 Dropping the Archimedean axiom allows for an agent to have lexicographic preferences (Blume, Brandenburger, &amp; Dekel 1991); that is, the omission of  A2  allows the possibility for an agent to prefer one option infinitely more than another. One motivation for developing a non-Archimedean version of expected utility theory is to address a gap in the foundations of the standard subjective utility framework that prevents a full reconciliation of admissibility (i.e., the principle that one ought not select a weakly dominated option for choice) with full conditional preferences (i.e., that for any event, there is a well-defined conditional probability to represent the agent’s conditional preferences; Pedersen 2014). Specifically, the standard subjective expected utility account cannot accommodate conditioning on zero-probability events, which is of particular importance to game theory (P. Hammond 1994). Non-Archimedean variants of expected utility theory turn to techniques from nonstandard analysis (Goldblatt 1998), full conditional probabilities (Rényi 1955; Coletii &amp; Scozzafava 2002; Dubins 1975; Popper 1959), and lexicographic probabilities (Halpern 2010; Brickhill &amp; Horsten 2016  [Other Internet Resources]),  and are all linked to imprecise probability theory.