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Does Irrelevant Information Play a Role in Judgment?
Boicho Kokinov ([email protected])12
Penka Hristova ([email protected])1
Georgi Petkov ([email protected])1
1Central and East European Center for Cognitive Science, Department of Cognitive Science and Psychology, New Bulgarian University, 21 Montevideo Street 2Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, bl.8 Abstract
category. He believes individuals have their “ideal points”and therefore judging a stimulus can be described as This paper presents an unusual prediction made by the comparing it to this standard and measuring the distance DUAL-based model of judgment JUDGEMAP and its toward it. The Adaptation Level Theory (Helson, 1964) falls verification. The model is shortly presented as well as the into the same category, however, here the standard simulation data obtained with it. These data predict that (adaptation level) is changed depending on context. Finally, people will use the information on an irrelevant dimension the Norm Theory (Kahneman & Miller, 1986) follows a when judging another dimension. This prediction is thentested in a psychological experiment and confirmed.
similar approach, however, the standard here is called“norm” and what is more important is that this norm is Introduction
constructed on the spot rather than retrieved from long-termmemory. A comparison set is constructed in working Suppose that you are judging how tall a person is. Do you memory consisting of known exemplars and its norm is expect that the color of his or her eyes will play a role in computed. Thus all three theories can be described as that process? Or suppose you are judging the quantity of oil relying on comparison of the target stimulus with a standard in the bottle you are buying, do you expect that the font (Figure 1), but they differ in the degree to which they used on its label will have an effect? Finally, suppose you subscribe to the constructivist approach toward this are judging the length of a given line segment. Do you expect that the color of the line will make a difference? Both our intuition and the theories of judgment would answer these questions negatively. Basically they wouldassume that when judging length we ignore all irrelevantfeatures (including color) and only physical length plays arole. Of course, many other factors, like order of presentation and context, may play a role, but only thelength of the lines will take part in the judgment.
This paper is challenging this assumption of standard theories of judgment and is trying to answer the aboveseemingly surprisingly to show that all features (including theirrelevant ones) do matter or more precisely they may matter Figure 1. Judgment as comparison with a standard.
Judgment as classification task. Within this approach
Approaches to Judgment
the comparison set is subdivided into subcategories each of There are a number of theories of judgment and a few them corresponding to a judgment label (or scale element) running models. Most of the theories originate from and the target stimulus is classified within one of these psychophysics and are mathematical in their nature; they do subcategories. The Range-Frequency Theory (Parduci, 1965, not describe the process of judgment, but only characterize 1974) postulates the constraints which should be met by the end result. Since we are interested in describing the such category subdivision: the range of value variation process of judgment we will briefly outline only the main within all subcategories should be about the same, and the approaches proposed so far in that direction.
number of examples in all subcategories should be about the Judgment as measuring similarity/dissimilarity with a
same. The Theory of Criterion Setting (Treisman & standard. The classical ideal point approach proposed by
Williams, 1984, Treisman, 1985) is a process model that Coombs (1964, Wedell & Pettibone, 1999) falls into this explains how dynamically we change the boundaries of thesubcategories. Finally, the ANCHOR model (Petrov & Anderson, 2000, in press) describes the process of learning DUAL-Based Model of Judgment
of these subcategories and solves the classification task bycomparing the target stimulus to the prototypes of each The current model – JUDGEMAP (Judgment as Mapping) – subcategory, these prototypes are supposed to be hold in is based on a general cognitive architecture – DUAL long-term memory and are called anchors (Figure 2). The (Kokinov, 1994b, 1994c). This architecture is a hybrid comparison set represented by the set of anchors is (symbolic/connectionist) one and is explicitly designed to model context-sensitivity of human cognition. It is basedon decentralized representations of concepts, objects, andepisodes and parallel emergent computations.
The AMBR1 (Kokinov, 1988, 1994a) and AMBR2 (Kokinov, 1998, Kokinov & Petrov, 2001) models are built on DUAL and integrate memory and analogy-making. Sincethe process of judgment, as described above, involves memory (construction of the comparison set in working memory) and mapping (which is a central mechanism inanalogy-making) the JUDGEMAP model is most naturally integrated in DUAL and borrows many of the mechanismsdeveloped for analogy-making in AMBR. Because of the lack of space the model is described only in broad strokes.
Interested readers are invited to consult the literature on Figure 2. Judgment as classification task. Comparing the target to the standard of each of the subcategories.
Construction of the comparison set. The comparison set
is formed from perception (the target as well as potential Judgment as a mapping task. The DUAL-based model
context stimuli) and from long-term memory (familiar or of judgment discussed in this paper follows a third recently presented exemplars as well as generalized approach: The target stimulus is not compared to the prototypes, if such exist in LTM). The mechanism comparison set, but is rather included in it and then a responsible for that construction is spreading activation. The mapping is established between the elements of the sources of activation are the INPUT and GOAL nodes, i.e.
comparison set and the set of rating labels (or scale the perceived target (and possibly context) stimuli and the elements). This mapping should be as close as possible to a goal to judge the stimuli on a scale predefined in the homomorphism, i.e. the relations among the elements of instruction (e.g. a scale from 1 to 7). Thus the the comparison sets should be kept among their representations of the target and the scale elements become corresponding rating labels. Thus the process of judgment sources of activation which is then spread through the involves construction of the comparison set, joining the network of micro-agents. Naturally, concepts related to the target to it, and mapping between the comparison set and representation of the target become active, e.g. various features of the target – these include both relevant andirrelevant features (of course, relevant features receive more activation than irrelevant ones). The activation spreads further from the general concepts (like RED, GREEN, etc.)towards specific examples of the concepts (other red or greenobjects). However, there are only a few links from thegeneral concepts to their exemplars – only to the most familiar (typical) exemplars or to recently experienced ones.
Thus gradually a number of exemplars (and possiblyprototypes) are activated and become part of workingmemory – all these form the comparison set (Figure 4).
Figure 3. Judgment as mapping in the DUAL-based model.
Figure 4. Formation of the comparison set in WM by the spreading activation mechanism of DUAL.
Mapping of the comparison set onto the scale elements.
of the comparison set (Figure 7). Now, if it happens that the We can now consider the comparison set as a retrieved base known red lines are longer than the known green lines, then and map it onto the scale elements which are the target. The the two target stimuli (differing only in color) will be mapping process should preserve the relations among the included in different comparison sets and thus judged elements of the comparison set among their images on the differently and there will be a shift in favor of the green scale. The mapping should also follow the range-frequency target. Therefore the speculative prediction of JUDGEMAP principle described in the previous section. How is the will be that even such irrelevant feature of the line like its mapping achieved in JUDGEMAP? Similarly to AMBR, a color will play a role in the judgment process. This constraint-satisfaction network is constructed by the marker- prediction is in sharp contrast to all theories and models passing and structure-correspondence mechanisms. This described in the first section, which assume that only the network consists of temporal agent-hypotheses representing possible correspondences between members of comparison set and elements of the scale. These initial hypotheses are formed according to the range principle.
Excitatory and inhibitory links are constructed among the hypotheses and the spreading activation mechanism selectsthe winning hypotheses which form the mapping (Figure 5).
The competition among the hypotheses implements thefrequency principle. As result of this process not only the target stimulus but also each element of the comparison setreceives a judgment. This does not mean that people would be aware of all these judgments – most or even all of them Figure 6. The target stimulus is red and therefore we expect more red exemplars in the comparison set. They happened to be larger in size and thus they compete for the upper part of the scale. In this case the target stimulus (of the same size as in Figure 7) will compete with them and will be Figure 5. The process of mapping accomplished by the constraint satisfaction mechanism. The winning hypotheses Speculative prediction. Since the activation spreads from
the target stimulus (represented in a decentralized way bymany agents), exemplars, similar in some respect to it (sharing some feature with the target), can be potentiallyactivated and thus become members of the comparison set Figure 7. The target stimulus is green and therefore we in working memory. This means that in addition to expect more green exemplars in the comparison set. They currently perceived stimuli, to recently activated exemplars, happened to be smaller in size and thus they compete for the and to highly familiar (typical) exemplars, exemplars which lower part of the scale. In this case the target stimulus (of are simply similar to the target will also participate in the the same size as in Figure 6) will compete with them and comparison set. Moreover, these exemplars might be similar eventually will be mapped onto 5. In this way we receive an along the relevant (judged) dimension or along an irrelevant Let us consider the following example. Suppose we are judging the length of line segments but the lines arecolored. Let the target stimulus be a red line of certain Thus we will first describe a simulation experiment with length. In this case we may expect that there will be more JUDGEMAP that tests in practice this speculation and will red lines in the comparison set (Figure 6) – they will be also give us a rough estimation of the order of this color activated through the RED concept which is shared with the effect (if any). If we are successful, we will run a target. On the other hand, if the target stimulus is a green psychological experiment to text the model’s prediction and line of the same length, more green lines will become part Simulation Experiment
Thus the mean of the mean ratings of all red categories is4.012, while the mean of the mean ratings of all green In this simulation experiment we use a stimulus set of 56 categories is 4.065, which makes a difference of 0.053 lines. They are all in the long-term memory of the model.
which turns out to be almost significant tested with repeated The lines differ in length and color. There are 7 different measurements analysis (F(1,41)=3.917, p=0.055). The data sizes (from 10 units of length to 34 unit with increment of show that the possible size of the color main effect is very 4 units) and two different colors (red and green). Thus in small, but may still be significant. This prediction makes each size group there are 8 lines. The frequency of the red sense: on one hand it is small enough, so that we can ignore (respectively green) lines varies across the size groups. In it in everyday life and this explains why our intuition says size group one (the shortest lines - length 10 units) there are that irrelevant information does not play a role in judgment.
7 green and 1 red line, in the second shortest group (length On the other hand, the simulation predicts that the irrelevant 14 units) there are 6 green and 2 red lines, etc. In the largest information does play a role and shifts a bit the evaluation.
group size (length of 34 units) there are 7 red lines and one This means that under specific circumstances this shift green line. Thus we have positively skewed distribution of might be larger and become significant.
the green lines and negatively skewed distribution for thered lines.
The experiment described below is designed to test this Each line is represented by a coalition of 5 agents prediction of the model. Basically it replicates the standing for the line itself, for its color, for its length, and simulation experiment with a larger number of lines.
for the two relations (color_of and length_of). In additionthere are agents standing for the numbers from 0 to 8, but Psychological Experiment
only the agents standing for 1 to 7 are instances of “scale In this experiment human participants rate the length of red and green lines of various sizes. The interesting question is On each run of the program we connect one of these lines whether we will obtain a main effect of color, i.e. whether to the input list thus simulating the perception of the target there will be a difference between the ratings of the red and “scale_from_1_to_7” to the goal node thus simulating theinstruction for rating on a 7 point scale.
We have produced 42 variations of the knowledge base of the system thus simulating 42 different participants in the experiment. The knowledge bases differ mainly in the The experiment has a 14x2 within-subject factorial design.
associative and instance links among the agents, thus The independent variables are length (varying at 14 levels) although all our “artificial participants” will know the same and color (varying at 2 levels: green and red) of the lines.
lines and the same concepts, they will activate different The dependent variable is the rating of the length of the lines on a 7-point-scale. The experimental question is For each of these knowledge bases we have run two whether there will be a main effect of color, which is judgment trials: one for a red line of size 22 and one for a supposedly an irrelevant factor in judging length.
Simulation Results
Material
The results from the simulations are presented in Figure 8.
A set of 14 color lines has been presented horizontally As we can see the mean rating of the green lines are in most against a gray background on a 17-inch monitor. The cases slightly higher than the mean rating of the red lines shortest line is 12 pixels, the longest one is 727 pixels and the increment is 55 pixels. Each particular line length hasbeen shown eight times in red or green color. The shortlines were predominantly green while the long ones were predominantly red. The color distribution within the set of all 112 lines (14 lengths x 8 times) is presented in Table 1.
The frequency of the stimuli was calculated in order to receive a positively skewed distribution for the green color and a negatively skewed one for the red lines.
Figure 8. Simulation data. The mean rating of each line with a certain length (1-7) and color (green and red) obtained Table 1. Frequency of the presented stimulus lines (where 1 represents stimulus length 12 pixels, 2-67 pixels and so lengths
number of the
number of the red
green lines
lines
mean rating 2
line length
Figure 9. The mean rating of each line with a certain length (1-14) and color (green and red) obtained from all subjects.
Conclusions
The JUDGEMAP model of human judgment has been Procedure
presented. This model is based on a general cognitive The participants were tested individually in front of a architecture (DUAL) and is thus integrated with the memory computer screen where all 112 stimuli were shown and analogy-making model AMBR. Moreover, this model sequentially and in random order. They were instructed to inherits the underlying assumptions of DUAL and AMBR: judge the length of each line presented on the screen on a human cognition is context-sensitive (Kokinov, 1994c), seven point scale: 1-“it is not long at all”, …, 7-“it is very judgment included; human memory is constructive long”. No feedback was provided to the participants and no (Kokinov & Hirst, 2003), analogy-making is at the core of time restrictions have been imposed on them. The whole human cognition (Gentner, Holyoak & Kokinov, 2001) and experiment typically lasted about 15 minutes.
its mapping mechanisms may be used in judgment.
Participants
The JUDGEMAP model is similar to the Norm theory The participants were 18 undergraduate students (9 men and and the ANCHOR model with respect to the constructive 9 women none of whom was color-blind) from the approach to the formation of the comparison set. However, introductory classes in psychology at New Bulgarian unlike all the models described in the first section judgment University who participated in order to satisfy a course in JUDGEMAP is not based on comparison of the target with some aspect of the comparison set, but rather the targetstimulus is included in the comparison set and it receives a Results and Discussion
rating along with all other members of this set. This rating We had 14x2=28 data points for each participant. The process is based on establishing a mapping between the results averaged over subjects are shown in Figure 9. Each comparison set and the set of scale elements which mapping bar stands for the mean rating that a line of the corresponding size and color has received during the Unlike all other models JUDGEMAP does not ignore the experiment. The repeated measurements analysis showed irrelevant features of the to be judged targets, moreover that the difference (0.046) between the mean judgment of these irrelevant features play a role in the construction of the the green lines (4.239) and the mean judgment of the red comparison set (retrieving similar objects according to these lines (4.193) is significant (F(1, 17)=5.966, p=0.026).
irrelevant dimensions). The model makes a strange Surprisingly enough we obtained a difference (0.046) that prediction that the color of the target line may play a role in is almost the same as the difference we obtained in the the rating of its length and thus predicts a shift of the mean simulation (0.053). No tuning of the model was possible rating (although a small one) with the change of color. This since we did not have the experimental data in advance.
prediction has been tested in a psychological experiment and Thus the prediction of the JUDGEMAP model has been The size of this color effect is very small, but the stimuli have been very simple and the features unremarkable. It isdifficult to imagine that the green color reminds us of aparticular green line. That is why we plan to repeat theexperiment with more complex stimuli (human figures andclothes) and more memorable features (human faces). It ispossible the size of the effect in this case to become larger.
Acknowledgments
Petrov, A. & Anderson, J. (submitted). The Dynamics of Scaling: A Memory-Based Anchor Model of Category We would like to thank the AMBR research team for their continuous support and stimulating environment as well as Sarris, V., Parducci, A. (1978) Multiple Anchoring of Stefan Mateeff and Maurice Grinberg for the valuable Category Rating Scales. Perception and Psychophysics, Thurstone, L. (1927). A Law of Comparative Judgments.
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