Probabilistic sophistication and multiple priors.

We show that under fairly mild conditions, a maximin expected utility preference relation is probabilistically sophisticated if and only if it is subjective expected utility.

A strong law of large numbers for capacities

We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.Comment: Published at http://dx.doi.org/10.1214/009117904000001062 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Concavity and Supermodularity

Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the Choquet property. We extend in this way the results of Choquet [2] and Konig [5].Concavity, Supermodularity

A strong law of large numbers for capacities.

We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.Capacities; Choquet integral; Strong law of large numbers

Physician Assisted Dying as an Extension of Healing

The role of a physician is to provide care for those who seek their assistance. Lisa Yount attributes the most ancient statement about this activity to the Hippocratic Oath. Many doctors, in fact, still take this oath, part of which reads, “I will [not] give a deadly drug to anybody if asked for it, nor will I make a suggestion to that effect,” (8). This vow is still widely considered to be the ultimate statement of the physician’s moral creed (Yount 8). Debate over whether active physician assisted dying is an extension of healing ability or a violation of their moral code is a longstanding argument. As medicine has developed, legal systems around the world have attempted to meet the needs of the patients in end of life care, but the practice of active physician assisted dying remains illegal in most parts of the world. Passive physician assisted dying is a generally accepted legal option for patients in extreme suffering, or terminal cases based on the intent to relieve pain. Due to its legal status and its shared intent with active physician assisted dying, it presents a strong pretense for the legalization of active physician assisted dying. Arguments posed against the legalization of active physician assisted dying are founded on hasty assumptions of extremity that can be disproven. Critics are worried that patients will be forced to make hasty decisions to end their lives, will be vulnerable to a pressured request for death even if they are unwilling to die, that physicians will end lives of patients who could have been adequately alleviated otherwise, and that regrettable societal consequences will result from people losing the ability to distinguish between permissible and impermissible forms of death. Active physician assisted dying should be legalized for all suffering persons because it is an extension of the physicians healing abilities in correspondence with a person’s right to die

Subcalculus for set functions and cores of TU games.

This paper introduces a subcalculus for general set functions and uses this framework to study the core of TU games. After stating a linearity theorem, we establish several theorems that characterize mea- sure games having finite-dimensional cores. This is a very tractable class of games relevant in many economic applications. Finally, we show that exact games with Þnite dimensional cores are generalized linear production games.TU games; non-additive set functions; subcalculus; cores

Magnetic fields in cosmological simulations of disk galaxies

Observationally, magnetic fields reach equipartition with thermal energy and cosmic rays in the interstellar medium of disk galaxies such as the Milky Way. However, thus far cosmological simulations of the formation and evolution of galaxies have usually neglected magnetic fields. We employ the moving-mesh code \textsc{Arepo} to follow for the first time the formation and evolution of a Milky Way-like disk galaxy in its full cosmological context while taking into account magnetic fields. We find that a prescribed tiny magnetic seed field grows exponentially by a small-scale dynamo until it saturates around $z=4$ with a magnetic energy of about $10\%$ of the kinetic energy in the center of the galaxy's main progenitor halo. By $z=2$, a well-defined gaseous disk forms in which the magnetic field is further amplified by differential rotation, until it saturates at an average field strength of \sim 6 \mug in the disk plane. In this phase, the magnetic field is transformed from a chaotic small-scale field to an ordered large-scale field coherent on scales comparable to the disk radius. The final magnetic field strength, its radial profile and the stellar structure of the disk compare well with observational data. A minor merger temporarily increases the magnetic field strength by about a factor of two, before it quickly decays back to its saturation value. Our results are highly insensitive to the initial seed field strength and suggest that the large-scale magnetic field in spiral galaxies can be explained as a result of the cosmic structure formation process.Comment: 5 pages, 4 figures, accepted to ApJ

Efficiency of gas cooling and accretion at the disc-corona interface

In star-forming galaxies, stellar feedback can have a dual effect on the circumgalactic medium both suppressing and stimulating gas accretion. The trigger of gas accretion can be caused by disc material ejected into the halo in the form of fountain clouds and by its interaction with the surrounding hot corona. Indeed, at the disc-corona interface, the mixing between the cold/metal-rich disc gas (T ~ 10^6 K) can dramatically reduce the cooling time of a portion of the corona and produce its condensation and accretion. We studied the interaction between fountain clouds and corona in different galactic environments through parsec-scale hydrodynamical simulations, including the presence of thermal conduction, a key mechanism that influences gas condensation. Our simulations showed that the coronal gas condensation strongly depends on the galactic environment, in particular it is less efficient for increasing virial temperature/mass of the haloes where galaxies reside and it is fully ineffective for objects with virial masses larger than 10^13 Msun. This result implies that the coronal gas cools down quickly in haloes with low-intermediate virial mass (Mvir <~ 3 x 10^12 Msun) but the ability to cool the corona decreases going from late-type to early-type disc galaxies, potentially leading to the switching off of accretion and the quenching of star formation in massive systems.Comment: 14 pages, 8 figures, accepted for publication in MNRA

The convexity-cone approach to comparative risk and downside risk.

We establish a calculus characterization of the core of supermodular games, which reduces the description of the core to the computation of suitable Gateaux derivatives of the Choquet integrals associated with the game. Our result generalizes to infinite games a classic result of Shapley (1971). As a secondary contribution, we provide a fairly complete analysis of the Gateaux and Frechet differentiability of the Choquet integrals of supermodular measure games.

How to cut a pizza fairly: fair division with descreasing marginal evaluations.

Existential and constructive solutions to the classic problems of fair division are known for individuals with constant marginal evaluations. By considering nonatomic concave capacities instead of nonatomic probability measures, we extend some of these results to the case of individuals with decreasing marginal evaluations.