J-value

judging the risk

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VPF papers

Papers relating to the "Value of a Prevented Fatality" or "VPF".

• 1. Thomas, P. J., and Chrystal, A., 2013a, "Generalized Demand Densities for Retail Price Investigation", American Journal of Industrial and Business Management, 3, 279–294. doi: 10.4236/ajibm.2013.33034

  The paper introduces generalized demand densities as a new and effective way of conceptualizing and analyzing retail demand. The demand density is demonstrated to contain the same information as the demand curve conventionally used in economic studies of consumer demand, but the fact that it is a probability density sets bounds on its possible behavior, a feature that may be exploited to allow near-exhaustive testing of possible demand scenarios using candidate demand densities...

• 2. Thomas, P. J., and Chrystal, A., 2013b, "Retail price optimisation from sparse demand data", American Journal of Industrial and Business Management, 3, 295–306. doi: 10.4236/ajibm.2013.33035

  It will be shown how the retailer can use economic theory to exploit the sparse information available to him to set the price of each item he is selling close to its profit-maximizing level. The variability of the maximum price acceptable to each customer is modeled using a probability density for demand, which provides an alternative to the conventional demand curve often employed...

• 3. Thomas, P. J., 2013, "Safety at level crossings – written evidence from Professor Philip Thomas, Risk Management team at City University London (SLC 009)", House of Commons, Transport Committee, London. inquiry page (direct link to PDF)

  My evidence reviews the problem of level-crossing safety, and considers how to assess the amount that should be spent on uprating safety against the background of UK and international safety law. The principles of cost-benefit analysis (CBA) are considered, including the difficult question of how to value human life. The current rail industry practice is reviewed, and deficiencies in the approach are pointed out. It is shown that a CBA using the DfT value of a prevented fatality (VPF) will understate the safety benefit of a measure to reduce level-crossing risk. The J-value method is recommended as a fully objective and better technique for assessing level-crossing safety upgrades.

• 4. Thomas, P. J., and Chrystal, A., 2013c, "Explaining the 'Buy One Get One Free' promotion: the Golden Ratio as a Marketing Tool", American Journal of Industrial and Business Management, 3(8), 655–673. doi: 10.4236/ajibm.2013.38075

  Buy-one-get-one-free (BOGOF) promotions are a common feature of retail food markets, but why are they so widespread? The theory of Relative Utility Pricing (RUP) developed in this paper provides an explanation not only for supermarket promotional offers but also for more general pricing of packs of different sizes in supermarkets and on the internet...

• 5. Thomas, P. J., and Chrystal, A., 2013d, "Using Relative Utility Pricing to Explain Multibuy Prices in Supermarkets and on the Internet", American Journal of Industrial and Business Management, 3(8), 687–699. doi: 10.4236/ajibm.2013.38078

  The Relative Utility Pricing (RUP) model is used to explain the prices for commodities being sold in supermarkets and on the internet. Grocery prices offered by the supermarkets, Tesco, Sainsbury and Waitrose in December 2009 and August 2013, are considered, as well as the prices of electronic items offered by Amazon on the internet at the same dates. The observed price for a pack can be given an explanation in terms of its size relative to the smallest pack considered by the customer (the baseline pack), the price and variable cost associated with the baseline pack and the demand density...

• 6. Thomas, P. J., 2014, "Structural view independence: A criterion for judging the objectivity of economic parameters measured by opinion survey", Measurement, 47, 161–177. Available here

  Economic measurements have a great influence over all our lives, but as with other soft measurements, significant effort is needed to ensure their objectivity. This is particularly true of the process of consolidating into a single representative figure different people's valuations of a non-market good ('views'), as measured by opinion survey. Sometimes the views are transformed and averaged before being returned to the original domain as the back-transformed mean. Examples are the geometric mean resulting from a logarithmic transformation and the root-mean-squared (r.m.s.) value from a square transformation. Such transformations are tested for objectivity using the new criterion of structural view independence...

• 7. Thomas, P. J., Vaughan, G. J., 2014, "Explaining Perceived Inconsistencies in 'Stated Preference' Valuations of Human Life", American Journal of Industrial and Business Management, 4(9), 687–699. doi: 10.4236/ajibm.2014.49052

  The Relative Utility Pricing model is used to explain the fact that when faced with two 'safety packs', the second giving three times the safety benefit of the first, discriminating respondents will place a value on the second pack that is, on average, twice the amount they say they will be prepared to pay for the first. When the safety packs reduce fatal accident frequencies, the 'value of a prevented fatality' (VPF) figures deduced from the valuations of the two safety packs must then be significantly different. Such response patterns on the part of respondents were found in a high-profile study carried out on behalf of a number of UK Government Departments...

• 8. Thomas, P. J., 2015, "Testing the impartiality of surveys to measure differential risk perception", Measurement, 60, 155–173. Available here

  The paper addresses the validation of opinion measurement by survey, specifically how the 'readings' or views are consolidated for policy use into a single figure held to be representative of the population as a whole. While the sample mean might seem the obvious choice, a number of influential safety studies have employed a more complicated metric, the Valuation Index, as discussed within, to assess whether more should be spent to protect against some hazards than others. The question arises as to whether the Valuation Index treats the views of the different people in the survey sample impartially or not...

• 9. Thomas, P. J., Vaughan, G. J., 2015a, "Testing the validity of the 'value of a prevented fatality' (VPF) used to assess UK safety measures", Process Safety and Environmental Protection, 94, 239–261. Available here

  The 'value of a prevented fatality' (VPF), the maximum amount that it is notionally reasonable to pay for a safety measure that will reduce by one the expected number of preventable premature deaths in a large population, is published by the UK Department for Transport (DfT). The figure, updated for changes in GDP per head, is used by the DfT, the Health and Safety Executive and other UK regulatory bodies as well as very widely in the process, nuclear and other industries as the standard by which to judge how much to spend to reduce harm to humans. The paper tests the validity of the 1999 study on which the VPF is based and finds that that study fails numerous tests of its validity. It is concluded that there is no evidential base for the VPF that has been used for many years in the UK and is still in standard use today. Given the difficulties evident in the interpretation of survey results, an urgent re-appraisal is needed of alternative statistical methodologies that can allow robust regulatory and industry safety decision making and, vitally, give adequate protection to the UK public and to those working in the UK's transport, process, nuclear and other industries.

• 10. Thomas, P. J., Vaughan, G. J., 2015b, "Testing the validity of the 'value of a prevented fatality' (VPF) used to assess UK safety measures: measures’: Reply to the comments of Chilton, Covey, Jones-Lee, Loomes, Pidgeon and Spencer", Process Safety and Environmental Protection, 93, 299–306. Available here

  Thomas and Vaughan (2015a) drew attention to the weaknesses in the approach underpinning the 'value of a prevented fatality' (VPF) used as a reference for health and safety decisions across the UK's process, nuclear and other industries, as well as the NHS. It is important for the UK's future health and safety strategy that the lack of evidence for the VPF should be debated openly in the pages of a learned journal. Hence we are pleased that Chilton, Covey, Jones-Lee, Loomes, Pidgeon and Spencer, authors from the Carthy study (Carthy et al., 1999), have attempted to answer our criticisms and that we have been given the opportunity to respond...

• 11. Thomas, P. J., Vaughan, G. J., 2015c, "Pitfalls in the application of utility functions to the valuation of human life", Process Safety and Environmental Protection, 98, 148–169. Available here

  Safety strategies in the process and other industries depend ultimately on how much the owners and operators decide should be spent on protection systems to protect workers and the public from potential plant hazards. An important input to decisions of this sort is the value of life, which needs to be assessed in a valid manner so that safety decisions can be made properly. A key reference point for decisions on safety investment decisions in the UK is a 1999 study on the 'value of a prevented fatality' (VPF), which employs a two-injury chained model that has been shown previously by the present authors to possess internal inconsistencies. The 1999 study made extensive use of utility functions to interpret survey data, and it is this feature that is explored in this paper...

• Thomas, P., Waddington, I., 2017, "What is the value of life? A review of the value of a prevented fatality used by regulators and others in the UK", Nuclear Future, Volume 13 Issue 1, 32–39. Available here

  The UK Department for Transport (DfT) values the prevention of a fatality on Britain’s roads at £1.8 million (2016 £s). This value is used across government departments and agencies, including the Office for Nuclear Regulation, as a de facto standard for valuing the benefit of safety measures that preserve human life; however, there is no evidential basis for this valuation as it is derived from a statistical analysis of sparse survey data carried out 20 years ago that has now been found to be flawed. The methodology used to infer the VPF has been shown to be internally inconsistent, with the final recommended value being subjective. Members of the public whose opinions were rejected by the survey team actually gave entirely rational and understandable valuations based on human perceptions of utility. Another influential study – used to justify a significant reduction in spending to prevent multi-fatality rail accidents – has been found to be systematically biased against those very people who wanted more to be spent on preventing accidents causing multiple deaths. In contrast to the one-size-fits-all VPF, the J-value provides an objective, rational and statistically rigorous methodology that values the prevention of a premature death in terms of the amount of life that the potential victim would lose.

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