The Brown-Colbourn conjecture on zeros of reliability polynomials is false

We give counterexamples to the Brown-Colbourn conjecture on reliability polynomials, in both its univariate and multivariate forms. The multivariate Brown-Colbourn conjecture is false already for the complete graph K_4. The univariate Brown-Colbourn conjecture is false for certain simple planar graphs obtained from K_4 by parallel and series expansion of edges. We show, in fact, that a graph has the multivariate Brown-Colbourn property if and only if it is series-parallel.Comment: LaTeX2e, 17 pages. Version 2 makes a few small improvements in the exposition. To appear in Journal of Combinatorial Theory

Ex Ante Liability Rules in New Zealand's Health and Safety in Employment Act: A Law and Economics Analysis

In addition to penalties imposed for breaches of statutory duties in the event of workplace accidents involving physical harms, New Zealand's Health and Safety in Employment Act 1992 also provides for penalties where accidents have not occurred. Ordinary negligence rules are ex post in that both an accident and harm must occur before liability accrues, whereas ex ante liability rules create liability for deficient care per se. This paper examines whether liability for breaches of duty that do not give rise to accidents have a useful incentive-enhancing role for health and safety decisions by employers in the New Zealand context when used in conjunction with ex post liability rules. We argue that ex post rules by themselves are insufficient to induce appropriate levels of precaution due to the combined presence of weak penalties and considerable uncertainty surrounding the Courts' required standard of care. Merely augmenting ex post liability with ex ante liability, however, is unlikely to induce desirable levels of employer precautions. Further, more strict ex ante standards than socially optimal precaution levels may be desirable since inspection probabilities, prosecution rates, and penalties for breaches of ex ante standards are relatively low, providing some justification for the relatively stringent safety regulations and required standard of care observed in New Zealand. Nevetheless, a weaker but less uncertain standard may instead induce a small degree of overprecaution, removing the need for ex ante regulations from this particular perspective.ex ante and ex post liability; safety incentives, health and safety standards; uncertainty

Incentives and the Changing Structure of Penalties in New Zealand's Health and Safety in Employment Act

This article argues that it is doubtful that the fivefold increase in maximum fines under New Zealand's Health and Safety in Employment Amendment Act 2002 will be successful in providing suitable precautionary incentives. Expected penalties remain at relatively low levels, with the continued use of capped fines along with substantial margins for deterrence of the most serious cases. On average, fines were initially substantially lower in response to the introduction of the Sentencing Act 2002 for which uncapped (but insurable) reparations take precedence over fines, and must be accounted for in setting fines. The combined effects of the legislation led to average total financial penalties approximately doubling through 2004 rather than increasing at anything like the rate signalled for fines by the amendments. Subsequently, while fines have grown in absolute terms, even more rapid growth in reparations has caused relative crowding-out while total penalties remain well below those signalled by the amendments alone. The case for low caps on fines appears weak, while 'asset-testing' fines is unlikely to be an efficient practice. Absent further significant changes in workplace safety incentives, New Zealand is likely to face an ongoing (if possibly somewhat abated) stream of prosecutions for serious breaches of relatively onerous statutory health and safety duties.health and safety incentives; expected penalties; capped fines; reparations

Market Wages, Reservation Wages, and Retirement Decisions

The paper is an empirical cross-section study of the retirement decisions of American white men between the ages of 58 and 67. predicated on the theoretical notion that an individual retires when his reservation wage exceeds his market wage. Reservation wages are derived from an explicit utility function in which the most critical taste parameter is assumed to vary both systematically and randomly across individuals. Market wages are derived from a standard wage equation adjusted to the special circumstances of older workers. The two equations are estimated jointly by maximum likelihood, which takes into account the potential selectivity bias inherent in the model (low-wage individuals tend to retire and cease reporting their market wage). The model is reasonably successful in predicting retirement decisions, and casts serious doubt on previous claims that the social security system induces many workers to retire earlier than they otherwise would. The normal effects of aging (on both market and reservation wages) and the incentives set up by private pension plans are estimated to be major causes of retirement.

Cormorants and the Loch Leven trout fishery

Perceived conflicts between piscivorous birds and commercial freshwater fisheries are common, and such a perception exists at Loch Leven, a wetland of international importance for nature conservation and a famous commercial brown trout Salmo trutta fishery, where Great Cormorants Phalacrocorax carbo have been shot in large numbers. This thesis describes the foraging behaviour of cormorants wintering on Loch Leven. It summarises changes in wintering numbers over a 32 year period, and reviews data on fish populations, fish stocking rates, angling catches and angling effort in order to seek evidence of detrimental impacts of cormorants on the fishery, and beneficial effects of large-scale cormorant shooting. Finally, this thesis considers turnover within the wintering cormorant population, and its implications for cormorant control. Cormorants spent most of the time roosting, and a single peak of feeding activity occurred early in the morning. Compared to early or late winter, cormorants showed higher foraging activity during mid-winter. Both solitary feeding and flock feeding were recorded, with flock feeding predominating. Solitary feeding was distributed over a wide area. The intensity of flock feeding was less evenly distributed, with 36% of grid squares not used. Overall, 78% of flock feeding activity took place in 23% of grid squares and 59% took place in 13% of grid squares. The best predictor of both solitary feeding and flock feeding intensity of use was mean water depth. Mean water depth was also the best predictor of winter brown trout distribution, although winter brown trout distribution was not a predictor of either solitary feeding or flock feeding intensity of use