This thesis consists of three research papers which have been conceived together with my coauthors Christian Gollier and Sarolta Lacz´o. All of the papers have been written while pursuing my PhD at the Toulouse School of Economics in the years 2006–2010. While each is self-contained, the papers share a unifying methodological theme, which is to be incremental on the standard model of decision making under risk –the expected utility model– in allowing for small departures from along the lines suggested by data in two ways.