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A semi-compensatory choice model with probabilistic choice set: combining implicit choice set within probabilistic choice set formation

The idea of a semi-compensatory choicemodel is a very generic one that can refer to awide variety of modelling structures. As soon as the stochastic choice model formulation moves away, at least partially, from the notion that all alternatives in the choice set are considered by the choice maker with absolute certainty, it falls into the general category of the semi-compensatory choice model. In this regard, the original idea of Manski’s (1977) probabilistic choice set is the originator of this approach. Ourmodel is based on this very idea of probabilistic choice set, and we enhanced it further by incorporating implicit penalty function in the conditional choice model. Our formulation is pivoted on two streams of works. One is the Independent Availability Logit (IAL) of Swait and Ben-Akiva (1987) that advocates for the stochastic choice set formation model for a conventional logit conditional choice model. Theother is theworks ofMartinez andhis colleagues (Martínez, Aguila, andHurtubia 2009; Castro, Martínez, and Munizaga 2013) who addressed the implicit choice set inclusion/exclusion penalty in the choice model, but in the context of deterministic choice set only. It also needs to be acknowledged that Ortúzar and his colleagues also worked along this line asmentioned in this note andwere first to use the term ‘semi-compensatory’. Swait and Ben-Akiva (1987) is an older paper thanmost of the onesmentioned in the note to cite. However, Castro, Martínez, and Munizaga (2013) did not cite any of the papers of Ortúzar and his colleagues. Martínez, Aguila, and Hurtubia (2009) cited only one of the papersmentioned in the note, but just as a reference to the concept of semi-compensatory approach in the introduction. In our paper, we had to make the literature review section as concise as possible with a specific focus on empirical models using revealed preference data. Citing the papers mentioned in the note could widen the context of the discussions on the semicompensatory choice model, but not necessarily change/modify our proposed modelling structure.