A model of selection by aspects - Science Direct

Acta Psychologica North-Holland

79 (1992) 1-19

A model of selection

by aspects

J.P. Barthklemy * &ole Nationale Supbieure de.7 T&kommunications

E. Mullet I%& Pratique Accepted

June

des Hautes &de.r,

dr Bretagne, Brest. Fruncr

Paris, France

1991

A choice process model is discussed. This model retains the sequential nature of Tversky’s Elimination by Aspect (EBA) heuristics: subjects are assumed to split the set of alternatives into increasingly smaller subsets until a one-element set is obtained. It differs from EBA in the way these splits are performed. We assume that: (i) the process cannot be reduced to elimination, (ii) subjects may process several attributes at the same time, (iii) at a given level of the selection/ elimination process, the alternatives may be examined relative to several attribute groupings. The results of an experiment supporting our model are presented.

According to Simon (e.g. 1979), a human decision maker is able to exhibit rationality within the limits of his own representation of the decision situation (see also Klein 1983; Payne 1982). Several choice models, involving this concept of bounded rationality, have been put forward and tested under various conditions (Montgomery and Svenson 1976; Svenson 1983). Many models for the choice of one (or more> stimuli characterized by several attributes have been designed. These models are deterministic or probabilistic. Deterministic models primarily deal with the study of decision rules that may account for the decision process in terms of the selection of information and the integration of selected information. Non-deterministic models mainly focus on decision outcomes and generally try to account for a set of decisions rather than describing the fine processes of selection and * Requests for reprints should be sent to J.-P. Barthelemy, Ecole Nationale Telecommunications de Bretagne, BP 832, 29285 Brest cedex, France.

OOOl-6918/92/$05.00

0 1992 - Elsevier

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Publishers

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integration of information. Since this paper is concerned with the deterministic point of view, we shall emphasize these kinds of rules. In the case of a binary choice between multi-attribute alternatives these rules or models include: (a) the maximin and maximax rules (Dahlstrand and Montgomery 1984); (b) the dominance rule (Lee 1971); (cl the conjunctir>e (Coombs 1964) and the disjunctir’e rules (Dawes 1964); (dl the majority rule (May 1954; Russo and Dosher 19831, and the weighted set of dimensions rule (Huber 1979); (e) the choice by greatest attructir’eness rule (Montgomery and Svenson 1976); (f) the lexicographic rule (Fishburn 19741, the minimum difference lexicographic rule (Montgomery and Svenson 1976), and the Iexicographic semi order rule (Tversky 1969); (g) the addition of utility dqyer-ences rule (Tversky 19691, and the sequential accumulation of dqyerences rule (Aschenbrenner et al. 1984); (h) the moring basis heuristics (Mullet 1985; Barthelemy and Mullet 1986). Most of these rules arc well known. According to the dominance rule, one alternative is chosen over the other if it is better on at least one attribute and not worse on all other attributes. The weighted sets of dimensions rule is a variant of the majority rule: the decision maker divides the set of attributes into two subsets. Subset A, (A,) contains all the attributes that speak for s, (s,). These two sets are weighted and s, is chosen whenever A, has more weight than A I. According to the lexicographic rule, the chosen alternative has the highest value on an attribute judged as the most important; in the case of a tie on this attribute, the decision is based on the second most important attribute, and so on. The lexicographic semiorder rule is like the lexicographic rule with the additional assumption that for the first attribute, there is a difference threshold. If the difference between the evaluation of one alternative and the other is greater than this threshold, then the highest alternative is chosen. If not, the second attribute is used, and so on, as in the lexicographic rule (i.e., without difference thresholds). The minimum difference lexicographic rule is obtained as a generalization: each attibute is associated with a difference threshold and the differences on each attribute are lexicographitally compared to the corresponding threshold. The moving basis heuristics coordinates four types of rules: lexicographic, threshold, conjunctive. and disjunctive. It is built on the principle that the dominance rule is used as the major one and that all the other rules are only used to obtain a dominance structure, as

J. P. Barth&my,

3

E. Mullet / A model of selection by uspects

quickly as possible (Montgomery 1983). For further discussion of the model and the principles it involves, the reader is referred to Barthelemy and Mullet (1986, 1989). Here we only need to know that a given realization of the process can be summarized in a single formula, which we call a choice polynomial: L” + LF + FM4.

(1)

Here, {L), {L, F}, {F, M) are the sets of attributes examined successively by a given expert; in other words they are the successive points of view the expert uses; the exponents denote a difference threshold. The polynomial reads: If there is a difference of at least three alternative. then this alternative is chosen.

levels

in L favouring

one

Or else, If there is a difference of at least one level on L (exponent omitted in this case) and a difference of at least one level in F favouring one alternative, then this alternative is chosen. Or else, If there is a difference of at least one level on F and a difference of at least four levels in M favouring one alternative, then this alternative is chosen. Or else, there

is a non-choice.

Note that this model may be viewed as a generalization of the minimum difference lexicographic rule (e.g., L3 + F4 + M”), the lexicographic semiorder rule (e.g., L” + F + M), the lexicographic rule (e.g., L + F + M), the conjunctive rule (e.g., LF”), the strict dominance rule (LFM), and the majority rule (LF + LM + FM). Other models deal with the choice of one stimulus out of several. The most well known is the Elimination by Aspect (EBA) model (Tversky 1972a,b). In the deterministic version of this model (see Gati 1986; Payne et al. 1988; Svenson 1983) the alternatives are described by attributes; one (and only one> attribute is selected, together with a threshold value. Each alternative is then examined relative to this

attribute. Alternatives with a value on this attribute that falls below the threshold are eliminated. A second attribute with an associated threshold is then selected and the remaining alternatives are considered relative to this new attribute and threshold. This leads to a second elimination and the process continues until a single alternative (the selected one) is obtained.

Selection

by aspects and moving basis

In this article we discuss an alternative model (the selection by aspects model) that retains the sequential nature of the EBA. Here subjects split the set of alternatives into increasingly smaller subsets until a one-element set is obtained. Our model differs from the EBA in the way these splits arc made. We assume the following: (1) The process cannot be reduced to eliminations. It also involves selections as a function of circumstances (i.e. experimental design, task). (21 [Conjunctive rules]: at each level of the selection/elimination process, subjects can process several attributes at the same time (and not only one as the EBA assumes). (31 At each level of the selection/elimination process, the alternatives may be examined relative to several groupings of attributes. A concrete example may help to clarify the differences between the two models. Consider some hotels with restaurants described by several attributes in some specialized guide. These attributes are: the price of the menu, the price of the rooms, the quality of the service, the noise, the quality of the accommodation, and so on. Assume a person has to choose one of these hotels. According to EBA heuristics, this person will select an attribute, for instance the price of the menu, consider a threshold on this attribute and eliminate all the hotels that fall below this threshold on this attribute. Then a second attribute with threshold is selected and the elimination process goes on until one and only one hotel remains. In our model, the subject first examines all the alternatives under consideration and makes selections (and/or eliminations) on the basis of aspects (i.e. attribute values) considered as favourable (or unfavourable). For example, a hotel may be selected, in this first stage,

J.P. Barth&my,

E. Mullet / A model of selection by aspects

5

because its menu is cheap or because the quality of the service is very good and the rooms are cheap,. . . In the second stage the remaining alternatives are examined, with more stringent requirements. This continues until one and only one hotel remains at the end of the process. The way in which the subject proceeds may be expressed as follows: (1)Hh+B4Dh+B4H4+C6~4+C4~5, (2) H6 + B4H’ + C5D6 (3) B4H” + C4Hb + E4;ih. H, B, C, D, E are the attributes and these rules must be interpreted in the following way. In the first stage, each hotel having a value on attribute H that is at least 6 was selected, as well as the hotel whose value is at least 4 on B and 6 on D, etc. In the second stage, the number of groupings of attributes under consideration decreases, but the values of the thresholds increase. In the third stage, the fact that the value of H is at least 6 no longer guarantees selection.. . Hence, EBA is a special case of our selection by aspects model. For instance, EBA process may be expressed as follows:

(1) H’, (2) HhD5, (3) H”D5Ch. Although EBA only pre-supposes a coordinated use of two types of rules: lexicography and threshold, our model involves two other types of rules: conjunction and disjunction. Thus, it appears as an extension of the moving basis heuristics as described above to the case of choices among many alternatives.

The process A ‘polynomial’ such as H6 + B4Dh + B4H4 + C”D4 + C4H5 can be seen as an algebraic representation of the process described below (see fig. 1). Box 1 represents the subprocess of selection of one or more attributes at a given time (Montgomery’s pre-editing phase). These

Consider 1

a set of

attributes and thresholds on these attw butes

o the

corresponding

thresholds

No

f 6

Ellmlnate

Fig. 1. Selection

by aspects.

attributes and thresholds are used for the selection of stimuli. Boxes 2 and 3 show the subprocess of comparing the superiority of one stimulus over the thresholds for the corresponding attributes. If at least one aspect is lower than the corresponding threshold, another set of attributes can be taken into account (boxes 5 and 7). After several iterations, the subject selects the stimulus or he/she eliminates it (box 61.

J.P. Bartht?emy, E. Mullet / A model of selection by aspects

7

This model acts as a decision heuristic in the sense of Groner et al. (1983) and Huber (1986). It is built on the basis that the dominance principle is the major one and that all the other rules are only used to obtain (as quickly as possible) a dominance structure (Montgomery 1983). Three basic principles are involved in the model: (1) A parsimony principle. Due to his/her inability to process the whole data set, the subject extracts some subsets whose magnitudes are small enough to be compatible both with human short-range storage abilities (there is no intermediate storage in long term memory) and with human computational abilities (see Aschenbrenner and Kasubek 1978; Johnson and Payne 1985). (2) A reliability / warrantability principle. This principle operates, in some ways, as the reverse of the preceding one (De Hoog and Van de Wittenboer 1986;Payne et al. 1988). Concerned by reliability (socially as well as personally), the subject extracts from the data set a subset that is large enough and composed in such a way as to appear meaningful (evaluations on several attributes, conjunctive rules). A selection is made if and only if the evaluations are large enough (threshold rules; see Adelbratt and Montgomery 1980; Huber 1983; McAllister et al. 1979; Montgomery 1983; Ranyard and Crozier 1983). (3) A decidubility principle. Concerned with the need to achieve a choice in almost all cases, the subject extracts subsets of data in a way flexible enough to obtain a decision almost every time and on relatively short notice. This decision corresponds to minimal conflict (see Huber 1986; Klayman 1982: 39; Montgomery 1983; Svenson 1979: 106-107). Applying such a heuristic is generally consistent with a low probability of error and a small magnitude for errors that may occur (Stillwell et al. 1981). One reason for this may be that the attributes are correlated (Vicariant Process, Einhorn et al. 1979: 466). Applying this heuristic is also consistent with a high probability of context effects such as those found by Eagle (19881 with binary choices (variation of the weight of attributes according to the difference between the two objects on these attributes). Moreover it is worth noting that although the information processing is assumed to follow a flow chart, such a representation should not be considered literally. The sequence of events is surely not strictly determined. Rather, it

J. P. BartitAw~y,

E.

Mdlet / A nwdel of selection by aspects

c Eliminate

Fig. 2. A realization

of the heuristics.

corresponds to stochastic tendencies. As in the Aschenbrenner et al. (1984) model, the sequence of selecting attributes may fluctuate. Fig. 2 represents an application of the heuristics. In the first polynomial occurring in the example below {H}; {B, D}; {B, H}; (C, D}; {C, H) are the sets of attributes one subject considered successively; in other words, they are the successive points of view that the subject

J.P. Barthklemy, E. Mullet / A model

of selection by aspects

9

uses. The as are evaluations (aspects) of the stimulus on H, B, D, C. The numbers 6, 4, and 5 are the corresponding threshold values. Clearly, in this example, the model presupposes a process that includes both interdimensional and intradimensional strategies. This seems compatible with many previous observations (e.g. Bettman and Jacoby 1976; Ranyard and Crozier 1983). The polynomial: H” + B4D6 + B4H4 + C6D4 + C4H5, with the interpretation given above, can be expressed as a formula that summarizes the first step of the selection/elimination process. The whole process itself may be represented as a sequence (P,, . . . , Pm> of polynomials, such that each monom of Pi+1 is obtained by adding one or more attributes and thresholds, or by increasing degrees on some monom of P,, or by considering new conjunctions of attributes with thresholds (cf. Appendix).

Illustration

In the experiments we performed, subjects were required to select, or eliminate, some of the stimuli. The selection process was repeated as many times as the subject wished, until one and only one stimulus remained. If the deterministic version of EBA applies, it should be possible to account for selections, for each subject, on step one, with one and only one attribute. The stimuli that are selected at this first step are those that go beyond some threshold associated with the attribute in question. Moreover, it should be possible to account for the selections processed after the second step with exactly two attributes (and thresholds) used conjunctively. On the other hand, if. the process is more complex, and if our model applies, then it is impossible to account for selections, for each subject, on the basis of one, and only one, attribute. Rather, several attributes need to be considered as of the first step. Method Subjects Subjects were 15 unpaid volunteers (teachers), vacations in hotels with restaurants in France.

aged 25 to 42, who tend to spend

Material The material consisted of 36 sheets. Each described a hotel according to certain attributes. These attributes include, in addition to the name of the establishment: (A) the scale of prices of the menus (for example from FF80 to FF160); (B) the

J.P. Barthklemy, E. Mullet / A model

10

of selection by u.spects

quality/price ratio of the restaurant; (Cl the quality of the decor; (D) the scale of room prices; (El the cost of brcakfest; (F) the number of rooms; (G) the quality of service; (H) the distance from the tourist bureau; (I) the accessability of the establishmcnt; and (J) its noise level. Each of the ten attributes (from A to J) can have six values. Procedure

Subjects were read the following instructions (in French): ‘You have just arrived in an area with a major tourist attraction. You plan to stay there for some time. You go to the tourist bureau to get a list of hotels with restaurants. The list you receive is the one I will give to you now. It includes 36 hotels. Each establishment is described by: its name, file scale of prices of the menus.. and its noise level. To select one hotel that looks attractive, proceed in the following way: first, examine each sheet scparately, then put the sheets that correspond to hotels that seem acceptable into this box. Second, r-e-examine the selected sheets and put the most attractive ones into the box, etc... You may repeat these steps as often as you like.’ Three experimental conditions wcrc used. In the first, the subjects (N = 5) merely performed the above task. Then they had to reexamine the sheets corresponding to hotels selected in the first step. For each selcctcd sheet they had to give the aspects (e.g. H, A, G) leading up to their selection. In the second, the subjects (N = 5) were required, after the selection, to specify the aspects they had used. In the third, the subjects (N = 5) were required to write down, at the moment of elimination, the reasons for eliminating hotels. Our hypothesis specifically focuses on the amount and the diversity of information used, or expressed, at each step.

Principle

of data

anulysis

A simple example is sufficient to understand the way polynomials arc computed. Consider table 1. The columns represent hypothetical hotels, a to i. The letters A. B, C. D represent attributes. The numbers 1, 2, 3, 4 are the attribute values. Assume that c, d and h were selected in the first stage. All these stimuli have a high value on A in common (3, 4, 4). Is ‘monom’ A4 sufficient to explain a part of the choices? In other words: is a stimulus selected each time it has a 4 on A? The answer is YES since none of the eliminated stimuli present such a value. Do we actually need value 4, rather than value 3, on A? Here the answer is NO, since stimulus g, with

Table

1 a

b

‘

d

e

f

I:

11

I

A

I

2

3

4

I

3

B C D

2 3 4

3 4

4 I

1

3

2

2

3

‘l 2 I 3

3 3 2

1

2 4

2 4 3 1

1 4 2

1

J.P. Barthklemy, E. Mullet /A

model of selection by aspects

11

value 3 on A, was not selected. Hence monom A4 explains the choices of d and h. What about c? c has a value of 3 on A and 4 on B. Does A’B4 suffice to explain choices? Here the answer is YES. The fourth question is: do we need 4 on B? The answer is YES (since i was not selected). The fifth question is: do we need 3 on A? The answer is YES (since f was not selected). Thus, the polynomial A4 + A’B4 is sufficient to explain all the choices. This polynomial will be called an equation of the selection {c, d, h). A more formal point of view is developed in the Appendix, where this notion is defined and where a characterization of selections accepting such an equation is provided. An experimental program to compute selection equations has been written in Turbo-Pascal (cf. Barthelemy and Mullet 1987). It runs on MS-DOS compatible material. In the spirit of Tversky’s original EBA, the corresponding algorithm first searches for monoms reduced to a single attribute and as a second priority for polynomials with a minimal number of monoms. For instance assume that the program computes the polynomial: Hh + B4Dh + B4H4 + ChD4 + C4Hs. This means that: (a) There is only one dimension which is able to explain selections conjunctively with others. (b) Within this case, there is no way to explain all selections conjunctions of at most two attributes.

when it is not used with

fewer

than

5

Note that our program only computes one polynomial among many possible (however, the equation of a selection is unique when the subject has to select from the enormous set of all possible descriptions of stimuli by the attributes). But this point is irrelevant here: the fact that the program finds a polynomial with several monoms as a selection equation, and, among these, monoms with several attributes, supports the hypothesis that subjects, at a given level of the selection process, proceed with several attributes at the same time, and that at the same level of the selection process, the alternatives may be examined relative to several groupings of attributes, even if the same selection can be explained by several different polynomials. Analysis of polynomials

Table 2 presents all the equations on the first selection for the 15 subjects. For subjects 2, 9, 10, 11 the polynomial obtained is rather simple: for subjects 2, 9, 11 it is reduced to one monom (containing a single attribute for subjects 2 and 11). Subject 10 selected each stimulus with an attribute value 2 3 on B. For all other subjects the polynomials are rather complex and display strategies involving the use of conjunctive and disjunctive rules. Nevertheless these polynomials are quite easy to interpret. For instance, by simple algebra manipulation, the polynomial of subject 10 may be written: B”(E’+

G” + H” + D4H’)

+ B”F”.

It may be interpreted as: each time the quality/price ratio is at least average; and either the breakfast is very cheap, or the quality of the service is very good, or the

12 Table

2

Subject

Equation of the first selection Bh+G5+Ih+Jh+A~bi+A(‘BJ+A~Ch+B311S+BJH’+C~J4+... B’ B6+J”+A’B5+ASFh+B4C’+BJJ’+CJHh A3J”+B3Ch+BhCS+BJJi+DhE?+E5Hh AhB’+AJG”+BiCZ+BZGh+B’III’+EJJh F6+AhB’+A’Ch+A5Fi+B’C’+BJC’ Hh + BJD” + ChD” + B”HJ + C”H’ Gh+Jh+AJG~+BhC~+BSE3+BZIlh B3H’ B3E” + B’FI + B7C;h + B3H’ + B3D”H 1

distance from the tourist bureau is short, or this distance is average, but the rooms are quite cheap, then the establishment is retained in step one. The hotel is also retained when the quality/price ratio is good and there arc enough rooms.

Table 3 Subject 1 2 3 4 5

Equation of the second selection B”+Gh+AsBS+AhBJ+A515+B’Gi+B4HJ+CiJi D’ + B”H? + B7D’J3 B” + A’B’ + B”C’ + B’J’ B4Ch + BhC’ + BJ5 + DhE3 BhC’ + B5F4 + B 3Hh + D”E’ + E’Jh

6 7 8 9 10

AhB”+A?Ch+BSCS+B5H~+B~JS+CCjFh+CIHh Hh +B”HSC’Dh

11 12 13 14 15

A7J”+A4JS+B”Dh+B’Eh+C4D5 BhCS+BsH4 +E4Jh +G”J’

G” +B’H’ + E”J” B?Hh +B4H5 +,-XJs BlEh+BiHh+B4Hs+C~JS+B3H3J?

ASE~+B~C?+B?“~+B”J’+C”J’+A~C~D’+B~H~J~

B”HS +D’I” +GhH’ J”+ASBh+A(,D3+A4JS+ghc~+RiFZ+BSJj+CZJi+GhHl+ A’B3D3

B, I B, C. J B, C, G, J

S4 s5

S6

G, J (3)A. B, C. I (2) B, C, G (4) 1 B,I B, G (2) A C, G (2) B, C (4) J A B. C. G (2) B, C. J (2) C, G, J A B, C, B, C, G B, G B, C, G, I, J A, B, C, G, I A.B,G A B, C, D, G, I B, C, I A, B, G, I B, D, H B, F, G. I, J A, B, C, G, H, I B>G, H A, B, Q G, H, I B, C, G, J C, G, H, I B, C, G, H. J A, B, C, D. G, H. I, J

B, I(5) B (21) B, D (6) I, J (4) A. B, I B. G, I G, H A, B, F, I B. F, G, I

G (4) G, I(4) C, J (3) J (2) B

B, G (6)

s3

s2

Sl

Table 4

B, G (4) F, H A, B, G G, H, I F, I, J B, F, H A, B. D F, G, H G, H, I, J E, H, I, J

Sl

(3b)

G (2) B, D, G (2) G, H G, J C, G B, D, G, H C, D, G, H B, C, G, J B, C, D, G, J B, D, G. H. J

H, I(2)

S8

SlO

B, D, I D, 1, J A, G, H B, D, G, H B, D, E, J B, H, I, J

B, H, I (2) D, J H H, I G, H B, D H, J B, H, J

B. G

s9

Compensatory cffccts wcrc also prcscnt. For aubjcct 4, for instance. attributes B and C partially compcnsatc for effects: BJC” or B”C’. Suhjcct I shows the greatest number of simple monoms (i.e. monoms with a single attribute). The ten monoms reported in the table explain 21 selections (respectively 3, 7, I, 3. I, I, I, 2, I, I selections). In particular monoms with two attributes explain a third of the selections. For the whole set of IS subjects the selections explained by simples monoms are by far a minority. Table 3 presents equations for the second sclcctions. For subjects 2 and I I, the polynomials become more complex. In the first step, subject 2 sclcctcd all the stimuli with an average lcvcl on B. Now this subject bccomcs much more demanding; either an average level on B does not suffice alone any more (B’DJJ3), or the evaluation on B has to bc better (BJH’). Further a new monom (D’) S.Y~Z.Sto appear. All the hotels with cheap rooms (Di) have an avcragc quality/price ratio (B3). Thus, D5 may bc read as B”D’. A similar situation occurs frcqucntly for the polynomials in table 2. In the first step, subject Y seemed to apply a strict conjunctive rule. Now this subject exhibits disjunctive rules (BJHS + C”J’) together with compensatory effects (B3H” + BJHL). Subject 1 again shows the greatest number of simple monoms. Each monom explains respectively 3, 3. I, I. 1, 1. 3. 2 sclcctions. A 11i11ysis o/ jt1.sf+cufi0tr.s

Table 4 gives rationales for selection as stated by the subjects cithcr at the end of the cxpcrimcnt (3a). .or during the cxpcrimcnt (3b). In each cast the majority of subjects gave multiple, not ncccssarily overlapping, rationales. It is worth noting that subject 2, who previously appeared as an unidimensional subject is also the subject who gives the most unidimensional rationales (8, 21 times). Similar remarks apply to subject 9.

Discussion Right from the first step of the selection process, recourse to terms with several attributes (mostly two) is needed to account for the behaviour of a majority of subjects, despite the fact that data processing tends to minimize the number of attributes. Moreover, for a majority of subjects, right from the first step, it is necessary to consider shifts in points of view (they are indicated by the monoms occurring in an equation). At the second step, the characteristics of the obtained polynomials remain the same. Furthermore, when writing motives for each selection (elimination), subjects spontaneously consider such shifts of point of view and generally mention several attributes each time. It is worth noting that there is no difference between the structures of the statements whether made during the selection process or a posteriori.

The EBA model apparently fails to account for the selection behaviour of a majority of subjects. Only two subjects seem to implement such a simple model on the first step. Accounting for all other subjects calls for a more complex model at each selection level in which both conjunctive and disjunctive rules occur. Given the way polynomials computation has been programmed, and except for two subjects there is no way to account for all the selections and all the eliminations with a single attribute Generally, subjects deal disjunctively with many (groupings of) attributes. This evidence runs counter the deterministic version of EBA heuristics. Moreover, except the aforementioned subjects, it is impossible to explain all the selections or eliminations with a disjunctive one dimensional model: conjunctions of two attributes are needed by all other subjects. However, just a few attributes occur in each conjunction (2 and exceptionally 3). Recall however that the program gives priority to small monoms. The alternative model put forward here provides an explanation of subjects’ selection behaviour (and their justifications). Presented with a varied set of options, and asked to process a first selection, the subjects do not seem to follow a fixed selection/elimination criterion. Initially they probably examine the strong points (and the weak points) of each option. If a given option appears to be a feasible candidate, then it is selected. This does not mean that subjects’ behaviour is solely determined by the design of the data. A particular attribute is not necessarily significant for a particular subject. Moreover, a high value (low value) for one attribute does not imply the selection (elimination) of the corresponding option even when this attribute seems significant to the subject. Rather there are interactions between the characteristics of the subject (order of attractiveness of the attributes) and the characteristics of the task (observed designs). An option may be selected because it has an attractive value on an ‘important’ attribute. But another option could also be selected, despite the fact that its value may be low on this attribute, because this option has a system of high values, with compelling attractiveness. In the first case, the subject forces the structure of the process. In the second case the design of data appealed to the subject. As a result, the global behaviour is quite complex, but may be taken into account in the model. This model is able to account for both shifts ill points of view (disjunctions), compensatory effects and conjunctive effects.

However, this flexible model is not irrefutable: two subjects clearly demonstrate the use of a fixed, permanent criterion at the first step of the selection process.

Appendix

Selection polynomials:

A formal approach

Consider an expert faced with the following task: select a subset from a stimulus set S = (s,, . , s,~}.described by attributes X,, , X,,, taking values on ordinal scales. The data may be summarized in a stimulus matrix Z: having rows corresponding to to X,. . X,,, the coefficient r,, of’ the matrix s ,) ) s,,. and columns corresponding being the rank of stimulus s, with respect to attribute X,. The stimuli arc point wise ordered: p.r,,