Take Action

Home | Faculty & Research Overview | Research

Research Details

Symmetry axioms and perceived ambiguity, Mathematics and Financial Economics


Since at least de Finetti [7], preference symmetry assumptions have played an important role in models of decision making under uncertainty. In the current paper, we explore (1) the relationship between the symmetry assumption of Klibanoff, Mukerji and Seo (KMS) [21] and alternative symmetry assumptions in the literature, and (2) assuming symmetry, the relationship between the set of relevant measures, shown by KMS [21] to reflect only perceived ambiguity, and the set of measures (which we will refer to as the Bewley set) developed by Ghirardato, Maccheroni and Marinacci [14], Nehring [24, 25] and Ghirardato and Siniscalchi [15, 16]. This Bewley set is the main alternative offered in the literature as possibly representing perceived ambiguity. Regarding symmetry assumptions, we show that, under relatively mild conditions, a variety of preference symmetry conditions from the literature (including that in KMS [21]) are equivalent. In KMS [21], we showed that, under symmetry, the Bewley set and the set of relevant measures are not always the same. Here, we establish a preference condition, No Half Measures, that is necessary and sufficient for the two to be same under symmetry. This condition is rather stringent. Only when it is satisfied may the Bewley set be interpreted as reflecting only perceived ambiguity and not also taste aspects such as ambiguity aversion.




Peter Klibanoff, Sujoy Mukerji, Kyoungwon Seo

Date Published



Klibanoff, Peter, Sujoy Mukerji, and Kyoungwon Seo. 2018. Symmetry axioms and perceived ambiguity. Mathematics and Financial Economics.(1): 33-54.


Explore leading research and ideas

Find articles, podcast episodes, and videos that spark ideas in lifelong learners, and inspire those looking to advance in their careers.
learn more


Review Courses & Schedules

Access information about specific courses and their schedules by viewing the interactive course scheduler tool.


Discover the path to your goals

Whether you choose our Full-Time, Part-Time or Executive MBA program, you’ll enjoy the same unparalleled education, exceptional faculty and distinctive culture.
learn more