The Selection of Dimensions when Choosing Between Multiattribute Alternatives

The criterion—dependent choice model (Aschenbrenner, Albert & Schmalhofer, 1984) assumes that choice between two multidimensionally described alternatives is a sequential comparison process. The decision maker is assumed to select one dimension at a time and to compare the alternatives standings on this dimension according to attractiveness. The resulting value differences are accumulated over the processed dimensions until enough evidence is accumulated so that the decision maker is convinced that one alternative is better than the other. This study concentrates on the process of sequentially selecting dimensions and its relation to judgments of the dimensions' importance. In three experiments the dimensional selection process was observed by different process tracing techniques. Although subjects displayed considerable variability in their dimensional selection over repeated choice tasks, this process was well described probabilistically by Luce's choice axiom. Parameters of dimensional importance which were inferred from the subjects' sequences of processing information agreed well with independently elicited judgments of the dimensions' importance when the judgments were obtained by a magnitude estimation procedure. Importance judgments obtained by rating scales showed worse agreement. When choosing between two alternatives that are described by their features on a number of dimensions or attributes, people often do not consider all the available information about the alternatives; further, people appear to consider neither information on the same dimensions, nor even the same amount of information when choosing among different pairs of alternatives of the same kind, e.g., pairs of journal subscriptions (Schmalhofer, Albert, Aschenbrenner & Gertzen, 1986). We tried to model this phenomenon by means of the criterion —dependent choice (CDC) model (Aschenbrenner, Albert & Schmalhofer, 1984). For binary choices among multidimensionally described alternatives, this model assumes that: a) people process information about the alternatives sequentially; b) people compare the alternatives with respect to the subjective evaluations of the alternatives's features on one dimension at a 1) This research was supported by the Attitude and Behavior research program of the Deutsche Forschungsgemeinschaft (Grant Al 205/1 5 ) . Maria Bannert, Heiner Gertzen, Roland Layer, Walter Saffrich, Iris Schafer, and Thomas Schneyer helped to conduct the reported experiments. Franz Schmalhofer is now at the Albert-Ludwigs-Universitat, Freiburg. time; c) the results of these comparisons are accumulated over the processed dimensions; and d) this comparison stops and an alternative is chosen when a person has accumulated enough evidence to be convinced that one alternative is better, i.e., when the accumulated comparison results reach or exceed a critical value. In this paper a special aspect within this model framework is analyzed in more detail, namely, the process of selecting the dimensions on which the choice alternatives are compared. We will consider two questions: a) How can an individual's process of selecting dimensions be described? and b) Are there relations between this selection process and independently elicited judgments of the importance of the dimensions? As an example, Table 1 displays two subjects' sequences of processing dimensions when choosing between 15 pairs of journal subscriptions. Schmalhofer et al. (1986) showed that the resulting choices may be well described by the CDC —model when these selection sequences are known. Table 1 also demonstrates, however, that the subjects did not inspect the same dimensions for all choices. Rather, the inspected dimensions, their number, and their order vary from choice to choice. Furthermore, Table 1 displays some individual differences; for instance, the second subject appears to be much more variable than the first subject. Thus, under conditions where the sequence of inspected dimensions is not known, prediction of a subject's choices may fail even if an appropriate model is used and the subject's evaluations of the alternatives' features are known, simply because one does not know which dimensions are incorporated into the choice process. Since, as Table 1 demonstrates, the processed dimensions often cannot be predicted with certainty, we tried to model this selection process probabilistically. The assumption that will be tested in this paper is that the selection process may be described by Luce's (1959) choice axiom. Let J denote the set of dimensions that have not been processed, i.e., initially J is the set of all dimensions; during the choice process the considered dimensions are successively removed from J. Then the choice axiom states that a subject's probability, pjj, for choosing a dimension i from set J for comparing the alternatives is PiJ = s i / L S J , (1) where si are parameters of the dimensions which are independent of the respective set J. Additionally, we assume that s{ are some function of the dimensions' importance for the subject in the given choice situation. Although it has been shown repeatedly that the choice axiom usually does not hold for choices among multidimensional alternatives (Luce, 1977), there are reasons to consider it for the selection of dimensions, because dimensional importance is considered to be a one—dimensional continuum. Indeed, in an experiment where the subjects were presented with all information about pairs of alternatives simultaneously and no data about dimensional selection were collected, Aschenbrenner et al. (1984) obtained a reasonably good fit of subjects* choices for the CDC—model combined with Equation 1. In that study, it was additionally assumed that sj=exp(wj), where WJ was the importance that the subject independently assigned to dimension i using a 7—point rating scale. With this assumption, the CDC—model yielded better (probabilistic) predictions of the subjects* choices than the weighted additive model using all presented dimensions. Table 1: Two subjects' sequences of inspecting alternatives' features on up to 11 dimensions when choosing between 15 pairs of journal subscriptions. The dimensions' names are given in Table 2 Choice Sequence of inspected dimensions Choice pair Subject 154, Experiment I: 1/6 i 4 5 6 3/8 1 11 4 6 1/2 11 1 4 6 8 9 5/6 1 11 4 5 6 7 8 9 1/8 1 11 4 6 5/3 1 11 4 5 6 8/2 1 11 4 7 8 9 3/1 1 11 10 7 8/6 1 11 4 6 7 9 2/3 1 11 4 6 7 8 5/8 1 11 4 6 7 6/2 1 4 11 8 9 7 5/1 1 4 11 9 7 6 3/6 1 11 4 5 6 7 8 9 2/5 1 4 6 7 Subject 37, Experiment II with consequences: 1/6 1 11 7 6 9 8 B 3/8 1 5 7 6 9 B 1/2 1 3 5 9 6 11 B 5/6 11 1 3 5 7 6 9 8 B 1/8 1 5 8 9 7 6 10 11 3 A 5/3 4 3 10 11 1 9 8 A 8/2 5 1 11 3 6 7 9 8 A 3/1 8 1 3 B 8/6 9 11 5 1 6 7 B 2/3 6 1 5 11 A 5/8 9 7 6 10 3 8 1 5 B 6/2 1 11 5 3 8 A 5/1 6 7 9 1 5 A 3/6 9 6 5 1 7 8 11 8 2/5 6 9 7 8 1 5 B Here, we will analyse data from three experiments in which the subjects' sequences of selecting dimensions were directly observed. It will be tested whether the observed selection data are compatible with the choice axiom. The choice axiom also allows us to estimate the assumed parameters sj from the selection data. These parameters will be compared with the subjects' explicit judgments of the dimensions' importance. The first two experiments were originally conducted for a different purpose (Schmalhofer et al., 1986) and are reanalyzed here. The third experiment was especially designed for the purpose of this paper. Experiments I and II (Reanalyses) The two experiments which are reanalyzed here were identical except for an additional experimental variable in the second experiment and some additional tasks that are not of interest here. They are described in more detail in Schmalhofer et al. (1986). In both experiments, the choice tasks consisted of choosing a one year subscription to a news magazine. Six descriptions of real journals were used as choice alternatives, each of which was described by its features on 11 dimensions. All possible pairs of alternatives were constructed, thus yielding a complete paired comparison with 15 choice pairs. An English translation of a sample choice pair is shown in Table 2. Table 2: A sample choice pair as it would be seen by a subject who uncovered all 11 dimensions. (The dimensions' numbers were not given in the display.) alternative No. Dimension A 6 1 Frequency of publication monthly weekly 2 No. of a r t i c l e s on science 4 1 3 No. of advertisements 120 180 4 Price of magazine 6.DM*) 4.DM*) 5 No. of a r t i c l e s on p o l i t i c s 70 25 6 No. of a r t i c l e s on ecology 1 5 7 No. of a r t i c l e s on entertainment 5 3 8 No. of a r t i c l e s on cu l tura l events 3 5 9 No. of pictures 15 15 10 No. of color pictures 10 3 11 No. of pages in magazine 350 300 *) DM: West German marks Subjects first evaluated the importance of the 11 dimensions on 7-point rating scales which ranged from 1 (unimportant) to 7 (very important). These ratings were collected in random order and interspersed with attractiveness ratings of the alternatives' features on the dimensions. Then the subjects were individually presented with the choice pairs on an information display board. While this display board always revealed the names of the dimensions by which the alternatives were described, the features of a choice pair had to be separately uncovered for every dimension. Thus, subjects had to successively request the alternatives' features on one of the dimensions until they wished to make a choice. At the beginning of every choice, subjects only saw the names of the 11 dimensions used to describe the alternatives. By opening a door on the display, the subject could then inspect a feature pair on a dimension which remained visible thereafter. After inspecting these features, the subject could request the features of another dimension. This procedure was repeated until a subject wanted to make a choice. Subjects were instructed to inspect as many feature pairs or dimensions as they liked before making a choice. The journals' names were not revealed to the subjects. The choices and the selected dimensions were recorded. Two sample protocols are shown in Table 1. Whereas all the choices were hypothetical in the first experiment, half of the subjects received a free copy of the journal they had chosen in a randomly selected pair in addition to their payment at the end of the second experiment. This was announced to the respective subjects before they made their choices. Subjects were students from the University of Heidelberg, who were paid 10 German marks per hour. Twenty—eight subjects participated in Experiment I; Experiment II had 21 subjects without consequences and 21 subjects who additionally received a copy of a chosen journal as a consequence.