Subjective Expected Utility Theory with “Small Worlds”

We model the notion of a "small world" as a context dependent state space embedded into the "grand world". For each situation the decision maker creates a "small world" reflecting the events perceived to be relevant for the act under consideration. The "grand world" is represented by an event space which is a more general construction than a state space. We retain preference axioms similar in spirit to the Savage axioms and obtain, without abandoning linearity of expectations, a subjective expected utility theory which allows for an intuitive distinction between risk and uncertainty. We also obtain separation of subjective probability and utility as in the state space models.subjective expected utility; decision making under uncertainty; uncertainty aversion; Ellsberg paradox

Self-reported cardiorespiratory fitness:prediction and classification of risk of cardiovascular disease mortality and longevity--a prospective investigation in the Copenhagen City Heart Study

BACKGROUND: The predictive value and improved risk classification of self‐reported cardiorespiratory fitness (SRCF), when added to traditional risk factors on cardiovascular disease (CVD) and longevity, are unknown. METHODS AND RESULTS: A total of 3843 males and 5093 females from the Copenhagen City Heart Study without CVD in 1991–1994 were analyzed using multivariate Cox hazards regression to assess the predictive value and survival benefit for CVD and all‐cause mortality from SRCF. The category‐free net reclassification improvement from SRCF was calculated at 15‐year follow‐up on CVD and all‐cause mortality. Overall, 1693 individuals died from CVD. In the fully adjusted Cox model, those reporting the same (hazard ratio [HR], 1.17; 95% confidence interval [CI], 1.04 to 1.32) and lower (HR, 1.91; 95% CI, 1.62 to 2.24) SRCF than peers had an increased risk of CVD mortality, compared with individuals with higher SRCF. Compared with individuals with higher SRCF, those with the same and lower SRCF had 1.8 (95% CI, 1.0 to 2.5) and 5.1 (95% CI, 4.1 to 6.2) years lower life expectancy, respectively. Individuals with lower SRCF had a significantly increased risk of CVD mortality, compared with individuals with higher SRCF, within each strata of leisure time physical activity and self‐rated health, and SRCF significantly predicted CVD mortality independently of self‐rated health and walking pace. A net reclassification improvement of 30.5% (95% CI, 22.1% to 38.9%) for CVD mortality was found when adding SRCF to traditional risk factors. Comparable findings were found for all‐cause mortality. CONCLUSIONS: SRCF has independent predictive value, is related to a considerable survival benefit, and improves risk classification when added to traditional risk factors of CVD and all‐cause mortality. SRCF might prove useful in improved risk stratification in primary prevention