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Estimating Arbitrator's Hidden Judgement in Final Offer Arbitration

Author

Listed:
  • Yigal Gerchak

    (Tel-Aviv University)

  • Eitan Greenstein

    (Technion-Israel Institute of Technology)

  • Ishay Weissman

    (Technion-Israel Institute of Technology)

Abstract

In Final Offer Arbitration the arbitrator has to choose between two prices – salary offer a and demand b, presented by two negotiating sides. This situation is common e.g., in Major League Baseball since 1974, for players with at least three years experience. We model the arbitrator's decision process as follows. First, the arbitrator chooses an appropriate sum Z. Then he selects the one among a and b which is closer to the ‘proper sum’Z. The final amount selected is Y . Based on the history of n cases, the information available is the triplets {(Y i, a i, b i) : i= 1, 2, . . . n}(the {Z i} are hidden). It is assumed that the {Z i} are random variables with a distribution which depends on an unknown parameter q and the challenge is to estimate q. Furthermore, since each case had different merits and characteristics, the resulting distribution is case-specific. Thus, our model allows the inclusion of explanatory variables. The statistical algorithm which we shall use is the Expectation-Maximization(EM) algorithm. In the paper, the statistical model is introduced in detail and the application of the EM algorithm to the available data is explained. Two numerical examples illustrate the use of the EM algorithm in estimating the arbitrator's hidden judgements.

Suggested Citation

  • Yigal Gerchak & Eitan Greenstein & Ishay Weissman, 2004. "Estimating Arbitrator's Hidden Judgement in Final Offer Arbitration," Group Decision and Negotiation, Springer, vol. 13(3), pages 291-298, May.
    • Handle: RePEc:spr:grdene:v:13:y:2004:i:3:d:10.1023_b:grup.0000031090.95226.db
    DOI: 10.1023/B:GRUP.0000031090.95226.db
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    References listed on IDEAS

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    1. Brams, Steven J. & Merrill, Samuel III, 1991. "Final-offer arbitration with a bonus," European Journal of Political Economy, Elsevier, vol. 7(1), pages 79-92, April.
    2. Brams, Steven J. & Kilgour, D. Marc & Merrill, Samuel III, 1991. "Arbitration Procedures," Working Papers 91-38, C.V. Starr Center for Applied Economics, New York University.
    3. Henry S. Farber, 1980. "An Analysis of Final-Offer Arbitration," Journal of Conflict Resolution, Peace Science Society (International), vol. 24(4), pages 683-705, December.
    4. Steven J. Brams & Samuel Merrill, III, 1983. "Equilibrium Strategies for Final-Offer Arbitration: There is no Median Convergence," Management Science, INFORMS, vol. 29(8), pages 927-941, August.
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    Cited by:

    1. Eran Hanany & D. Marc Kilgour & Yigal Gerchak, 2007. "Final-Offer Arbitration and Risk Aversion in Bargaining," Management Science, INFORMS, vol. 53(11), pages 1785-1792, November.
    2. Mazalov, Vladimir & Tokareva, Julia, 2012. "Arbitration procedures with multiple arbitrators," European Journal of Operational Research, Elsevier, vol. 217(1), pages 198-203.

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