A subjective spin on roulette wheels.

We provide a behavioral foundation to the notion of ‘mixture’ of acts, which is used to great advantage in he decision setting introduced by Anscombe and Aumann. Our construction allows one to formulate mixture-space axioms even in a fully sub-jective setting, without assuming the existence of randomizing devices. This simplifies the task of developing axiomatic models which only use behavioral data. Moreover, it is immune from the difficulty that agents may ‘distort’ the probabilities associated with randomizing devices. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including the maxmin expected utility model of Gilboa and Schmeidler, and Bewley’s model of choice with incomplete preferences.

Rational Preferences under Ambiguity

This paper analyzes preferences in the presence of ambiguity that are rational in the sense of satisfying the classical ordering condition as well as monotonicity. Under technical conditions that are natural in an Anscombe-Aumann environment, we show that even for such general preference model it is possible to identify a set of priors, as first envisioned by Ellsberg (1961). We then discuss ambiguity attitudes, as well as unambiguous acts and events, for the class of rational preferences we consider.Rational Preferences; Ambiguity; Unambiguous Acts and Events

Plant patch hydrodynamics in streams : Mean flow, turbulence, and drag forces

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Long term results of down-staging and liver transplantation for patients with hepatocellular carcinoma beyond the conventional criteria

The objective of the study is to evaluate 10 years of down-staging strategy for liver transplantation (LT) with a median follow-up of 5 years. Data on long-term results are poor and less information is available for hepatocellular carcinoma (HCC) non-responder patients or those ineligible for down-staging. The outcome of 308 HCC candidates and the long-term results of 231 LTs for HCC performed between 2003 and 2013 were analyzed. HCCs were divided according to tumor stage and response to therapy: 145 patients were T2 (metering Milan Criteria, MC), 43 were T3 successfully down-staged to T2 (Down-Achieved), 20 were T3 not fully down-staged to T2 (Down-not Achieved), and 23 patients were T3 not receiving down-staging treatments (No-Down). The average treatment effect (ATE) of LT for T3 tumors was estimated using the outcome of 535 T3 patients undergoing non-LT therapies, using inverse probability weighting regression adjustment. The 24-month drop-out rate during waiting time was significantly higher in the down-staging groups: 27.6% vs. 9.2%, p < 0.005. After LT, the tumor recurrence rate was significantly different: MC 7.6%, Down-Achieved 20.9%, Down-not Achieved 31.6%, and No-Down 30.4% (p < 0.001). The survival rates at 5 years were: 63% in Down-Achieved, 62% in Down-not Achieved, 63% in No-Down, and 77% in MC (p = n.s.). The only variable related to a better outcome was the effective down-staging to T2 at the histological evaluation of the explanted liver: recurrence rate = 7.8% vs. 26% (p < 0.001) and 5-year patient survival = 76% vs. 67% (p < 0.05). The ATE estimation showed that the mean survival of T3-LT candidates was significantly better than that of T3 patients ineligible for LT [83.3 vs 39.2 months (+44.6 months); p < 0.001]. Long term outcome of T3 down-staged candidates was poorer than that of MC candidates, particularly for cases not achieving down-staging. However, their survival outcome was significantly better than that achieved with non-transplant therapies

A Subjective Spin on Roulette Wheels

We provide a simple behavioral definition of 'subjective mixture' of acts for a large class of (not necessarily expected-utility) preferences. Subjective mixtures enjoy the same algebraic properties as the 'objective mixtures' used to great advantage in the decision setting introduced by Anscombe and Aumann (1963). This makes it possible to formulate mixture-space axioms in a fully subjective setting. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including Bewley's model of choice with incomplete preferences (2002). Copyright The Econometric Society 2003.