L.S. Penrose was the first to propose a measure of voting power (which later came to be known as 'the [absolute] Banzhaf (Bz) index'). His limit theorem-which is implicit in his booklet (1952) and for which he gave no rigorous proof-says that in simple weighted voting games (WVGs), if the number of voters increases indefinitely while the quota is pegged at half the total weight, then-under certain conditions-the ratio between the voting powers (as measured by him) of any two voters converges to the ratio between their weights. We conjecture that the theorem holds, under rather general conditions, for large classes of variously defined WVGs, other values of the quota, and other measures of voting power. We provide proofs for some special cases.

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BackgroundType I hypersensitivity is characterized by the overreaction of the immune system against otherwise innocuous substances. It manifests as allergic rhinitis, allergic conjunctivitis, allergic asthma or atopic dermatitis if mast cells are activated in the respective organs. In case of systemic mast cell activation, life-threatening anaphylaxis may occur. Currently, type I hypersensitivities are treated either with glucocorticoids, anti-histamines, or mast cell stabilizers. Although these drugs exert a strong anti-allergic effect, their long-term use may be problematic due to their side-effects.ResultsIn the course of a routine in vitro screening process, we identified beta-escin as a potentially anti-allergic compound. Here we tested beta-escin in two mouse models to confirm this anti-allergic effect in vivo. In a model of the early phase of allergic reactions, the murine passive cutaneous anaphylaxis model, beta-escin inhibited the effects of mast cell activation and degranulation in the skin and dose-dependently prevented the extravasation of fluids into the tissue. Beta-escin also significantly inhibited the late response after antigen challenge in a lung allergy model with ovalbumin-sensitized mice. Allergic airway inflammation was suppressed, which was exemplified by the reduction of leucocytes, eosinophils, IL-5 and IL-13 in the bronchoalveolar lavage fluid. Histopathological examinations further confirmed the reduced inflammation of the lung tissue. In both models, the inhibitory effect of beta-escin was comparable to the benchmark dexamethasone.ConclusionsWe demonstrated in two independent murine models of type I hypersensitivity that beta-escin has potent anti-allergic properties. These results and the excellent safety profile of beta-escin suggest a therapeutic potential of this compound for a novel treatment of allergic diseases.

The paper presents the long-run equilibrium and development dynamics in the neoclassical growth model and a simple model of endogenous growth when property rights are absent. The results are compared to the outcome in a corresponding model economy with secure property rights. The main findings are that there exists a considerable gain in level and growth of consumption from establishing secure property rights, that economic performance without property rights worsens with increasing number of competing groups, and that the existence, or absence of property rights explains conditional convergence.