Thurstonian-type representations for ``same-different'' discriminations: probabilistic decisions and interdependent images.
The present paper is a continuation of the one just preceding [ ibid. 47, no. 2, 184--204 (2003; Zbl 1048.91103)] in the Journal where the current appears, and the reader is referred to the relative review for background and introduction to the problem. The main result reported here extends the negative result proved in that paper about Thurstonian-type representations of `same-different' stimuli comparisons. For psychometric functions satisfying the regularity properties of `regular minimality' and `non-constant similarity', the result of the previous paper shows the non-existence of well-behaved probabilistic representations with independent probabilities on the perception space and deterministic assignments of same-different judgments. In the present paper the author reaffirms the previous result by extending it to the non-existence of well-behaved probabilistic representations even allowing for probabilistic assignments and interdependent probabilities. A somewhat natural restriction on interdependence is that the distributions of the paired stimuli should be independent conditionally on the value of a `common source' of uncertainty. The skeptical attitude towards appropriateness of Thurstonian `language' to deal with same-different discriminations is thus reinforced. But the author concludes with some positive comments concerning other possible, non probabilistic ways of approaching the problem. In particular, he proposes a representation of psychometric functions via subjective distances the individual may perceive between stimuli in the stimulus space. The interested reader is referred to the discussion in the paper and the relative cited bibliography for this alternative line.
scientific article; zbMATH DE number 1956184