Decision with Dempster–Shafer belief functions: Decision under ignorance and sequential consistency

This paper examines proposals for decision making with Dempster–Shafer belief functions from the perspectives of requirements for rational decision under ignorance and sequential consistency. The focus is on the proposals by Jaffray & Wakker and Giang & Shenoy applied for partially consonant belief functions. We formalize the concept of sequential consistency of an evaluation model and prove results about sequential consistency of Jaffray–Wakker’s model and Giang–Shenoy’s model under various conditions. We demonstrate that the often neglected assumption about two-stage resolution of uncertainty used in Jaffray–Wakker’s model actually disambiguates the foci of a belief function, and therefore, makes it a partially consonant on the extended state space.