Preferred by “All” and Preferred by “Most” Decision Makers: Almost Stochastic Dominance

Abstract

W A hile "most" decision makers may prefer one uncertain prospect over another, stochastic dominance rules as well as other investment criteria, will not reveal this preference due to some extreme utility functions in the case of even a very small violation of these rules. Such strict rules relate to "all" utility functions in a given class including extreme ones which presumably rarely represents investors' preference. In this paper we establish almost stochastic dominance (ASD) rules which formally reveal a preference for "most" decision makers, but not for "all" of them. The ASD rules reveal that choices which probably conform with "most" decision makers also solve some debates, e.g., showing, as practitioners claim, an ASD preference for a higher proportion of stocks in the portfolio as the investment horizon increases, a conclusion which is not implied by the well-known stochastic dominance rules. (Stochastic Dominance; Almost Stochastic Dominance; Mean-Variance; Risk Aversion) The detailed development of SD paradigm is given in the survey of Levy (1992, 1998).

Spaces for Agreement: A Theory of Time-Stochastic Dominance and an Application to Climate Change

“…Put another way, the downside of a flexible, nonparametric approach is that the broad classes of preference on which the dominance criteria are based include a small subset of "extreme" or "pathological" functions, whose implications for choice would be regarded by many as perverse. 11 Leshno and Levy (2002) recognized this problem in the context of SD and developed a theory of almost stochastic dominance (Almost 11. What is "extreme" is clearly subjective, an obvious difficulty faced by the Almost SD approach.…”

“…The intellectual antecedents of this paper lie in the theory of Stochastic Dominance (Fishburn 1964;Hadar and Russell 1969;Hanoch and Levy 1969;Rothschild and Stiglitz 1970) and its offshoots, in particular, Almost Stochastic Dominance (Leshno and Levy 2002), Time Dominance (Bøhren and Hansen 1980;Ekern 1981), and extensions of dominance analysis to multivariate problems (Levy and Paroush 1974b; Atkinson and Bourguignon 1982;Karcher, Moyes, and Trannoy 1995).…”

“…While it would seem that virtually any investor would prefer the former, SD cannot be established. 4 Arguably this paradox betrays the disadvantage of SD's generality-within the classes of utility function considered, there are some "extreme" (Leshno and Levy 2002) or even "pathological" (Levy 2009) utility functions, according to which the latter prospect is preferred. 5 For this reason Leshno and Levy (2002) derived Almost Stochastic Dominance (Almost SD), according to which one compares the area between the cumulative distributions in which SD is violated with the total area between the distributions.…”

“…4 Arguably this paradox betrays the disadvantage of SD's generality-within the classes of utility function considered, there are some "extreme" (Leshno and Levy 2002) or even "pathological" (Levy 2009) utility functions, according to which the latter prospect is preferred. 5 For this reason Leshno and Levy (2002) derived Almost Stochastic Dominance (Almost SD), according to which one compares the area between the cumulative distributions in which SD is violated with the total area between the distributions. Crucially, the ratio of the former to the latter can be given an interpretation in terms of restrictions on the class of utility functions, and if the restriction is very small, an Almost SD relation can be argued to exist.…”

Foreign market entry mode decision – approach based on stochastic dominance rules versus multi-actor multi-criteria analysis / Wybór sposobu wejścia na rynek zagraniczny - podejście oparte na dominacjach stochastycznych a wieloaktorska analiza wielokryterialna

“…Because all the criteria are measured on the ordinal scale, the ordinal stochastic dominance approach proposed in Spector et al [1996] is applied: For modelling preferences the ordinal almost stochastic dominances are also utilized 7 : 6 It is assumed that the decision-maker(s) is (are) risk-averse and all the criteria are maximized. 7 Almost stochastic dominances were proposed in [Leshno, Levy 2002]. …”