Uniquely determined uniform probability on the natural numbers

In this paper, we address the problem of constructing a uniform probability measure on $\mathbb{N}$. Of course, this is not possible within the bounds of the Kolmogorov axioms and we have to violate at least one axiom. We define a probability measure as a finitely additive measure assigning probability $1$ to the whole space, on a domain which is closed under complements and finite disjoint unions. We introduce and motivate a notion of uniformity which we call weak thinnability, which is strictly stronger than extension of natural density. We construct a weakly thinnable probability measure and we show that on its domain, which contains sets without natural density, probability is uniquely determined by weak thinnability. In this sense, we can assign uniform probabilities in a canonical way. We generalize this result to uniform probability measures on other metric spaces, including $\mathbb{R}^n$.Comment: We added a discussion of coherent probability measures and some explanation regarding the operator we study. We changed the title to a more descriptive one. Further, we tidied up the proofs and corrected and simplified some minor issue

Assessing forensic evidence by computing belief functions

We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We use a calculus of belief functions which does not use the much criticized Dempster rule of combination, but only the very natural Dempster-Shafer conditioning. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our setup can and should be interpreted as a generalization of the classical methodology, allowing more flexibility. We show how our calculus can be used to develop an analogue of Bayes' rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice.Comment: arXiv admin note: text overlap with arXiv:1512.01249. Accepted for publication in Law, Probability and Ris

Allocating Conservation Resources under the Endangered Species Act

The necessity to develop a priority system to guide the allocation of resources to the conservation of endangered species is widely recognized. The economic theory of biodiversity has established a framework to do so, and has identified priority criteria that should be considered when making conservation decisions. This paper uses a random effects ordered probit model of endangered species recovery to simulate the effects of reallocating conservation funds among species listed under the Endangered Species Act according to these criteria. Our results suggest that if the goal of conservation policy is to preserve a diverse set of species, reallocating conservation funds according to criteria identified by economic theory would yield an improvement over actual spending patterns without significant tradeoffs in terms of overall species recovery.Endangered Species Act, endangered species, recovery plans, U.S. Fish and Wildlife Service, biodiversity, critical habitat, Research and Development/Tech Change/Emerging Technologies,

SUCCESS OR FAILURE? ORDERED PROBIT APPROACHES TO MEASURING THE EFFECTIVENESS OF THE ENDANGERED SPECIES ACT

The Endangered Species Act (ESA) is one of the most controversial pieces of environmental legislation. Part of the controversy stems from doubts about its effectiveness in generating improvements in species viability. This paper uses ordered probit models to test whether the ESA has been successful in promoting species recovery. We find a negative correlation between listing and species recovery. Additionally, we find evidence of positive effects for species-specific spending and the achievement of recovery goals. The evidence also shows that recovery plan completion and the designation of critical habit are not correlated or negatively correlated with recovery.Resource /Energy Economics and Policy,

Integrating Writing in All Curriculum Areas

Writing is a foundational tool and skill that appears in schools and classrooms around the world. As writing takes on many different forms and is taught in many different ways, one thing remains the same: its purpose is to get a message to the audience. However, the audience should not be limited to an English teacher in an English classroom. This literature review shows the connection of writing and the importance of its use outside of the regular English classroom and being infused into other content areas. As a simple tool to integrate into those other classrooms, writing can boost the students\u27 content knowledge through informative, opinion, and narrative pieces while practicing the skills that have been learned in an English classroom. Writing across the curriculum (WAC) is a movement that emphasizes this point. Looking at many different educational levels and incorporating writing into the curriculum, the ease of integration through a collaboration of teachers and the different methods used will be evident

Are High Wage Jobs Hazardous to Your Health? The Myth That Attracting Higher Paying Extractive Industry Jobs Is a Desirable Community Economic Development Strategy

Community/Rural/Urban Development,