The purpose of this paper is to show how some of the controversial questions concerning utilitarianism can be clarified by the modelling techniques and the other analytical tools of decision theory (and, sometimes, of game theory). It is suggested that the moral rules of utilitarian ethics have a logical status similar to that of the normative rules (theorems) of such formal normative disciplines as decision theory and game theory.The paper argues that social utility should be defined, not in hedonistic or (...) in ideal-utilitarian terms, but rather in terms of individual preferences, in accordance with the author's equiprobability model of moral value judgments. (shrink)

the theory of modal groups is an abstract theory that may be used to show formal similarities between various formulations of epistemic logics (eg Hintikka, Chisholm, and von Wright) and formal systems in other domains.

The basic theory of preference relations contains a trivial part reflected by axioms A1 and A2, which say that preference relations are preorders. The next step is to find other axims which carry the theory beyond the level of the trivial. This paper is to a great part a critical survey of such suggested axioms. The results are much in the negative — many proposed axioms imply too strange theorems to be acceptable as axioms in a general theory of preference. (...) This does not exclude, of course, that they may well be reasonable axioms for special calculi of preference. I believe that many axioms which are rejected here may be plausible if their range of application is restricted by conditions which are possible to formulate only in a language richer than that of the propositional calculus, e.g. in one containing modal operators or probabilistic concepts. (shrink)

(1) This paper uses the following binary relations: > (is preferred to); ⩽ (is not preferred to); < (is less preferred than); ~ (is indifferent to). (2) Savage used primitive ⩾, postulated to be connected and transitive onA (the set of acts), to define the others: [x ~ y ⇔ (x ⩽ y and y ⩽ x)]; [y < x ⇔ notx ⩽ y]; [x > y ⇔ y < x]. Independently of the axioms, this definition implies that ⩽ and (...) > are complementary relations onA: [x < y ⇔ notx > y]. (3) Pratt, Raiffa and Schlaifer used primitive ⩽, postulated to be transitive onL (the set of lotteries), to define the others with a different expression for <: [x < y ⇔ (x ⩽ y and noty ⩽ x)]. Thus, ⩽ and > are not necessarily complementary onL; since ⩽ is not postulated to be connected onL, but connected ⩽ is necessary and sufficient for such complementarity. Since the restriction of ⩽ to the subsetA ofL is connected, ⩽ and > are complementary onA. (4) Fishburn used primitive < onA to define the others with different expression for ~ and ⩽: [x ~ y ⇔ (notx < y and noty < x)]; [x ⩽ y ⇔ (x < y orx ~ y)]. His version of Savage's theory then assumed that < is asymmetric and negatively transitive onA. Thus, ⩽ and > are complementary, since asymmetric < is necessary and sufficient for such complementarity. (5) This analysis provides a new proof that the same list of elementary properties of binary relations onA applies to all three theories: ⩽ is connected, transitive, weakly connected, reflexive, and negatively transitive; while both < and > are asymmetric, negatively transitive, antisymmetric, irreflexive, and transitive; but only ~ is symmetric. (shrink)

This paper contributes to the mathematical foundations of the model for utility theory developed by Richard Jeffrey in The Logic of Decision [5]. In it I discuss the relationship of Jeffrey's to classical models, state and interpret an existence theorem for numerical utilities and subjective probabilities and restate a theorem on their uniqueness.