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Social science puzzles: a systems analysis challenge

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Abstract

As shown, a common source for a wide range of problems and complexities that arise in the social sciences is an unexpected loss of needed information. This includes concerns from social choice, economics, probability/statistics, etc. But by identifying the content of the lost information, negative assertions may be replaced with positive conclusions; this requires finding ways to reincorporate the missing information.

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Notes

  1. A positional method tallies ballots by assigning specified points to candidates according to how their ballot position. This example has seven different positional rankings; four have no ties.

  2. Whenever agents are to select an alternative, which is true of all Sen examples that I have seen, Sen’s non-cyclic condition becomes a special case of Arrow’s condition of a complete, transitive outcome.

  3. By examining the proof, it follows that this assertion holds for all settings with a cyclic outcome.

  4. If \(s<\frac{1}{2},\) these rankings are reversed. The \(s=\frac{1}{2}\) choice defines the Borda Count, which is immune to this symmetry distraction by having complete ties and agreeing with pairwise and the quadruple positional outcomes.

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Authors and Affiliations

  1. Departments of Economics and of Mathematics, Institute for Mathematical Behavioral Sciences, University of California, Irvine, CA, 92697-5100, USA

    Donald G. Saari

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  1. Donald G. Saari
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Correspondence to Donald G. Saari.

Additional information

This paper is an extended version of my presentation at an August 2014 workshop “Recent developments on geometrical and algebraic methods in Economics” at Hokkaido University, Sapporo, Japan. My thanks to Prof. Simona Settepanella for inviting me to participate and her hospitality while I was there. Also, my thanks for the several useful suggestions that were offered by two referees.

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Saari, D.G. Social science puzzles: a systems analysis challenge. Evolut Inst Econ Rev 12, 123–139 (2015). https://doi.org/10.1007/s40844-015-0008-z

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