Choice architecture for architecture choices: Evaluating social housing initiatives putting together a parsimonious AHP methodology and the Choquet integral

Choice architecture concerns different forms and procedures to present and handle a decision problem. It is a paradigm around which many theoretical results have been collected within behavioural psychology and experimental economics and many successful applications have been implemented in the domains of health, finance and social choices. In this work, we propose an application of the basic idea of architecture choice that is designing decision support procedures for complex problems, with a focus on housing realm. We consider a real-world problem in which 21 Social Housing initiatives sited in the Piedmont region (Italy) had to be evaluated taking into account several criteria and, to this aim, we propose a decision analysis methodology for supporting assessment in such complex problems. Our main preoccupations in designing the decision aiding procedure were related to build a model that, on one hand, permits to take into consideration the many delicate points of the problem, while, on the other hand, requires to the Decision Maker (DM) an affordable cognitive burden in terms of preference elicitation and interpretation of the obtained results. Since synergy and redundancy of criteria constitute important aspects of the decision problem, we aggregated evaluations on considered criteria by means of the Choquet integral. To maintain the preference information asked to the DM simple and not too requiring, we put together a recently proposed parsimonious approach of the Analytical Hierarchy Process (AHP) and the Non-Additive Robust Ordinal Regression (NAROR). The Parsimonious AHP permitted to assign a value on a common scale to the performances of all criteria, while the NAROR permitted to elicit the importance and the interaction of criteria taking into account all the possible values for the preference parameters compatible with the preference information supplied by the DM. Our methodology allowed a fruitful interaction with the DM that had the possibility to update the preference information during the decision process until he/she felt convinced and satisfied of the obtained result. The suitability and the interest of the proposed methodology were confirmed by the subjective final appreciation of the DM as well as by the objective absence of specific inconsistencies in the AHP procedure and in the non-additive robust ordinal regression, which witnessed the beneficial contribution of our approach.