scholarly journals Application of a weighted average model to a psychophysical averaging task

1967 ◽  
Vol 8 (6) ◽  
pp. 227-228 ◽  
Author(s):  
Norman H. Anderson
Keyword(s):  
Weighted Average ◽  
Average Model ◽  
Weighted Average Model

scholarly journals Mathematical Model of Person Judgment, Part 1 - Manuscript

2021 ◽  
Author(s):  
Daniel Leising ◽  
Rene Schilling
Keyword(s):  
Mathematical Model ◽  
Weighted Average ◽  
Research Area ◽  
Continuous Variable ◽  
Lens Model ◽  
Rater Agreement ◽  
Average Model ◽  
Weighted Average Model ◽  
Person Judgment ◽  
Target Effects

We present the first part of a fully parametrized mathematical model of person judgment, in an attempt to streamline and better organize theory in this research area. The model integrates several key concepts from Kenny’s (1994) Weighted Average Model and Brunswik’s (1956) lens model with one another. It incorporates time as a continuous variable and also accounts for target-effects, situation-effects, target by situation interaction-effects, randomness overall and between-target differences in randomness. All of these can influence the average level of a substance variable that may be observed by perceivers („cues“) and thus inform their judgments of targets. We discuss the model’s implications with regard to reliability, inter-rater agreement, and predictive validity. We also explain how the model connects to – and sometimes helps specify – several important concepts from the person judgment literature.

scholarly journals Consistency of Pairwise Comparisons and Its Role in Optimal Detection of Customers’ Preferences

2020 ◽  
Vol 24 (3) ◽  
pp. 37
Author(s):  
Filip Tošenovský
Keyword(s):  
Decision Making ◽  
Case Studies ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Optimization Criterion ◽  
Optimization Techniques ◽  
Pairwise Comparisons ◽  
Average Model ◽  
Weighted Average Model ◽  
Decision Weights

<p><strong>Purpose:</strong> This paper analyses a problem that originates in the weighted-average model, a mathematical construct introduced by the theory of multicriteria decision-making that can be used to detect what product a customer desires. The problem occurs because the model needs to know the weight the customer assigns to each product feature, aside from the levels of all the product characteristics, in order to calculate the overall value of the product. And since by one approach the weights can be estimated by optimization, the question arises which optimization criterion to select for the procedure, as different criteria will lead to different weights and thus to different product evaluations. The paper analyses the problem in connection with the so-called consistency of pairwise comparisons, which are utilized in the optimization and describe how much the customer prefers one product feature to another. The analysis shows that the problem of which criterion to use to calculate the weights can be eliminated if the pairwise comparisons are consistent. The analysis is performed within pre-defined criteria and is supplemented with case studies supporting the findings.</p><p><strong>Methodology/Approach:</strong> Linear algebra, optimization techniques, case studies.</p><p><strong>Findings:</strong> The results represent a prescription customers can use if they want to avoid the pitfalls of selecting a specific optimization criterion when informing the product maker about what they want based on the weighted-average model.</p><p><strong>Research Limitation/Implication:</strong> The results are related to a specific decision-making model, although that model is still very general and natural.</p><strong>Originality/Value of paper:</strong> The problem of selecting an optimization criterion to determine decision weights is not discussed in the theory.

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