Thesis: Revealed preferences link choices, preferences, and welfare when choices appear consistent. The first chapter assesses how much structure is necessary to impose on a model to provide precise welfare guidance based on inconsistent choices. We use data sets from the lab and field to evaluate the predictive power of two conservative “model-free” approaches of behavioral welfare analysis. We find that for most individuals, these approaches have high predictive power, which means there is little ambiguity about what should be selected from each choice set. We show that the predictive power of these approaches correlates highly with two properties of revealed preferences. The second chapter introduces a method for eliciting the set of best alternatives of decision makers, in line with the theory on revealed preferences, but at odds with the current practice. We allow decision makers to choose several alternatives, provide an incentive for each alternative chosen, and then randomly select one for payment. We derive the conditions under which we partially or fully identify the set of best alternatives. The third chapter applies the method in an experiment. We fully identify the set of best alternatives for 18% of subjects and partially identify it for another 40%. We show that complete, reflexive, and transitive preferences rationalize 40% of observed choices in the experiment. Going beyond, we show that allowing for menu-dependent choices while keeping classical preferences rationalize 96% of observed choices. Besides, eliciting sets allows us to conclude that indifference is significant in the experiment, and underestimate by the classical method.