthy periods. Doing such modeling is useful for, among other things, evaluating the worth of safety equipment that had better be maintained and remain operable for long periods if it is to cope with catastrophic accidents of the unknown probability of occurrence.
The results, one among many that one might obtain from the ‘true’ range of train accident occurrence and fatality rates, suggest that over two and a half millennia there will be 500 accidents and 23 of these are likely to cause horrendous FE’s of 400 or more. More typically, the fatality equivalent rate will be closer to 21, still, a regrettable number when taken from the viewpoint of each commuter (and his family) who is harmed.
And yet, even these probable FE’s are low compared to those one might get for a country that experiences more than one railway accident annually. Were the frequency distribution of FE’s used in the model also applicable to that nation’s rail system, the model would have us expect ten times more FE’s overtime.
An Alternative Approach to the Ten Scenarios
The authors appear to have based their choice of the “most likely scenario” on the fact that the risk quotient is marginal to 50% odds of benefits overshadowing costs. One can take issue philosophically with this recommendation because of the assumption that the value of human life is variable, and so are social costs as well as the number of spads. One might well argue that even a Risk Quotient of 0.099 under scenario 1 is sufficient justification to outweigh the requisite investment, notably if special allotments are forthcoming or a community subscription is taken. Even the assumption of an increasing number of SPADs seems unnecessary since the minimum number of 7.9 itself should justify a railway safety system.