Economic preferences are a fundamental aspect of economic modeling but their measurement presents a number of puzzles such as order and framing effects, and paradoxes like the lack of additivity. This study focuses on how to understand such behavioral patterns as a natural construct of the measurement process itself, and not as an undesirable anomaly. We propose a model that departs from standard probability theory by including projective measurements that do not require a certain boolean structure in the underlying space of events. Instead, we rely on a more general condition of orthomodularity.
In order to illustrate the working of this theoretical setting, we propose a stylized laboratory experiment with three treatments. In all treatments, subjects will first face the same choice task regarding time preferences and they will finish facing the same choice task (Lottery A vs. Lottery B) regarding risk preferences with a neutral frame. There will be no other intermediate steps in baseline Treatment 1. In addition, Treatments 2 and 3 will include an intermediate elicitation task. Subjects will also make a choice between a safe option and a lottery, framed as a gain or a loss: Safe+ vs. Lottery+ in Treatment 2 and Safe- vs. Lottery- in Treatment 3, respectively. We will collect additional control variables in a questionnaire at the end of the sessions.
Comparing the choices in the final task in Treatments 2 and 3 to the outcomes in the final task in Treatment 1 will allow us to identify a potential lack of additivity as a result of order effects. Comparing Treatment 2 to Treatment 3 will allow us to formally include framing as part of a projective measurement. Finally, we aim at assessing the validity of our theoretical framework as a descriptive tool for the measurement of individual preferences by producing a model that incorporates all these building blocks from the experiment in one unified setting, and testing it against the data.