A taxonomy of rationalization by incomplete preferences

•We provide a taxonomy of 4 known models of rationalization with (possibly) incomplete preferences.•We provide a novel characterization of rationalizability that gives a new interpretation of WARP.•Our taxonomy provides a novel axiomatic rationale for a moderate attraction effect.

This paper provides a tight axiomatic relation between the following models: the standard rational choice model, non-domination rationalizability, rationalization by an incomplete Hype-relation (Aizerman and Malishevski, 1981), and the transitive version of the partial dominant choice model (Gerasimou, 2016). Thus, providing a taxonomy of rationalization by incomplete preferences.