Arrovian aggregation models
\textit{K. J. Arrow}'s [Social Choice and Individual Values, Wiley (1951; Zbl 0984.91513)] half century old paradox roughly goes as follows. There are at least three candidates and at least two voters, each (linearly) rank-ordering the candidates. A symmetric function, increasing in each vote, is defined for all possible rankings by the voters, yielding aggregate rankings such that for any pair of candidates neither aggregate ranking order is excluded (``citizen's sovereignity'') and the aggragate ranking of any two candidates is independent of the individual rankings of others (``independence of irrelevant alternatives''). Surprisingly, these assumptions are satisfied only by ``dictatorial'' aggregation functions, which yield exactly the ordering of one of the voters. An immense literature followed, partly containing similar paradoxes and partly offering ways to avoiding the paradox. The present book summarizes some (but by far not all) these results and offers the author's own contributions. After the introductory Preface and Introduction (Chapter 1), further chapters deal with ``rationality'' (reasonableness; Chapter 2), social decision functions (Chapter 3), ``functional aggregation rules'' (which transform individual choice functions into a social choice function; Chapter 4) and ``social choice correspondences'' (which transform individual binary relations into social choice functions; Chapter 5).
scientific article; zbMATH DE number 1461238