Asymmetrically fair rules for an indivisible good problem with a budget constraint

We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.

Low genetic diversity and functional constraint in loci encoding Plasmodium vivax P12 and P38 proteins in the Colombian population

Background Plasmodium vivax is one of the five species causing malaria in human beings, affecting around 391 million people annually. The development of an anti-malarial vaccine has been proposed as an alternative for controlling this disease. However, its development has been hampered by allele-specific responses produced by the high genetic diversity shown by some parasite antigens. Evaluating these antigens’ genetic diversity is thus essential when designing a completely effective vaccine. Methods The gene sequences of Plasmodium vivax p12 (pv12) and p38 (pv38), obtained from field isolates in Colombia, were used for evaluating haplotype polymorphism and distribution by population genetics analysis. The evolutionary forces generating the variation pattern so observed were also determined. Results Both pv12 and pv38 were shown to have low genetic diversity. The neutral model for pv12 could not be discarded, whilst polymorphism in pv38 was maintained by balanced selection restricted to the gene’s 5′ region. Both encoded proteins seemed to have functional/structural constraints due to the presence of s48/45 domains, which were seen to be highly conserved.

Allocation rules on networks

When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and an agent depicts the possibility of a transfer from the source to the agent. Given the supplies at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on consistent and resource monotonic rules in claims problems that satisfy equal treatment of equals. We call these rules fairness principles and we extend fairness principles to allocation rules on networks. We require that for each pair of citizens in the network, the extension is robust with respect to the fairness principle. We call this condition pairwise robustness with respect to the fairness principle. We provide an algorithm and show that each fairness principle has a unique extension which is pairwise robust with respect to the fairness principle. We give applications of the algorithm for three fairness principles: egalitarianism, proportionality and equal sacrifice.