 But these points merely tell us that attempts to formulate Take-the-Best in terms of an ordering of prospects on a real-valued index won’t do, not that ordering and numerical indices have all got to go. As we saw in  section 1.1,  there is a long and sizable literature on lexicographic probabilities and non-standard analysis, including early work specifically addressing non-compensatory nonlinear models (Einhorn 1970). Second, Gigerenzer argues that “cognitive algorithms…need to meet more important constraints than internal consistency” (Gigerenzer &amp; Goldstein 1996), which includes transitivity, and elsewhere advocates abandoning coherence as a normative standard (Arkes, Gigerenzer, &amp; Hertwig 2016). However, Take-the-Best presupposes that cues are ordered by cue validity, which naturally entails transitivity, otherwise Take-The-Best could neither be coherently specified nor effectively executed. More generally, the Fast and Frugal school’s commitment to formulating heuristics algorithmically and implementing them as computational models commits them to the normative standards of optimization, dominance reasoning, and logical consistency.