Last modified: 28 March 2017

#### Abstract

Most discrete choice models require the construction of a single figure of merit, such as utility in random utility models (McFadden, 1973) or regret in random regret models (Chorus, 2010). When postulating the *satisficing *theory, Simon (1955) highlighted which elements of the random utility maximization process, or any other model which fully inspects all alternative’s attributes and compares the whole choice set, were highly implausible. Among these, it was explicitly recognized that individuals may have trouble combining attributes of a different nature into a single utility measure (e.g. quality and cost into a utility function) and that it might not be feasible to consider all alternatives when a choice set is large. As a consequence of this principles, Simon explains the satisficing behaviour

Even though the satisficing behaviour has been proposed long time ago and several authors have attempted to implement it, we have found that no existing model achieves a full implementation of the principle exclusively choice set’s data. In this paper we propose a model that works with each attribute independently leading to the choice of a sufficiently satisfactory alternative, instead of the best one. For this, people are assumed to explore the choice set sequentially, thus this process is based on alternatives rather than on attributes (Golob and Richardson, 1981; Williams and Ortuzar, 1982).

This choice mechanism has several components. The first is the probability of starting the exploration with a particular alternative, which is relevant as the model is path-dependant. Depending on the nature of the choice set (e.g. alternatives described in a stated choice experiment or a supermarket’s shelf full of products) the probability of choosing any alternative first could vary. In the absence of information regarding which alternative the individual inspects first, the probability of starting with each alternative is assumed to be the same for all alternatives.

The second component is the transition probability between alternatives. Once an alternative is inspected, the probability of inspecting another one could be identical or could vary in terms of the attributes of the alternatives (e.g., a given alternative could be harder to reach than another one, reducing the probability of inspection of the former). Because the search path is unknown, the model must assume identical probabilities to each available alternative.

The third component is the *acceptability function*. Simon (1955) suggests that this function must be dynamic. This implies that people build and adapt their preferences rather than having fixed preferences. Different choice sets could change the expectation regarding the attributes and therefore also change the acceptability threshold. Acceptability must be related to attributes rather than to whole alternatives due to the possible limitation of mixing attributes of a different nature. The model proposed in this paper is flexible in the sense of enabling both approaches, but with static acceptability functions.

Eye-tracking data (Stüttgen et al., 2012) suggests that once an individual finds a satisfactory alternative s/he does not choose it right away. Indeed, people tend to continue making a brief search and only choose that alternative if none better is found in the brief search. Hence, the fourth component is the probability of choosing the satisfactory alternative after each inspection, conditional on the fact that a satisfactory alternative has already been found.

The objective of this paper is to generate a model for satisficing behaviour when data about the full choice set (i.e. all alternatives available, inspected or not) and the chosen alternative is available. Indeed, there is no need to know which alternative was inspected first, which was the search path, and how many alternatives the person checked after finding the chosen alternative.

The model is developed and solved analytically. Several properties are inspected as well as identifiability issues, marginal rates of substitution in terms of alternative acceptability and the linkage to the search cost. To show an application and interpretation of the results, the model is tested on the database that served as model for the synthetic experiment. The model is estimated and marginal rates of substitution are obtained through the whole data spectrum.

The model is tested through a synthetic population to understand model’s properties. With the objective of guaranteeing a realistic scenario, random samples are taken from a well-tested data base (Gaudry et al., 1989; Jara-díaz and Ortúzar, 1989) of mode choice in Santiago de Chile. Several data bases of 500, 1000 and 5000 observations are employed.

This model explicit characterize non-compensatory behaviours and allows to understand why people could not be influenced by the improving of high order attributes if basic ones aren’t fulfilled. It is a flexible model that allows the obtaining of constant or highly variable marginal rates of substitution.

The main contribution of this model is that it can capture extreme behaviours where one attribute isn’t compensated (e.g. cost for poor people or comfort for richer ones) and the traditional model working where it is best, on compensatory people. Thus, being a good complement to the traditional multinomial logit models.

Chorus, C.G., 2010. A new model of random regret minimization. European Journal of Transport and Infrastructure Research 10, 181–196.

Gaudry, M.J.I., Jara-Diaz, S.R., Ortuzar, J. de D., 1989. Value of time sensitivity to model specification. Transportation Research Part B: Methodological 23, 151–158.

Golob, T., Richardson, A., 1981. Noncompensatory and Discontinuous Constructs in ravel-Behavior Models, in: New Horizons in Travel-Behavior Research. Lexington Books, pp. 369–384.

Jara-díaz, S.R., Ortúzar, J.D.D., 1989. Introducing the Expenditure Rate in the Estimation of Mode Choice Models. Journal of Transport Economics and Policy 23, 293–308.

McFadden, D., 1973. Conditional logit analysis of qualitative choice behavior, in: Frontiers of Econometrics. New York: Academic Press, New York.

Simon, H., 1955. A Behavioral Model of Rational Choice. Oxford University Press 69, 99–118.

Stüttgen, P., Boatwright, P., Monroe, R.T., 2012. A Satisficing Choice Model. Marketing Science 31, 878–899.

Williams, H.C.W.L., Ortuzar, J.D., 1982. Behavioural theories of dispersion and the mis-specification of travel demand models. Transportation Research Part B: Methodological 16, 167–219.