Probability and time are integral dimensions of virtually any decision. To treat them together, we consider the prospect of receiving outcome x with a probability p at time t. We define risk and time distance, and show that if these two distances are traded off linearly, then preferences are characterized by three functions: a value function, a probability discount rate function, and a psychological distance function. The concavity of the psychological distance function explains the common ratio and common difference effects. A decreasing probability discount rate accounts for the magnitude effect. The discount rate and the risk premium depend on the shape of these three functions. This paper was accepted by Peter Wakker, decision analysis.

Risk and time preferences, Common ratio effect,

There is an ongoing debate, in Concrete Science and Engineering, whether cementitious materials can be viewed as poromechanics materials in the sense of the porous media theory. The reason for this debate is that a main part of the porosity of these materials manifests itself at a scale where the water phase cann ot be considered as a bulk water phase, but as structural water; in contrast to water in the gel porosity and the capillary porosity. The focus of this paper is two-fold: (1) to review the microstructure of cementitious materials in the light of microporomechanics theory by starting at the scale where physical chemistry meets mechanics, and which became recently accessible to mechanical testing (nanoindentation); (2) to provide estimates of the poroelastic properties (drained and undrained stiffuess, Biot coefficient, Biot modulus, Skempton coefficient) of cementitious materials (cement paste, mortar and concrete) by means of advanced homogenization techniques of microporomechanics. This combined experimental-theoretical microporomechanics approach allows us to deliver a blueprint of the elementary poroelastic properties of all cementitious materials, which do not change from one cementitious material to another, but which are intrinsic properties. These properties result from the intrinsic gel porosity of low density and high density C-S-H, which yield a base Biot coefficient of0.61 < b :S0.71 and a Skempton coefficient of B = 0.20-0.25. While the base Biot coefficient decreases gradually at larger scales, because of the addition of non-porous solid phases (Portlandite, ... , aggregates), it is shown that the Skempton coefficient is almost constant over 3-5 orders of magnitude. ' interlayer spaces' in the C-S-H gel, containing strongly adsorbed water [27). Wittmann's Munich model. is based on so me of the concepts of colloidal science, rel ying particularly on the idea of a disjoining pressure that develops in the interlayer space as a consequence of hindered adsorption [3, 5]. Similar conclusions were arrived at by other authors as well (see e.g. (4)): given the characteristic size of the interlayer space of less than ten water molecules in size (elementary dimension of water is distance between 0-atoms 0.284 x 10• 9 m), it was quickly

We generalize and extend the second-order stochastic dominance condition for expected utility to cumulative prospect theory. The new definitions include preferences represented by S-shaped value functions, inverse S-shaped probability weighting functions, and loss aversion. The stochastic dominance conditions supply a framework to test different features of cumulative prospect theory. In the experimental part of the paper, we offer a test of several joint hypotheses on the value function and the probability weighting function. Assuming empirically relevant weighting functions, we can reject the inverse S-shaped value function recently advocated by Levy and Levy (2002) in favor of the S-shaped form. In addition, we find generally supporting evidence for loss aversion. Violations of loss aversion can be explained by subjects using the overall probability of winning as a heuristic.second-order stochastic dominance, cumulative prospect theory, value function, probability weighting function

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