Applications
Latest publications
- Corroboration of the J-value model for life expectancy growth in industrialized countries. (Thomas, P., 2017, Nanotechnology Perceptions)
- Does health spending need to outpace GDP per head? (Thomas, P., 2017, Nanotechnology Perceptions)
This is a collection of papers that develop the J-value methodology of the core papers, and highlight applications of the J-value.
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6. Thomas, P. J., Stupples, D. W., and Jones, R. D., 2007, "Analytical techniques for faster calculation of the life extension achieved by eliminating a prolonged radiation exposure", Trans IChemE, Part B, Process Safety and Environmental Protection, May, Vol. 85 (B3), 1 – 12.
The life extension achieved by a safety scheme that reduces or eliminates a prolonged radiation exposure is a necessary parameter for calculating the Judgment-or J-value, which enables the scheme's worth to be measured on a common, objective scale against which health and safety spend across all economic sectors can be assessed. The life expectancy calculation for radiation exposure is necessarily complex because of the long and stochastic incubation periods associated with radiation-induced cancers. Analytical methods are presented to reduce the size of this calculation approximately a hundredfold. This renders the J-value assessment much quicker and easier for new safety systems that may be considered for nuclear plant.
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7. Jones, R. D., Thomas, P. J., and Stupples, D. W., 2007a, "Numerical techniques for speeding up the calculation of the life extension brought about by removing a prolonged radiation exposure", Process Safety and Environmental Protection, July, 85(B4), 269 – 276. Erratum: Process Safety and Environmental Protection, November, 85(B6), 599.
The judgement- or J-value, which enables the worth of any health or safety scheme to be measured on a common, objective scale, may be applied to a scheme to reduce or eliminate a prolonged radiation exposure provided the life extension achieved can be calculated. The calculation is necessarily complex because of the long and stochastic incubation periods associated with radiation-induced cancers. However, numerical techniques are presented here that speed up the calculation of the improved life expectancy by a factor of about one hundred. The J-value assessment of new safety systems on nuclear plant is thus made much quicker and easier.
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9. Jones, R. D., and Thomas, P. J., 2009, "Calculating the life extension achieved by reducing nuclear accident frequency", Trans IChemE, Part B, Process Safety and Environmental Protection, Vol. 87, 81 – 86.
Improvements in nuclear safety are often achieved through introducing a new safety measure that reduces the frequency of a hazardous accident rather than its consequences. To carry out a J-value analysis, it is necessary to calculate how a reduction in accident frequency extends the life expectancy of the potentially exposed group of people. The paper presents two methods for calculating the loss of life expectancy associated with accidents of a certain severity occurring with a defined frequency. The first begins by using an equivalent, prolonged radiation exposure to represent the effects of the accident occurring once per year over the given period of operation. The resultant loss of life expectancy is then scaled by multiplying by the frequency of occurrence. The second method calculates the loss of life expectancy brought about by a single accident occurring during the given period of operation and scales this by multiplying by both the length of the operational period and the frequency of occurrence. Results derived using the first method show that there is a relatively small effect on loss of life expectancy per accident if several accidents are assumed to occur during a typical period of operation. This conclusion permits a simple assessment of the effect of possible, multiple accidents. The accuracy of the second method is found not to be compromised materially by ignoring the possibility ofmultiple accidents. The second method is shown to be slightly more conservative than the first, and also somewhat more accurate. Calculations of the loss of life expectancy may be carried out before and after the new safety improvement has been implemented, and the difference between the two results will be the life extension brought about by the new safety measure.
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10. Thomas, P. J. and Jones, R. D., 2009, "Calculating the benefit to workers of averting a prolonged radiation exposure for longer than the working lifetime", Trans IChemE, Part B, Process Safety and Environmental Protection, Vol. 87, 161 – 174.
The J-value method enables health and safety schemes aimed at preserving or extending life to be assessed on a common, objective basis for the first time, irrespective of industrial sector. For this it requires an estimate of the improvement in life expectancy that the health and safety scheme will bring about. This paper extends the range of nuclear-safety-system lifetimes for which it is possible to calculate the increased life expectancy amongst nuclear-plant workers whose radiation exposure the safety system has reduced. Whereas the previous mathematical technique was able to cater for a nuclear-safety-system lifetime up to the working lifetime of the nuclear-plant workers (typically between 45 and 50 years), the new method extends without limit the range of tractable, safety system lifetimes. This is important now that the design lifetime of nuclear power stations can be up to 60 years. The development will also facilitate the assessment of safety systems and procedures to protect workers on long-term nuclear decommissioning and waste sites; in the latter case, the service life-time could be hundreds of years. The case when the safety-system lifetime is greater than the working lifetime is addressed by splitting the workforce into a set of three cohorts, one for existing workers and two for new recruits. The discounted life expectancy is found for each cohort, and then a weighted average is used to give the overall value. An additional mathematical device is then used to reduce the number of cohorts required from three to two, namely existing workers and new recruits. A similar mathematical device is applied (in Appendix A) to reduce from three to two the number of workforce cohorts needed when the length of the safety system’s service lifetime is less than the working lifetime. Finally, a further mathematical instrument is incorporated in the model equations, which allows a unified treatment to be applied to each of the cohorts, existingworkers and newrecruits, across all possible service lifetimes of a nuclear safety system. Since newresults on gain in life expectancymay be fed into a J-value analysis, this development extends significantly the range of nuclear-safety systems for which the J-value technique may be used to measure cost-effectiveness.
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11. Thomas, P. J. and Jones, R. D., 2009, "The effect of the exposure time on the value of a manSievert averted", Trans IChemE, Part B, Process Safety and Environmental Protection, Vol. 87, 227 – 231.
The basis of the manSievert as a unit for collective radiation dose is discussed and previous recommendations are considered for how much should be spent to avert a collective dose of one manSievert. New calculations are given using the J-value method. It is shown that, irrespective of whether the exposed group consists of workers or the general public, the value to be assigned to averting a manSievert depends on the duration of averted exposure as well as on the discount and loan rates thought to be appropriate. The variation with dose-duration is so large that it is not possible to recommend a single figure for the value of a manSievert. Instead, tables are given at two conservative, loan and net discount rates for the value of a manSievert as a function of exposure time. The base data for the J-value method need to be updated annually, and this means that the values given in the tables will increase over time as people live longer and become richer.
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12. Thomas, P. J. and Jones, R. D., 2009, "Incorporating the 2007 recommendations of the International Committee on Radiation Protection into the J-value analysis of nuclear safety systems", Trans IChemE, Part B, Process Safety and Environmental Protection, Vol. 87, 245 – 253.
The newly released findings by the International Commission on Radiation Protection (ICRP) led to a review of the lifetime risk coefficients for fatal cancer used in J-value analysis of nuclear safety systems. The change in life expectancy a safety system brings about by averting a radiation exposure needs to be estimated in order to calculate the safety system's J-value, and this is done following the ICRP's practice of using risk coefficients that are uniform across both genders and all ages in the defined population group (either workers or the general population). The ICRP predicted uniformly lower radiation risks in 2007 than in 1990 on a like-for-like basis, but it was found that the ICRP's new risk coefficients needed to be multiplied by a compensating factor specific to each population when used in calculating the radiation-induced change in life expectancy. Incorporating the new compensating factor leads to a decrease in the J-value calculated of about 5% for workers and 15% for the general population compared with earlier, reported results. This will strengthen slightly the case for spending on a nuclear safety measure.
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14. Thomas, P., Jones, R. and Kearns, J., 2009, "Measurement of parameters to value human life extension", Proc. XIX IMEKO World Congress, Fundamental and Applied Metrology, September 6–11, 2009, Lisbon, Portugal, pp 1170 – 1175.
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15. Collins, D., 2009, "Health Protection at the World Trade Organization: The J-Value as a Universal Standard for Reasonableness of Regulatory Precautions", Journal of World Trade, Vol. 43, no. 5: 1071 – 1091. ssrn.com/abstract=1552945
Article XXb of the General Agreement on Tariffs and Trade (GATT) and the Sanitary and Phytosanitary (SPS) Agreement prohibit health safety measures which are unreasonable restrictions on trade, which WTO case law has shown to mean not based upon sound scientific principles or international consensus. However the existing difficulty in ensuring uniformity in these criteria as implemented by the WTO Dispute Settlement Body (DSB) necessitates resort to a universal scale for assessing the legitimacy of health and safety precautions by reference to an objective cost benefit analysis. This paper attempts to apply the J-Value scale, developed in the United Kingdom to gauge expenditures in industrial risk prevention, to evaluate the reasonableness of WTO member state product safety regulations in a readily quantifiable, judicially instructive manner. The J-Value can be implemented by WTO panels ex post as well as government regulators ex ante in order to assess whether or not a specific measure aimed at ensuring human health and safety is actually an unnecessary barrier to international trade. In keeping with WTO principles, key features of the J-Value formula allow for different tolerances towards health risks depending on the view of the Member states which implement them, based on factors such as life expectancy and Gross Domestic Product (GDP).
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17. Thomas, P. J., Jones, R. D. and Boyle, W. J. O., 2010a, "The limits to risk aversion: Part 1. The point of indiscriminate decision", Process Safety and Environmental Protection, Vol. 88, No. 6, November, pages 381 – 395.
The paper uses utility theory to investigate how much should be spent to avert all costs from an industrial accident apart from direct human harm. These “environmental costs” will include those of evacuation, clean-up and business disruption. Assuming the organisation responsible will need to pay such costs, the difference between its expected utility with and without an environmental protection system constitutes a rational decision variable for whether or not the scheme should be installed. The value of utility is dependent on the coefficient of relative risk aversion, “risk-aversion” for short. A model of an organisation’s decision-making process has been developed using the ABCD model, linking the organisation’s assets, A, the cost of the protection scheme, B, the cost of consequences, C, and the expected utility difference with and without the scheme, D. Increasing the organisation’s risk-aversion parameter will tend to make it less reluctant to invest in a protection system, but can bring about such investment only when the scheme is relatively close to financial break-even. For such borderline schemes, the amount the organisation is prepared to spend on the protection system will rise as the risk-aversion increases. The ratio of this sum to the break-even cost is named the “Limiting Risk Multiplier”, the maximum value of which is governed by the maximum feasible value of risk-aversion. However, the mathematical model shows that increasing the risk-aversion will reduce the clarity of decision making generally. Although the reluctance to invest in a protection scheme may change sign and turn into a positive desire to invest as the risk-aversion increases, the absolute value of this parameter is a continuously decreasing function of risk-aversion, tending asymptotically to zero. As a result, discrimination will gradually diminish, being lost altogether at the “point of indiscriminate decision”. Here the decision maker will be able to distinguish neither advantage in installing the scheme nor disadvantage in installing its inverse. There is a close correspondence between this mathematically predicted state and that of panic, where an individual has become so fearful that his actions become random. The point of indiscriminate decision provides a natural upper bound for the value of risk-aversion. This bounds the Limiting Risk Multiplier in turn, and so sets an objective upper limit on the amount that it is rational to spend on an environmental protection system.
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18. Thomas, P. J., Jones, R. D. and Boyle, W. J. O., 2010b, "The limits to risk aversion. Part 2: The permission point and examples", Process Safety and Environmental Protection, Vol. 88, No. 6, November, pages 396 – 406.
Part 2 extends the analysis to show that it is possible to find the “permission point”, the value of (the coefficient of relative) risk-aversion, at which decisions to sanction environmental protection are most likely to be made. The mathematical model describes the process by which the decision maker varies his risk-aversion over a range of feasible values to find the risk-aversion that will give him the greatest desire to invest in the protection system under consideration. If he can find such a risk-aversion before losing discrimination (because the system is too expensive, given its performance), he will adopt it as his “permission point” and decide in favour of the expenditure. The permission point is, of course, bounded above by the point of indiscriminate decision. A maximum Risk Multiplier calculated at the point of indiscriminate decision may be applied to the protection expenditure at monetary break-even to give the maximum, rational outlay on protection. Moreover, it is possible to model how the average UK adult should take decisions on protection to maximise his utility. Different situations will call for different values of risk-aversion, which may explain why economists have come up with differing estimates of this parameter in the past. However, a central, average risk-aversion may be calculated for the average UK adult as 0.85, which is within 4% of the value, 0.82, found from the newly reported method based on a trade-off between income and future free time, and is consistent with several recent economic estimates. Worked examples assess how much an organisation should spend on a protection scheme to prevent accidents with very large environmental consequences.
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23. Thomas, P., Boyle, W. and Kearns, J., 2010, "The quantum of wealth", Measurement + Control, Vol. 43, No. 5, June, pages 156 – 158.
The reluctance to invest is a key dimensionless variable used in the JT-value assessment of schemes to prevent industrial accidents with high human and environmental costs. The decision-variable is equal to the difference between the expected utility of assets without the protection system and that with it, normalised by dividing by the starting utility of assets. Thus a 100% reluctance, equivalent to a point-blank refusal to invest, will be associated with a protection system that is so expensive that it is expected to reduce the utility of the organisation's assets to zero, while a negative value will imply a positive desire to invest. In order to allow for risk-aversions that may be greater than unity (implying highly risk averse behaviour), it is necessary to use the Atkinson Utility function, which may be shown to provide an absolute scale for utility.
The Atkinson Utility function is a Scaled Power Utility function that takes as its datum one unit of money, and thus gives a utility value of zero for one unit of money and a negative value for the utility of any positive amount of money less than one unit. While the negative value returned by the Atkinson Utility function when it is applied to a strictly fractional sum of money is fully understandable in the terms just set down, the situation would change if the Atkinson Utility function were to be regarded as a utility function assumed valid over all positive sums of money. In fact, its advantage in allowing for risk-aversions greater than unity and its closeness at risk-aversions less than unity to the Scaled Power Utility mean that the Atkinson form is often used in practice as a utility function in its own right, without acknowledgement of its origin as a utility difference. From this viewpoint it appears anomalous that the utility of a strictly fractional sum of money should be negative. For, taking the unit of money to be £1, why should possessing just 50 pence leads to a negative satisfaction level? Equally, why should having £1 lead to no satisfaction? The resolution of these apparent anomalies is contained in the first line of this paragraph, but nevertheless the interesting question is raised as to whether there might be a quantum of wealth, the addition of less than which would be regarded by the average adult as giving him or her no discernable increase in wealth.
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24. Thomas, P. J., 2010, "An absolute scale for measuring the utility of money", Proc. 13th IMEKO TC1-TC7 Joint Symposium Without Measurement no Science, without Science no Measurement, September 1-3, City University, London, UK, IOP Publishing, Journal of Physics: Conference Series 238 (2010) 012039. doi:10.1088/1742-6596/238/1/012039
Measurement of the utility of money is essential in the insurance industry, for prioritising public spending schemes and for the evaluation of decisions on protection systems in high-hazard industries. Up to this time, however, there has been no universally agreed measure for the utility of money, with many utility functions being in common use. In this paper, we shall derive a single family of utility functions, which have risk-aversion as the only free parameter. The fact that they return a utility of zero at their low, reference datum, either the utility of no money or of one unit of money, irrespective of the value of risk-aversion used, qualifies them to be regarded as absolute scales for the utility of money. Evidence of validation for the concept will be offered based on inferential measurements of risk-aversion, using diverse measurement data.
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25. Kearns, J. O. and Thomas, P. J., 2010, "Assigning tolerances to J-values used in safety analysis", Proc. 13th IMEKO TC1-TC7 Joint Symposium Without Measurement no Science, without Science no Measurement, September 1-3, City University, London, UK, IOP Publishing, Journal of Physics: Conference Series 238 (2010) 012045. doi:10.1088/1742-6596/238/1/012045
This paper describes the methodology employed in the estimation of the input parameters required for J-value analysis. The conceptual foundations and theory behind J-value analysis are first presented, and the relevant parameters are derived. Evaluations of the parameters are then shown and their implications discussed, including an estimate of the coefficient of relative risk aversion, risk-aversion for short. Uncertainties of the parameters are calculated. It is shown that the internal accuracy of the J-value is +/−4%, but that other external, case-dependant effects may reduce this accuracy. Some of these case-dependant sources of uncertainty are discussed and quantified.
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26. Kearns, J. O., Thomas, P. J., Taylor, R. H., Boyle, W. J. O., 2012, "Comparative Risk Analysis of Electricity Generating Systems Using the J-Value Framework", Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, Vol. 226, No. 3, May, pages 414 – 426. doi:10.1177/0957650911424699
Decisions regarding the implementation of different forms of electricity generating systems necessarily require consideration of a large number of social, economic, environmental, and technical indicators. One such important indicator is the effect on health. This article presents a comparative risk analysis of mortality impacts arising from the generation of electricity by nuclear, coal, gas, onshore wind, and offshore wind UK power plants. The risk analysis was carried out using the J-value method, which provides a common, objective scale by which human harm can be valued. The analysis assessed human mortality impacts arising from the construction of future plants over the 60-year period from 2010 to 2070 for the entire fuel chain. Despite the considerable uncertainties in current estimates, the analysis provides evidence of the worth of the J-value methodology, particularly in relation to its ability to take explicit account of loss of life expectancy in evaluating delayed health effects. Risks are delineated according to two dimensions: whether the risk is occupational or public, and whether the risk is immediate or delayed. Impacts are also assessed for major accidents. The results indicate that nuclear generally has the lowest impacts, while gas, onshore wind and offshore wind have indicative impacts that are about an order of magnitude greater, although the estimates for both wind technologies carry considerable uncertainty. Coal power was found to present high impacts compared with the other technologies, mainly as a result of pollution emissions, even though the potential harm from some emissions has not been included because the effects are not fully understood. Total nuclear impacts were found to be sensitive to assumptions regarding the use of collective dose and the assumptions which are then used to calculate impacts. For the most pessimistic case, when world exposures are taken, total nuclear impacts increase by about an order of magnitude, which would render the risks from nuclear generation comparable with those from gas and wind generation.
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27. Thomas, P. J. and Taylor, R. H., 2012, "J-value analysis of different regulatory limits for workers and the public", Process Safety and Environmental Protection, Vol. 90, No. 4, July, pages 285 – 294. doi:10.1016/j.psep.2011.11.001
The J-value technique allows an objective determination to be made of the resources that should be applied cost effectively to improve heath and safety. This is essential if capabilities are to be employed optimally and risks reduced in a way that reflects their severity. Although other considerations such as good practice and socio-political influences may affect a final decision on the resources to be sanctioned, the incorporation of these additional factors should be made transparent if the decision is no longer to be based on cost effectiveness. The J-value provides an objective criterion by which to judge when “reasonable practicability” has been achieved in committing resources for safety improvement, which is the legal requirement under health and safety law in the UK.
Moreover, the J-value methodology also allows other related issues to be addressed objectively. Regulatory bodies apply different limits for workers and the general public, with higher risks being permitted for workers. Although a factor of about 10 has been used in several contexts, no objective rationale has been developed for this particular figure until now. However, it is shown that application of the J-value analysis can provide a justification for a ratio of workers’ risk to public risk of approximately this size if certain reasonable assumptions are made. Thus the paper provides the first quantitative explanation for the different levels of protection demanded by regulators nationally and internationally for workers and public.
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29. Kearns, J. O., 2012, "Comparing the risks of diverse methods of electricity generation using the J-Value framework", PhD thesis, City University London. openaccess.city.ac.uk/1321/
This thesis presents and extends the J-Value framework for assessing expenditure on risk mitigation, and then applies the method in a comparative risk assessment of UK electricity generating systems.
In part one, the J-Value framework is introduced and developed. The loss of life expectancy is a key parameter in the framework, and general risk models for calculating this parameter are developed in terms of exposures and responses. Specific examples of radiation and pollution models are also presented. The "Hazard Elimination Premium" is also introduced as a useful common metric for risk comparisons. There follows an assessment of the uncertainty of the J-value and its input parameters and it is found that the J-Value has an internal accuracy of around 3%, but that other, context dependant parameters can degrade this accuracy. A sensitivity analysis of the J-Value framework also found that the J-Value was reasonably robust against random variation of the input parameters as well as against the use of simplifying assumptions used in the development of the J-Value.
Part two describes the comparative risk analysis of the electricity generating systems. The analysis is carried out on nuclear, coal, natural gas, onshore wind and offshore wind. The analysis assesses human mortality impacts arising from the current and future plants over the sixty year period from 2010 to 2070 for the entire fuel chain. The results indicate that nuclear generally has the lowest impacts, while gas, onshore and offshore wind have indicative impacts that are about an order of magnitude greater, although the estimates for both wind technologies carry considerable uncertainty. Coal power was found to present high impacts compared with the other technologies, mainly as a result of pollution emissions. Total nuclear impacts were found to be sensitive to assumptions regarding the use of collective dose and the assumptions which are then used to calculate impacts. For the most pessimistic case, when world exposures are taken, total nuclear impacts increase by about an order of magnitude, which would render the risks from nuclear generation comparable with those from gas and wind generation.
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28. Waddington, I., Boyle, W. J. O., Kearns, J., 2013, "Computing the Limits of Risk Aversion", Process Safety and Environmental Protection, 91, 92–100. doi:10.1016/j.psep.2012.03.003
Utility theory can be used to model the decision process involved in evaluating the cost-effectiveness of systems that protect against a risk to assets. A key variable in the model is the coefficient of relative risk aversion (or simply “risk-aversion”) which reflects the decision maker's reluctance to invest in such safety systems. This reluctance to invest is the scaled difference in expected utility before and after installing the safety system and has a minimum at some given value of risk-aversion known as the “permission point”, and it has been argued that decisions to sanction safety systems would be made at this point. As the cost of implementing a safety system increases, this difference in utility will diminish. At some point, the “point of indiscriminate decision”, the decision maker will not be able to discern any benefit from installing the safety system. This point is used to calculate the maximum reasonable cost of a proposed safety system. The value of the utility difference at which the decision maker is unable to discern any difference is called the “discrimination limit”.
By considering the full range of accident probabilities, costs of the safety system and potential loss of assets, an average risk-aversion can be calculated from the model. This paper presents the numerical and computational techniques employed in performing these calculations. Two independent approaches to the calculations have been taken, the first of which is the derivative-based secant method, an extension of the referred derivative method employed in previous papers. The second is the Golden Bisection Method, based on a Golden Section Search algorithm, which was found to be more robust but less efficient than the secant method. The average risk-aversion is a function of several key parameters: the organisation's assets, the probability and maximum cost of an incident, and the discrimination limit. An analysis of the sensitivity of the results to changes in these parameters is presented. An average risk-aversion of 0.8–1.0 is found for a wide range of parameters appropriate to individuals or small companies, while an average risk-aversion of 0.1 is found for large corporations. This reproduces the view that large corporations will be risk neutral until faced with risks that pose a threat to their viability.
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Collins, D., Thomas, P., 2014, "Measuring gross disproportion in environmental precaution to establish regulatory expropriation and quantum of compensation in international investment arbitration", European Journal of Law and Economics, in press. doi: 10.1007/s10657-014-9433-4
This article applies a new methodology for the assessment of environmental risk prevention expenditure to the adjudication process of international investment arbitration. The Disproportion Factor Model can be implemented by investment arbitration tribunals to evaluate the reasonableness of environmental regulations imposed by host states that have a damaging impact upon foreign investment activity, such as would be the subject for a claim of indirect or regulatory expropriation. In this setting the Disproportion Factor Model can help illustrate whether a host state measure is unreasonable and in that sense should engage the investor’s entitlement to compensation under international law. It also acts as an objective guide to the setting of an appropriate quantum of compensation for the injured investor by reference to the environmental benefits that the regulation aimed to achieve relative to their costs, as evaluated by a rational decision-maker. The formula should be consequently viewed as a useful tool in judicial analysis by international investment tribunals.
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Thomas, P., 2017, "Does health spending need to outpace GDP per head?", Nanotechnology Perceptions, 13, 17–30. Download PDF
Decisions on health spending depend ultimately on the valuation of human life in the country concerned. Previous attempts in the UK have been linked to the one-size-fits-all "value of a prevented fatality" (VPF), now shown to be based on a fundamentally flawed method. An objective and validated alternative is available in the J-value (J for "judgment"), which addresses the improved life expectancy a treatment offers. The J-value sheds important light on what Man chooses to spend on life-extending measures, allowing lessons to be drawn for the desirable relationship between GDP and spending on health. -
Thomas, P., 2017, "Corroboration of the J-value model for life expectancy growth in industrialized countries", Nanotechnology Perceptions, 13, 31–44. Download PDF
After including an allowance for the gap between male and female life expectancies at birth diminishing over the past 50 years in industrialized countries, the J-value model incorporating "male catch-up" has been validated against actual UK data on life expectancy. A close correspondence has also been found between forecasts for life expectancy at birth in 35 countries made by the J-value model and those produced in a recent study that applied Bayesian model averaging to 21 demographic projection models.