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Decision Making Using Rating Systems: When Scale Meets Binary

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  • Bargagliotti, Anna E.
  • Li, Lingfang (Ivy)

Abstract

Rating systems measuring quality of products and services (i.e., the state of the world) are widely used to solve the asymmetric information problem in markets. Decision makers typically make binary decisions such as buy/hold/sell based on aggregated individuals' opinions presented in the form of ratings. Problems arise, however, when different rating metrics and aggregation procedures translate the same underlying popular opinion to different conclusions about the true state of the world. This paper investigates the inconsistency problem by examining the mathematical structure of the metrics and their relationship to the aggregation rules. It is shown that at the individual level, the only scale metric (1,. . . ,N) that reports people's opinion equivalently in the a binary metric (-1, 0, 1) is one where N is odd and N-1 is not divisible by 4. At aggregation level, however, the inconsistencies persist regardless of which scale metric is used. In addition, this paper provides simple tools to determine whether the binary and scale rating systems report the same information at individual level, as well as when the systems di®er at the aggregation level.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16947.

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Date of creation: 25 Aug 2009
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Handle: RePEc:pra:mprapa:16947

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Keywords: rating; ranking; preference; asymmetric information;

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  1. Klein, Tobias J. & Lambertz, Christian & Spagnolo, Giancarlo & Stahl, Konrad O., 2006. "Last Minute Feedback," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 62, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  2. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
  3. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-57, Jan.-Feb..
  4. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
  5. John Morgan & Phillip C. Stocken, 2008. "Information Aggregation in Polls," American Economic Review, American Economic Association, vol. 98(3), pages 864-96, June.
  6. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
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