 While the philosophical literature on the topic remains rather sparse, there is no shortage of first-rate summaries in the economics and psychology literatures. For thorough presentations of the technical results referred to in  Section 1,  see Fishburn (1970: Ch. 14) or the slightly less detailed Kreps (1988: Ch. 9). Ch. 3 of Joyce (1999) is also helpful here. Regarding the literature on Independence specifically, discussed in  Section 2,  see Machina (1987), Starmer (2000) and Weber &amp; Camerer (1987). Regarding the issue of probabilistic belief specifically, discussed in  Section 3,  see Camerer &amp; Weber (1992), Etner et al. (2012), Gilboa &amp; Marinacci (2013), Machina &amp; Siniscalchi (2014), and Trautmann &amp; van de Kuilen (2015).A number of broader surveys cover both the above issues, and some. These include most notably Camerer (1995) and the excellent Sugden (2004). Finally, for a clear and detailed historical account of the development of the experimental literature on decision-making, see Heukelom (2014).