The thesis is divided into two chapters. The first chapter studies the responsive random choice procedure. There, we show that a weakened version of Luce’s IIA is sufficient to characterize the General Luce Rule (GLR) considered in Echenique and Saito (2019) and Ahumada and Ülkü (2018), with the restriction that all elements from menus of size three are chosen with positive probability. We analyze a special form of the GLR called Responsive Luce Rule (RLR). We characterize Responsive Luce Rules by using stochastic counterparts of the axioms in Chambers and Yenmez (2018) and Eliaz et al. (2011). In the second chapter, we analyze path independent choice rules by looking at choice sets that block an alternative from being chosen. We show that these blocking set collections carry the minimal information needed to represent the choices and are in one-to-one relation with path independent choice rules. In addition, we show that the notion of blocking is a useful tool to minimally represent and characterize certain classes of path independent choice rules.