Abstract
We have seen in the previous section that for ratio judgements the reciprocal condition (7.40) is very natural, but the homogeneity condition (7.55) may be less so. If, however, the judgements to be synthesized are measures (weights, lengths, monetary values etc.) rather than their ratios, then the homogeneity condition is very natural, it expresses the property of scale-invariance now quite familiar to us (sections 2,3): If the scale (unit of measurement) is changed in the individual judgements, the same change of scale should occur in the synthesized judgement. On the other hand, in this case the reciprocal condition is not so natural. So for synthesizing measure judgements one could use just (7.55) and Corollary 7.6 or the first part of Corollary 7.7.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Aczél, J. (1987). Synthesis of measure judgements. Equations in a single variable. The Abel and Schröder equations. Iteration. In: A Short Course on Functional Equations. Theory and Decision Library, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3749-9_9
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DOI: https://doi.org/10.1007/978-94-009-3749-9_9
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