Weighted Proportional Losses Solution

We propose and characterize a new solution for problems with asymmetric bargaining power among the agents that we named weighted proportional losses solution. It is specially interesting when agents are bargaining under restricted probabilistic uncertainty. The weighted proportional losses assigns to each agent losses proportional to her ideal utility and also proportional to her bargaining power. This solution is always individually rational, even for 3 or more agents and it can be seen as the normalized weighted equal losses solution. When bargaining power among the agents is equal, the weighted proportional losses solution becomes the Kalai-Smorodinsky solution. We characterize our solution in the basis of restricted monotonicity and restricted concavity. A consequence of this result is an alternative characterization of Kalai-Smorodinsky solution which includes contexts with some kind of uncertainty. Finally we show that weighted proportional losses solution satisfyies desirable properties as are strong Pareto optimality for 2 agents and continuity also fulfilled by Kalai-Smorodinsky solution, that are not satisfied either by weighted or asymmetric Kalai-Smorodinsky solutions.

Additive adjudication of conflicting claims

In a “claims problem” (O’Neill 1982), a group of individuals have claims on a resource but its endowment is not sufficient to honour all of the claims. We examine the following question: If a claims problem can be decomposed into smaller claims problems, can the solutions of these smaller problems be added to obtain the solution of the original problem? A natural condition for this decomposition is that the solution to each of the smaller problems is non-degenerate, assigning positive awards to each claimant. We identify the only consistent and endowment monotonic adjudication rules satisfying this property; they are generalizations of the canonical “constrained equal losses rule” sorting claimants into priority classes and distributing the amount available to each class using a weighted constrained equal losses rule. The constrained equal losses rule is the only symmetric rule in this family of rules

Weighted proportional losses solution

We propose and characterize a new solution for problems with asymmetric bargaining power among the agents that we named weighted proportional losses solution. It is specially interesting when agents are bargaining under restricted probabilistic uncertainty. The weighted proportional losses assigns to each agent losses proportional to her ideal utility and also proportional to her bargaining power. This solution is always individually rational, even for 3 or more agents and it can be seen as the normalized weighted equal losses solution. When bargaining power among the agents is equal, the weighted proportional losses solution becomes the Kalai-Smorodinsky solution. We characterize our solution in the basis of restricted monotonicity and restricted concavity. A consequence of this result is an alternative characterization of Kalai-Smorodinsky solution which includes contexts with some kind of uncertainty. Finally we show that weighted proportional losses solution satisfyies desirable properties as are strong Pareto optimality for 2 agents and continuity also fulfilled by Kalai-Smorodinsky solution, that are not satisfied either by weighted or asymmetric Kalai-Smorodinsky solutions

Ethical allocation of scarce vaccine doses: the Priority-Equality protocol

Background: Whenever vaccines for a new pandemic or widespread epidemic are developed, demand greatly exceeds the available supply of vaccine doses in the crucial, initial phases of vaccination. Rationing protocols must then fulfill a number of ethical principles balancing equal treatment of individuals and prioritization of at-risk and instrumental subpopulations. For COVID-19, actual rationing methods used a territory-based first allocation stage based on proportionality to population size, followed by locally-implemented prioritization rules. The results of this procedure have been argued to be ethically problematic. Methods: We use a formal-analytical approach arising from the mathematical social sciences which allows to investigate whether any allocation methods (known or unknown) fulfill a combination of (ethical) desiderata and, if so, how they are formulated algorithmically. Results: Strikingly, we find that there exists one and only one method that allows to treat people equally while giving priority to those who are worse off. We identify this method down to the algorithmic level and show that it is easily implementable and it exhibits additional, desirable properties. In contrast, we show that the procedures used during the COVID-19 pandemic violate both principles. Conclusions: Our research delivers an actual algorithm that is readily applicable and improves upon previous ones. Since our axiomatic approach shows that any other algorithm would either fail to treat people equally or fail to prioritize those who are worse off, we conclude that ethical principles dictate the adoption of this algorithm as a standard for the COVID-19 or any other comparable vaccination campaigns

Ethical allocation of scarce vaccine doses: The Priority-Equality protocol

Background: Whenever vaccines for a new pandemic or widespread epidemic are developed, demand greatly exceeds the available supply of vaccine doses in the crucial, initial phases of vaccination. Rationing protocols must then fulfill a number of ethical principles balancing equal treatment of individuals and prioritization of at-risk and instrumental subpopulations. For COVID19, actual rationing methods used a territory-based first allocation stage based on proportionality to population size, followed by locally-implemented prioritization rules. The results of this procedure have been argued to be ethically problematic. Methods: We use a formal-analytical approach arising from the mathematical social sciences which allows to investigate whether any allocation methods (known or unknown) fulfill a combination of (ethical) desiderata and, if so, how they are formulated algorithmically. Results: Strikingly, we find that there exists one and only one method that allows to treat people equally while giving priority to those who are worse o. We identify this method down to the algorithmic level and show that it is easily implementable and it exhibits additional, desirable properties. In contrast, we show that the procedures used during the COVID-19 pandemic violate both principles. Conclusions: Our research delivers an actual algorithm that is readily applicable and improves upon previous ones. Since our axiomatic approach shows that any other algorithm would either fail to treat people equally or fail to prioritize those who are worse o, we conclude that ethical principles dictate the adoption of this algorithm as a standard for the COVID-19 or any other comparable vaccination campaigns

Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution

Many bargaining solutions anchor on disagreement, allocating gains with respect to the worst-case scenario. We propose here a solution anchoring on utopia (the ideal, maximal aspirations for all agents), but yielding feasible allocations for any number of agents. The negotiated aspirations solution proposes the best allocation in the direction of utopia starting at an endogenous reference point which depends on both the utopia point and bargaining power. The Kalai–Smorodinsky solution becomes a particular case if (and only if) the reference point lies on the line from utopia to disagreement. We provide a characterization for the two-agent case relying only on standard axioms or natural restrictions thereof: strong Pareto optimality, scale invariance, restricted monotonicity, and restricted concavity. A characterization for the general (n-agent) case is obtained by relaxing Pareto optimality and adding the (standard) axiom of restricted contraction independence, plus the minimal condition that utopia should be selected if available

Resultados de la técnica de Zarins en la reconstrucción del ligamento cruzado anterior

Se presenta una serie de 96 pacientes con lesión crónica del ligamento cruzado anterior de la rodilla que fueron intervenidos mediante un procedimiento combinado intra y extraarticular que utiliza como método de reconstrucción el tendón del semitendinoso y una tira de fascia lata. Ochenta y cinco pacientes pudieron ser revisados a una media de 119 meses de la intervención (rango 110-130). El test de Lachman instrumentado con Genucom fue inferior a 5mm en el 88% de los casos y el pívot-shift fue negativo en el 91%. Se observaron cambios radiológicos en 52% de las rodillas. De acuerdo con la escala de Zarins, 88% de pacientes fueron calificados de excelentes o buenos. En la escala de Lysholm, la puntuación media fue de 93 puntos. Los resultados demuestran que esta técnica puede restaurar la estabilidad de la rodilla con déficit del LCA a largo plazo.Ninety-six patients who had chronic lesions of the anterior cruciata were treated using a combined method of intraarticular and extraarticular transfer of the semitendinous tendon and a strip of fascia lata (Zarins technique). Eighty-five patients were studied at 119 (110 to 130) months after surgery. In 88 percent of the patients, instrumented measurement of anteroposterior laxity at 30 degrees knee flexion was zero to five milimeters. The pivot shift test was negative in 91 percent of them. Radiological changes were observed in 52 percent of the patients. According to the Zarins scale, 88 percent of the patients were rated as excellent or good. Lysholm evaluation showed an average of 93 points. This study demonstrates that this method can restore long term stability to a knee that has a torn anterior cruciate ligament

The Big Robber Game

We present a novel design measuring a correlate of social preferences in a high-stakes setting. In the Big Robber Game, a "robber" can obtain large personal gains by appropriating the gains of a large group of "victims" as seen in recent corporate scandals. We observed that more than half of all robbers take as much as possible. At the same time, participants displayed standard, prosocial behavior in the Dictator, Ultimatum, and Trust games. That is, prosocial behavior in the small is compatible with highly selfish actions in the large, and the essence of corporate scandals can be reproduced in the laboratory even with a standard student sample. We show that this apparent contradiction is actually consistent with received social-preference models. In agreement with this view, in the experiment more selfish robbers also behaved more selfishly in other games and in a donation question. We conclude that social preferences are compatible with rampant selfishness in high-impact decisions affecting a large group

Stagnation proofness in n-agent bargaining problems

Some bargaining solutions may remain unchanged under any extension of a bargaining set which does not affect the utopia point, despite the fact that there is room to improve the utility of at least one agent. We call this phenomenon the stagnation effect. A bargaining solution satisfies stagnation proofness if it does not suffer from the stagnation effect. We show that stagnation proofness is compatible with the restricted version of strong monotonicity (Thomson and Myerson in Int J Game Theory 9(1):37–49, 1980), weak Pareto optimality, and scale invariance. The four axioms together characterize the family of the bargaining solutions generated by strictly-increasing paths ending at the utopia point (SIPUP-solutions)

Generous with individuals and selfish to the masses

The seemingly rampant economic selfishness suggested by many recent corporate scandals is at odds with empirical results from behavioural economics, which demonstrate high levels of prosocial behaviour in bilateral interactions and low levels of dishonest behaviour. We design an experimental setting, the ‘Big Robber’ game, where a ‘robber’ can obtain a large personal gain by appropriating the earnings of a large group of ‘victims’. In a large laboratory experiment (N = 640), more than half of all robbers took as much as possible and almost nobody declined to rob. However, the same participants simultaneously displayed standard, predominantly prosocial behaviour in Dictator, Ultimatum and Trust games. Thus, we provide direct empirical evidence showing that individual selfishness in high-impact decisions affecting a large group is compatible with prosociality in bilateral low-stakes interactions. That is, human beings can simultaneously be generous with others and selfish with large groups