A Conflict between Finite Additivity and Avoiding Dutch Book

• DOI: 10.1086/289126
• Publication Date: 2002-11-25T18:25:56Z
• Authors: Teddy Seidenfeld; Mark J. Schervish
• Keywords: Argument (complex analysis); Additive function; Subjective expected utility

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence normative theory preference. (De achieves reduction belief to desire with his generalized Dutch-Book argument previsions. ) Both and rebel against legislating countable additivity probability. They require merely that be finitely additive. Simultaneously, they insist their theories preference are weak, accommodating all but self-defeating desires. In this paper we dispute these claims by showing following three cannot simultaneously hold: (i) Coherent reducible rational preference, i.e. fixes standards coherence. (ii) Finitely additive coherent. (iii) Admissible structures may free consequences , lack prizes whose values robust contingencies.