Finding Fair and Efficient Allocations for Matroid Rank Valuations

In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions . This is a versatile valuation class with several desirable properties (such as monotonicity and submodularity), which naturally lends itself to a number of real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e., utilitarian social welfare-maximizing) allocation that achieves envy-freeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfare-maximizing and the leximin allocations both exhibit this fairness/efficiency combination by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. To the best of our knowledge, this is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time. Additionally, we explore possible extensions of our results to fairness criteria other than EF1 as well as to generalizations of the above valuation classes.

Water Allocation and the Sustainability of Dairying in the Upper Waitaki River Basin

<p>Water as a resource management issue is gaining prominence in New Zealand, both in terms of quality and quantity. In the Waitaki this became critical in 2003 when several proposed development schemes exposed the inadequacies of the RMA and highlighted the need for a catchment wide plan. Legislation was promulgated and a Regional Plan developed to address the issues of efficient allocation. This thesis aimed to question the efficiency of water allocation within the recent legislation and to examine the sustainability of dairying in this area with regard to cumulative effects to the hydrological system. It was found the Plan has failed to achieve its stated aims. Dairying in the upper Waitaki is currently increasing and applications for resource consent are being heard under legislation that is not backed by the science required within its policies. Fieldwork was undertaken to explore some of the science required under the Regional Plan to enable a 'reasonable use' test to be made. The aim was to assess the response of soils in the upper Waitaki to intensive irrigation. This revealed that the potential impacts of intensive irrigation in this area are significant and highlighted the need for further research. This is a study of how poor policy and planning, based on a lack of robust science has resulted in the inefficient allocation of water. This has implications for long-term sustainable resource use.</p>

Water Allocation and the Sustainability of Dairying in the Upper Waitaki River Basin

<p>Water as a resource management issue is gaining prominence in New Zealand, both in terms of quality and quantity. In the Waitaki this became critical in 2003 when several proposed development schemes exposed the inadequacies of the RMA and highlighted the need for a catchment wide plan. Legislation was promulgated and a Regional Plan developed to address the issues of efficient allocation. This thesis aimed to question the efficiency of water allocation within the recent legislation and to examine the sustainability of dairying in this area with regard to cumulative effects to the hydrological system. It was found the Plan has failed to achieve its stated aims. Dairying in the upper Waitaki is currently increasing and applications for resource consent are being heard under legislation that is not backed by the science required within its policies. Fieldwork was undertaken to explore some of the science required under the Regional Plan to enable a 'reasonable use' test to be made. The aim was to assess the response of soils in the upper Waitaki to intensive irrigation. This revealed that the potential impacts of intensive irrigation in this area are significant and highlighted the need for further research. This is a study of how poor policy and planning, based on a lack of robust science has resulted in the inefficient allocation of water. This has implications for long-term sustainable resource use.</p>

Utilization of Risk Analysis of Hydraulic Structures for Efficient Allocation of Means

Efficient allocation of available means presuppose detailed knowledge about risks, costs and benefits within the area of interest. The societal demand for increased safety of hydraulic structures, as components of the critical infrastructure, requires considerable investment. To evaluate the effectiveness of potential measures in an environment influenced by epistemic and aleatory uncertainties, risk analysis and cost-benefit analysis are used in practice. The above described approach is now fully implemented when considering natural floods and structural flood protection measures, and also presented in the paper. For potential failures of dams and other important hydraulic structures however the procedure becomes rather more complex to comprehend the effect of designed measures on different failure modes. After introducing governing theoretical principles used for the natural flood vs structural measures analysis, the paper presents examples of application of combination of cost-benefit and risk analysis in the framework of the authors’ work as Strategic Expert of the Ministry of Agriculture of the Czech Republic for the different stages of the flood prevention program. The last part of the paper focuses on dam safety and the application of risk analysis as a support tool for decision making processes. It describes the practice applied in the Czech Republic and comments on the advantages and disadvantages of the current approach while suggesting further possible improvement.

Optimizing Sequencing Resources in Genotyped Livestock Populations Using Linear Programming

Low-cost genome-wide single-nucleotide polymorphisms (SNPs) are routinely used in animal breeding programs. Compared to SNP arrays, the use of whole-genome sequence data generated by the next-generation sequencing technologies (NGS) has great potential in livestock populations. However, sequencing a large number of animals to exploit the full potential of whole-genome sequence data is not feasible. Thus, novel strategies are required for the allocation of sequencing resources in genotyped livestock populations such that the entire population can be imputed, maximizing the efficiency of whole genome sequencing budgets. We present two applications of linear programming for the efficient allocation of sequencing resources. The first application is to identify the minimum number of animals for sequencing subject to the criterion that each haplotype in the population is contained in at least one of the animals selected for sequencing. The second application is the selection of animals whose haplotypes include the largest possible proportion of common haplotypes present in the population, assuming a limited sequencing budget. Both applications are available in an open source program LPChoose. In both applications, LPChoose has similar or better performance than some other methods suggesting that linear programming methods offer great potential for the efficient allocation of sequencing resources. The utility of these methods can be increased through the development of improved heuristics.

Risk Premium Shocks Can Create Inefficient Recessions

We develop a simple flexible-price model of business cycles driven by spikes in risk premiums. Aggregate shocks increase firms’ uninsurable idiosyncratic risk and raise risk premiums. We show that risk shocks can create quantitatively plausible recessions, with contractions in employment, consumption, and investment. Business cycles are inefficient—output, employment, and consumption fall too much during recessions, compared to the constrained-efficient allocation. Optimal policy involves stimulating employment and consumption during recessions.