The ignorant observer
The authors propose an extension of \textit{J. C. Harsanyi}'s impartial observer theorem [Rational behavior and bargaining equilibrium in games and social situations. Cambridge: Cambridge University Press (1977; Zbl 0395.90087)] based on the representation of ignorance as the set of all possible distributions over individuals. Let \(N\) and \(X\) be, accordingly, the set of individuals and of social alternatives (both finite), and assume that each individual has a preference relation on the set \(Y\) of lotteries over \(X\) (social-alternative lotteries). The obtained ``ignorant observer'' theorem asserts that the observer's preferences on social-alternatives lotteries can be represented by \(V(y)=\theta \min_{i \in N} V_{i}(y)+(1-\theta)\sum_{i \in N} \frac{1}{n}V_{i}(y)\) for all \(y\in Y\), where \(\theta \in [0,1]\) is uniquely determined (for a given observer) and the utility functions \(V_{i}\) are cardinally measurable and fully comparable representations of individual preferences. This includes both Harsanyi's utilitarian criterion (\(\theta = 0\)) and Rawls' maximum principle (\(\theta = 1\)). Moreover, the authors defend the view that both Harsanyi's and Rawls' solutions are unsatisfactory, whereas a mix of the two (i.e. with \(\theta \in (0,1)\)) is a reasonable criterion for social decision making.
scientific article; zbMATH DE number 5565991
scientific article