Collective judgement: combining individual value judgements
The mathematical part of the paper, preceded by a wide-ranging introduction, and followed by remarks on Arrow's paradox and by a 63 item bibliography, offers the continuous and in each variable strictly increasing solutions of the bisymmetry equation \[ B[B(x_{11},\dots ,x_{1n}),\dots ,B(x_{n1},\dots ,x_{nn})]=B[B(x_{11},\dots ,x_{n1}), \dots ,B(x_{1n},\dots ,x_{nn})]. \] The result has been announced in \textit{J. Aczél}'s 1948 paper [Bull. Am. Math. Soc. 54, 392--400 (1948; Zbl 0030.02702)] but proved only for \(n=2\). As application an axiomatization of group decision making is offered, where the group consists of \(n^2\) evaluators and their decision is aggregated from those of \(n\) subsets of \(n\) members each.
scientific article; zbMATH DE number 1319691
scientific article