Discussions |
Complex Expectations
Philosophy Program Research School of Social Sciences Australian National University Canberra, ACT 0200 Australia alan.hajek{at}anu.edu.au Department of Mathematics University of Wisconsin-Madison 480 Lincoln Dr Madison WI 53706-1388 USA nover{at}math.wisc.edu
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Abstract |
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In our 2004, we introduced two games in the spirit of the St Petersburg game, the Pasadena and Altadena games. As these latter games lack an expectation, we argued that they pose a paradox for decision theory. Terrence Fine has shown that any finite valuations for the Pasadena, Altadena, and St Petersburg games are consistent with the standard decision-theoretic axioms. In particular, one can value the Pasadena game above the other two, a result that conflicts with both our intuitions and dominance reasoning. We argue that this result, far from resolving the Pasadena paradox, should serve as a reductio of the standard theory, and we consequently make a plea for new axioms for a revised theory. We also discuss a proposal by Kenny Easwaran that a gamble should be valued according to its ‘weak expectation’, a generalization of the usual notion of expectation.
I can't imagine going on when there are no more expectations.
Dame Edith Evans