Acta Psychologica 76 (1991) 165-176

North-Holland 165

Prediction of preferences for and choices between verballv and numericallv

J

described altekatives *

Erik Lindberg and Tommy G5rling

Henry Montgomery University of Giiteborg, Gateborg, Sweden

Accepted June 1990

In order to investigate whether the format (verbal or numerical) of the information presented about different options affects the predictability of preference judgments and choices, a number of

hypothetical housing alternatives were described in terms of six attribute dimensions to 36 adult

subjects. The descriptions were either purely verbal, purely numerical, or mixed verbal and

numerical. Preferences and choices were predicted by means of a combined multi-attribute utility and expectancy-value model. It was found that the predictions of the preferences were more

successful when the most important attributes were described numerically than when those

attributes were described verbally. Regression analyses of aggregated data further showed that

numerically described attributes tended to carry a greater weight for the prediction of both

preferences and choices than did verbally described attributes in the mixed numerical and verbal

descriptions. These findings suggest that the higher precision conveyed by numerical descriptions

may have helped the subjects to evaluate different options in a consistent manner.

Studies of preferences and choices have almost invariably used quantitative information to characterize the attributes of different decision alternatives. However, only very rarely has any closer atten-

* The present study was financially supported by a grant from the Swedish Council for Building Research. The authors thank Jiirgen Garvill and Charles Vlek for comments on earlier versions of

the manuscript and Ms. Karin Erngrund for assistance in collecting the data.

Correspondence address: E. Lindberg, Department of Psychology. University of Umel, Umea. S-901 87, Sweden.

OOOl-6918/91/$03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)

166 E. Lindberg et al. / Verbal us. numerical information

tion been paid to possible effects of different ways of expressing such quantitative information about attributes. In one study, Huber (1980) used a process-tracing technique and found more attribute-wise com- parisons of alternatives in a choice set when information about attri- butes was presented numerically than when it was expressed in a verbal format. Another example is a study by Svenson and Karlsson (1986) in which verbal and numerical descriptions of the same set of decision alternatives were compared. They found generally weak effects of mode of presentation on judged attractiveness of the alternatives, but for poor alternatives numerical information on the most important attri- bute tended to lead to more negative evaluations.

A number of studies by Wallsten and others (e.g., Budescu et al. 1988; Wallsten et al. 1988) have demonstrated effects of expressing probabilities in gambling situations in a numerical or graphical format versus a verbal format. Their results indicate that verbally expressed probabilities may lead to less optimal decision behavior than the other modes of presentation, and that the vagueness of verbal probability expressions may vary across both probability levels and subjects.

There is thus some evidence suggesting that the format in which information about alternatives is presented may affect both the deci- sion-making process and its outcome. This, in turn, should have im- portant consequences for attempts to model and predict preferences for and choices among multi-attribute options. That this actually may be the case was suggested by the finding of Lindberg et al. (1988, 1989a) that the predictive performance of a combined multi-attribute utility and expectancy-value model seemed to differ depending on whether information was presented in a purely verbal or a mixed verbal and numerical format. It is, however, not possible to base any firm conclu- sions regarding the role of the format of the presented information on the results of those studies, since they did not vary the format of the information for the same subjects and alternatives. The aim of the present study was to investigate more systematically the effects of numerical and verbal information format on the possibility to predict preferences and choices.

The predictions of preferences and choices in the studies by Lind- berg et al. (1988, 1989a) were based on the assumption, derived from Multi-Attribute Utility Theory (MAUT) (e.g., Keeney and Raiffa 1976) that people’s evaluations of a given alternative are determined by a combination of their evaluations of its different attributes. It was also

E. Lindberg et al. / Verbal US. numerical information 167

assumed that a person’s evaluation of the particular level of each attribute is determined by (a) what effects he/she believes it to have on his/her possibilities to attain various goals, and (b) his/her evaluations of those goals. The latter assumptions are shared with the expectancy- value model which has been frequently used in the study of motivation, attitudes, and actions (Ajzen and Fishbein 1980; Atkinson and Birch 1970, 1974; Feather 1982). The goals used in the studies by Lindberg et al. (1988, 1989a) were various life values (Rokeach 1970, 1973), defined as desirable end-states which the individual strives to attain in his/her life (e.g. freedom, happiness, and security).

The above assumptions are formally expressed in the following model:

E All, = bC bAttr,,, E,/CE, + a. i k k

E A,t represents the evaluation of alternative i; pAttr,,, is the extent to which the particular level of attribute j for that alternative is believed to facilitate the attainment of life value k (or counteract it, in which case p assumes a negative value); E, is the evaluation of life value k; b and a are arbitrary scale constants. The first summation in eq. (1) thus represents the MAU component of the model whereas the follow- ing part specifies how the utility of each attribute is arrived at.

The predictions of preference ratings and choices by means of eq. (1) were somewhat more successful in the study by Lindberg et al. (1988) in which all attributes of the different options were described verbally, than in their subsequent study (Lindberg et al. 1989a) in which two thirds of the attributes were given numerical descriptions for all op- tions. A possible reason for this difference between the results of the two studies could be that since numerical descriptions of attributes convey a higher degree of precision than verbal descriptions (cf. Budescu et al. 1988) they may be perceived to be more authoritative than the latter. As a consequence, when some attributes are described verbally and others numerically, the latter may receive greater weights than those specified by the simple additive rule underlying eq. (1).

If numerically presented attributes receive greater weights than ver- bally presented ones, then the relative importance of different attri- butes for preferences and choices may change depending on the format of the information presented. This possibility was tested in the present

168 E. Lindberg et al. / Verbal OS. numerical informatmn

study by using mixed verbal and numerical descriptions with each attribute being given a verbal and a numerical definition for different descriptions of the same alternative. In addition, purely verbal and purely numerical descriptions of the same alternatives were used in order to investigate whether presenting all attributes in the same format would enhance the predictive performance of eq. (1) (by making the assumption about additivity across attributes underlying this model more tenable) and whether the verbal and numerical descriptions differ in this respect. It is for instance possible that the larger precision conveyed by the numerical descriptions could make it easier for the subjects to behave in a consistent manner towards the alternatives and thereby increase predictability.

Method

Materials

Like in the studies by Lindberg et al. (1988, 1989a), the materials were hypothetical housing alternatives. Six of the twelve housing attributes used in the previous studies were employed in the present study as well. These attributes, which were selected because they could easily be described in either a verbal or a numerical format, fall into two sub-categories: (a) intrinsic attributes of the dwelling unit itself (cost, size, and standard of in-home equipment), and (b) location attributes (distance to work, down- town, and recreational facilities). For each attribute, four verbal and four numerical levels were constructed. The numerical definitions of the attribute levels were selected so that in most cases they corresponded to what the subjects in the study by Lindberg et al. (1988) had reported to be the numerical equivalents of the same verbal descrip- tions as those used in the present study. The purpose when choosing the numerical attribute levels was not to achieve a perfect match to the verbal levels, but rather to obtain levels which would make it possible to construct a set of fairly realistic alternatives. The different levels of the attributes used in the present study are shown in table 1 below.

Twelve different hypothetical housing alternatives were constructed by combining different levels of the six attributes. Across alternatives, the most and least attractive levels occurred twice and the intermediate levels occurred four times for all attributes. For each of the twelve alternatives, four different descriptions were given: (a) verbal descriptions of both intrinsic and location attributes, (b) verbal descriptions of intrinsic attributes and numerical descriptions of location attributes, (c) numerical descriptions of intrinsic attributes and verbal descriptions of location attributes, and (d) numerical descriptions of both intrinsic and location attributes.

Thirty-six choice problems were constructed, each containing four alternatives. Each of the four types of descriptions occurred once in each problem. For each alternative,

E. Lindberg et al. / Verbal us. numerical information 169

each of the four descriptions occurred three times across the different problems. Across the four alternatives in each choice problem, at least three of the four possible levels were represented for each attribute. Using choice sets composed of all four types of descriptions, rather than using only one type of description for all alternatives in each set, has the disadvantage of not making it possible to evaluate the effects of the different descriptions on the performance of eq. (1) for individual choices. It is necessary, however, to use different types of descriptions in the same choice problem in order to detect whether the probability with which an alternative is chosen is affected by the way in which it is described. Since this was a major purpose of the present study, and since the effects of the different descriptions on the performance of eq. (1) could still be evaluated for preference ratings of the different alternatives, the use of different descriptions in each choice problem was preferred.

The 12 life values (also shown in table 1) included in the study in order to compute predicted evaluations according to eq. (1) were the same as those used by Lindberg et al. (1988, 1989a). They were originally selected among items used by Garling et al. (1989) Montgomery (1984) and Rokeach (1973).

Procedure

A booklet consisting of two major parts was administered to the subjects who served individually or a few at a time. The two parts were filled out in two different sessions separated by 5-10 days. Each session lasted for about 1: hour, and the experimenter stayed in the room whilst the subjects filled out the booklet in order to answer any questions which they might have. When filling out the booklet the subjects had access to a list of all attributes and life values which included explanations of the latter items.

In the first session; the first page of the booklet gave a general description of the purpose of the study. On the following page, the subjects answered questions about their age, sex, marital status, and present housing conditions. In order to obtain information on the degree of calibration between the verbal and numerical attribute descriptions the subjects thereafter rated, on 13-point scales ranging from -6 to +6, how good or bad they perceived the different levels of the housing attributes to be. The same type of ratings were also made for the different life values. The endpoints of the scales were defined as ‘extremely bad’ (- 6) and ‘extremely good’ ( + 6), respectively. Three intermediate scale values were defined as ‘rather bad’ (- 3), ‘neither good nor bad’ (0), and ‘rather good’ (+3), respectively. Separate ratings were given for the verbal and numerical descriptions of the different attribute levels. Six items were presented on each page, and the order between the pages was randomized individually for each subject.

The subjects then answered questions about their beliefs regarding the consequences of the different attribute levels for the attainment of the 12 life values. On each page, one level of an attribute was given in either verbal or numerical format, and the subject rated how much it facilitated or counteracted the attainment of each value. The same type of 13-point scales (ranging from ‘counteracts very much’ to ‘facilitates very much’ with three intermediate labels) were used for these ratings. This part of the booklet consisted of 48 pages (6 attributes X 4 levels x 2 descriptions) in individually rando- mized order.

170 E. Lmdberg et al. / Verbal vs. numerical information

In the second major part of the booklet, which was filled out in the second session, each of the four descriptions of the 12 housing alternatives were presented on separate pages and the subjects were required to estimate how good or bad they perceived each described alternative to be. These estimates were to be given as numbers in the range O-100, the endpoints representing extremely bad and good alternatives, respectively. The order between the pages was randomized individually for each subject with the restriction that different descriptions of the same housing alternatives never occurred on two consecutive pages. The 36 choice problems were also presented on separate pages in different random orders for each subject. The four alternatives on each page were labeled A to D, and the subject indicated which one he/she thought was the best by writing down the corresponding letter. The order between choices and ratings was counterbalanced across subjects.

Subjects

Thirty-six students attending a college for adults in Umel (80,000 inhabitants) were paid the equivalent of $15 each for their participation in the study. Twelve subjects (six women and six men) were sampled from each of three age groups (20-29, 30-39, and 40%49-year-olds, M = 23.9, 33.2, and 43,3 years, and SD = 1.2, 1.3, and 2.4 years, respectively).

Results

The mean evaluations of the different levels of the attributes are given in table 1. The mean rated attractiveness of the four different levels was somewhat higher for the numerical descriptions than for the verbal ones, and the differentiation of the attribute levels was less for the numerical descriptions than for the verbal ones. The evaluations of the life values, also presented in table 1, were quite similar to those obtained by Lindberg et al. (1989a).

Preferences for alternatives

The subjects’ beliefs about the effects of the attribute levels on the life values, and their evaluations of those values, were used in order to calculate predicted preferences according to eq. (1) for each subject and type of description. The mean correlations between predicted and observed preferences are given in table 2. These correlations were transformed to Fisher’s I and subjected to an ANOVA (age X sex X type of description, with repeated measures on the last factor).

The main effect of type of description was significant, F(3, 90) = 3.70 p < 0.05. A post-hoc comparison by means of ScheffC’s method showed that the correlations obtained when the intrinsic housing attributes were described numerically were reliably higher than those obtained when these attributes were given verbal descriptions ( p < 0.05).

The correlation between the predicted preferences and the observed ones was also

E. Lindberg et al. / Verbal us. numerical information 171

Table 1 Mean evaluations of attribute levels and life values.

Attribute Level M Level M Level M Level M

Verbal descriptions

Intrinsic attributes cost Very low 5.14 Rather low 5.22 Rather high -4.19 Very high - 5.03 Size Very large 3.14 Rather large 4.00 Rather small - 3.81 Very small - 4.53 Standard Very high 2.75 Rather high 3.63 Rather low - 2.83 Very low -4.19

Location (distance) Downtown Very short 0.06 Rather short 1.94 Rather long - 1.58 Very long - 1.83 Recreation Very short 3.25 Rather short 3.42 Rather long -2.63 Very long - 3.56 Work Very short 2.42 Rather short 3.72 Rather long - 3.03 Very long - 4.33

Numerical descriptions

Intrinsic attributes cost 1000 SEK/ 4.78 1300 SEK/ 4.19 1900 SEK/

month month month Size 4 rooms + 2.42 3 rooms + 0.86 2 rooms +

kitchen kitchen kitchen Standard Built in 1985 1.44 Built in 1970 1.17 Built in 1955

Location (distance) Downtown f km 0.92 1; km 1.58 6 km

Recreation f km 3.25 lf km 1.86 6 km

Work fkm 2.86 lf km 1.94 6 km

1.31 2700 SEK/ -2.78 month

-1.14 1 room+ -4.50 kitchen

- 0.36 Built in 1940 - 0.89

1.06 15 km - 0.75

-0.97 15 km - 2.78

-0.08 15 km - 2.50

Life values M

Health 5.97 Family 5.72 Security 5.69 Inner harmony 5.64 Happiness 5.58 Togetherness 5.44

Life values M

Excitement 5.14 Freedom 5.08 Leisure 5.06 Pleasure 5.03 Money 4.86 Comfort 3.53

computed for data aggregated across the whole sample of subjects. This raised the correlation to 0.909. The aggregated data were finally subjected to multiple regression analyses in order to identify the attributes which contributed to the predictions for the

Table 2 Mean correlations between predicted and observed preferences for different types of attribute descriptions.

Attribute descriptions r Attribute descriptions r

Intrinsic verbal-location verbal 0.586 Intrinsic numerical-Location verbal 0.666 Intrinsic verbal-Location numerical 0.596 Intrinsic numerical-Location numerical 0.694

172 E. L,indberg et cd. / Verhul us. numer~al informatron

Table 3

Contrihutiona of different types of attributes to predictions of preferences (contributions to R*).

Attribute descriptions

Intrinsic verb&Location verbal

Intrinsic verbal-Location numerical

Intrinsic numerical-Location verbal

Intrinsic numerical-Location numerical

Intrinsic attributes

0.000

0.222

0.950

0.979

Location attributes

0.609

0.743

0.025

0.000

different types of descriptions. As shown in table 3, the verbally described attributes contributed less to the predictions than did the numerically described ones. The squared multiple correlations were high in all cases except when both the intrinsic and location attributes were described verbally. When the intrinsic attributes were de- scribed numerically, size and cost contributed most to the predictions, whereas distance to recreation and work contributed most when the intrinsic attributes were described verbally.

The choices were predicted by computing for each subject and choice problem a predicted evaluation of each housing alternative according to eq. (1). In addition, the preference ratings of the alternatives were used in order to predict each choice. A choice was considered correctly predicted if the predicted evaluation of (or the preference for) the alternative which was chosen was higher than that of all other alternatives in the same choice problem. The mean proportions correct predictions were 0.663 and 0.575 for the preferences and eq. (1) respectively.

For data aggregated across the whole sample of subjects, product moment correla- tions were computed between the two predictors and the observed proportions of choices of each alternatives. The correlations obtained were 0.899 and 0.781 for the

preferences and eq. (1). respectively. The aggregated data were also subjected to multiple regression analyses in order to identify the attributes which contributed to the predictions for eq. (1). Since a choice proportion across subjects could be obtained for each alternative in each choice problem, it was possible to carry out separate analyses for each type of description in the same way as for the preferences. Table 4 shows the results of these analyses. Except for the fact that the squared multiple correlations were

Table 4 Contributions of different types of attributes to predictions of choices (contributions to R*).

PIttribute descriptions Intrinsic attributes Location attributes

Intrinsic verbal-Location verbal 0.000 0.571

Intrinsic verbal-Location numerical 0.072 0.692

Intrinsic numericalPLocation verbal 0.770 0.000 Intrinsic numerical-Location numerical 0.872 0.000

E. Lindberg et al. / Verbal vs. numerical information 173

somewhat lower in the case of the choices, the results were very similar to those obtained for the preferences (see table 3 above). Thus, verbally described attributes tended to contribute less to the predictions than numerically described ones. Size and cost contributed most to the predictions when the intrinsic attributes were described numerically, whereas the location attributes contributed most when the intrinsic attributes were given verbal descriptions.

Discussion

The present study has shown clear effects of the format (verbal or numerical) in which different attributes of a multi-attribute option are presented on the predictability of preference judgments and choices. Two types of effects were observed. First, the relative importance of different attributes for the prediction of preferences and choices was found to vary depending on whether the attributes were described verbally or numerically. Second, the predictability of the preference judgments was found to be higher for numerical than for verbal attribute descriptions.

The multiple regression analyses performed on the group data in order to identify the attributes which contributed to the predictions of the preference ratings and choices for eq. 1 showed that numerically described attributes generally contributed more to the predictions than did verbally described ones. This finding supports the notion that when both verbal and numerical information is available about the same alternative, the latter type of information may become more salient than the former. One reason for this could be that the numerical information, being more exact than the verbal information, may be conceived of as having a higher probability of being a correct descrip- tion of the alternative and may therefore receive a greater weight.

It should be noted that the greater impact of numerically described attributes on the prediction of preferences and choices is not likely to be an artefact attributable to the less than perfect calibration of the verbal and numerical attribute levels in the present study. This conten- tion is based on the assumption that attributes which are perceived to a have a wider range should be expected to have a greater impact on the predictions than attributes with a narrower range. The extreme case is of course when all alternatives have exactly the same level on an attribute, in which case that attribute would contribute nothing at all to the prediction of the evaluations of the alternatives. Perceived dif-

174 E. Lindberg et al. / Verbal us. numerical information

ferences in the ranges of verbally and numerically described attributes can however hardly explain the present results since they were largely in the opposite direction, that is, the evaluations of the different levels of the attributes were less clearly differentiated for the numerical descriptions than for the verbal ones. An interesting parallel can be drawn between the present finding that verbal descriptions were given higher evaluations for good attribute levels, and numerical descriptions were given less negative evaluations for bad attribute levels, and the results of Budescu et al. (1988) who found that verbally expressed probabilities were preferred when gambles were phrased in terms of probability of winning, whereas numerical probabilities were preferred in gambles framed in terms of probability of losing.

A possible reason for the finding that numerical descriptions of the intrinsic attributes (cost, size, and standard) yielded more successful predictions of the preferences than did verbal descriptions of those attributes could be that verbal information is more open to subjective interpretations which may vary from one alternative to another, whereas numerical information may facilitate behaving in a consistent manner towards different alternatives. The fact that this superiority for numeri- cal information was observed mainly for the intrinsic attributes is probably due to those attributes being more important for the evalua- tions than are location attributes (cf. Lindberg et al. 1988, 1989a). It is also possible that the effects of the location attributes on preferences and choices are not a direct function of distance per se but are mediated by perceived effects on for instance travel time. In that case, expressing distances numerically rather than verbally may reduce un- certainty to a lesser extent than when intrinsic attributes are given numerical descriptions.

The higher predictability of purely verbal descriptions as compared to mixed verbal and numerical ones found by Lindberg et al. (1988, 1989a) was not obtained in the present study. This could of course be due to the different subject samples used in those studies, but the fact that both studies demonstrated that eq. (1) seems to work about equally well across substantial variations in subjective belief-value structures renders this interpretation less credible. A more likely ex- planation could be that the present study used only half as many attributes as the previous ones. If numerically described attributes receive greater weights than specified by the additive rule underlying eq. (l), then predictability might decrease as the number of attributes

E. Lindberg et al. / Verbal us. numerical information 175

increases for mixed verbal and numerical descriptions. Additional research is needed in order to further explore the effects of different proportions of verbally and numerically described attributes for op- tions varying in total number of attributes.

The present results have important bearings on some current lines of research on preference judgments and choices. First, choices have often been found to be more difficult to predict by means of additive models like eq. (1) than have preference judgments. One explanation suggested for this finding is that choices can be assumed to pose greater informa- tion processing demands than preference ratings, which, in turn, may make the subject more prone to adopt simplifying heuristics which reduce the requirements of the task by for instance taking into account only the attributes and/or life values perceived to be the most im- portant ones (Aschenbrenner et al. 1984; Lindberg et al. 1989b; Montgomery 1983; Thorngate 1980). This line of reasoning is also compatible with the ‘prominence hypothesis’, which states that one tends to focus more on the most important attribute in a choice task than in a judgment task (Tversky et al. 1988; see also Slavic 1975). The results of the present study suggest that the format (numerical or verbal) of the presented information may be an important factor contributing to the perceived importance or prominence of different attributes.

Another line of research for which the present results are relevant is work done on so-called dominance structuring in choice tasks (Mont- gomery 1983; Montgomery and Svenson 1983). Briefly, dominance structuring refers to a decision maker’s attempts to bolster a decision by emphasizing and de-emphasizing attribute dimensions in such a way that the alternative finally chosen is not seen as worse than any of the other candidates in any relevant respect and as better than all others in at least some respect. If, as suggested by the present results, verbal descriptions of attributes are more likely to be interpreted differently on different occasions than are numerical descriptions, then a domi- nance structure may be easier to achieve with verbally described stimuli than with numerically described ones.

References

Ajzen, I and M. Fishbein, 1980. Understanding attributes and predicting social behavior. En- glewood Cliffs, NJ: Prentice-Hall.

Aschenbrenner. K.M., D. Albert and F. Schmalhofer. 1984. Stochastic choice heuristics. Acta Psychologica 56. 153-166.

Atkinson, J.W. and D. Birch, 1970. The dynamics of action. New York: Wiley.

Atkinson. J.W. and D. Birch, 1974. ‘The dynamics of achievement-oriented activity’. In: J.W.

Atkinson and J.O. Raynor (eds.). Motivation and achievement. Washington, DC: Winston. pp.

271-326.

Budescu, D.V., S. Weinberg and T.S. Wallsten, 1988. Decisions based on numerically and verbally

expressed uncertainties. Journal of Experimental Psychology: Human Perception and Perfor- mance 14, 281-294.

Feather, N.T. (ed.), 1982. Expectations and actions: expectancy-value models in psychology. Hillsdale. NJ: Erlbaum.

Garling, T., E. Lindberg and Montgomery. H. 1989. ‘Beliefs about attainment of life satisfaction

as determinants of preferences for everyday activities’. In: K. Grunert and F. Glander (eds.),

Understanding economic behavior. Dordrecht: Kluwer. pp. 3346.

Huber. O., 1980. The influence of some task variables on cognitive operations in an information-

processing decision mode. Acta Psychologica 45. 1877196.

Keeney, R.L. and H. Raiffa, 1976. Decisions with multiple objectives: Preferences and value

tradeoffs. New York: Wiley.

Lindberg. E., T. Garling and H. Montgomery, 1988. People’s beliefs and values as determinants of housing preferences and simulated choices. Scandinavian Housing and Planning Research 5,

181-197.

Lindberg, E.. T. GPrling and H. Montgomery, 1989a. Belief-value structures as determinants of

consumer behaviour: A study of housing preferences and choices. Journal of Consumer Policy

12.119-137.

Lindberg, E.. T. Garling and H. Montgomery, 1989b. Differential predictability of preferences and choices. Journal of Behavioral Decision Making 2, 205-219.

Montgomery, H., 1983. ‘Decision rules and the search for a dominance structure: Towards a

process model of decision making’. In: P.C. Humphreys. 0. Svenson and A. VBri (eds.), Analyzing and aiding decision processes. Amsterdam: North-Holland and Budapest: Academic

Press Hungary. pp. 343-369.

Montgomery, H., 1984. Cognitive and affective aspects of life values as determinants of well

being: A pilot study (Goteborg Psychological Reports, 14:3). University of Giiteborg. Depart-

ment of Psychology, Goteborg.

Montgomery, H. and 0. Svenson. 1983. ‘A think aloud study of dominance structuring in decision

processes’. In: R. Tietz (ed.), Aspiration levels in bargaining and economic decision making.

Berlin: Springer. pp. 366-383.

Rokeach, M., 1970. Beliefs, attitudes. and values. San Francisco. CA: Jossey-Bass. Rokeach, M., 1973. The nature of human values. New York: Free Press.

Slavic. P., 1975. Choice between equally valued alternatives. Journal of Experimental Psychology:

Human Perception and Performance 1, 280-287.

Svenson, 0. and G. Karlsson, 1986. Attractiveness of decision alternatives characterized by

numerical and non-numerical information. Scandinavian Journal of Psychology 27. 74-84.

Thorngate, W., 1980. Efficient decision heuristics. Behavioral Science 25. 2199225.

Tversky, A.. S. Sattath and P. Slavic. 1988. Contingent weighting in judgement and choice.

Psychological Review 95, 371-384.

Wallsten, T.S., D.V. Budescu and I. Erev, 1988. Understanding and using linguistic uncertainties. Acta Psychologica 68, 39952.