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Impartial Observer Theorem with Ambiguity
This paper revisits the debate between Harsanyi and Rawls on collective decision-making with impartiality. Harsanyi argued for judging resources distributions based on expected utility, while Rawls argued for a maxmin rule. Both of them relied on some kind of uncertainty to model their veil of ignorance. We propose a version of Harsanyi’s Impartial Observer Theorem that introduces ambiguity, adapting a model by Grant et al. (2010) to a Anscombe and Aumann (1963) setup. By keeping the independence between the states of nature defining the uncertainty over the distribution of identities (faced by the impartial observer) and the states of nature defining the uncertainty over the distributions of outcomes (faced by each individual), we can introduce ambiguity on both identity and outcome acts, in a multi-prior setup like Gilboa and Schmeidler (1989) maxmin model. Using different combinations of uncertainty and ambiguity on both levels, we can show that there are intermediate cases between Harsanyi’s and Rawls’ Social Welfare Functions that depend on how impartiality is modeled.