IDEAS home Printed from https://ideas.repec.org/a/kap/pubcho/v43y1984i3p329-343.html

Optimizing group judgmental accuracy in the presence of interdependencies

Author

Listed:
  • Lloyd Shapley
  • Bernard Grofman

Abstract

Consider a group of people confronted with a dichotomous choice (for example, a yes or no decision). Assume that we can characterize each person by a probability, p i , of making the ‘better’ of the two choices open to the group, such that we define ‘better’ in terms of some linear ordering of the alternatives. If individual choices are independent, and if the a priori likelihood that either of the two choices is correct is one half, we show that the group decision procedure that maximizes the likelihood that the group will make the better of the two choices open to it is a weighted voting rule that assigns weights, w i , such that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4DamaaBa% aaleaacaWGPbaabeaaiiaakiab-1Hi1kaabYgacaqGVbGaae4zamaa% laaabaGaamiCamaaBaaaleaacaWGPbaabeaaaOqaaiaaigdacqGHsi% slcaWGWbWaaSbaaSqaaiaadMgaaeqaaaaaaaa!423B!\[w_i \propto {\text{log}}\frac{{p_i }}{{1 - p_i }}\] We then examine the implications for optimal group choice of interdependencies among individual choices. Copyright Martinus Nijhoff Publishers 1984

Suggested Citation

  • Lloyd Shapley & Bernard Grofman, 1984. "Optimizing group judgmental accuracy in the presence of interdependencies," Public Choice, Springer, vol. 43(3), pages 329-343, January.
    • Handle: RePEc:kap:pubcho:v:43:y:1984:i:3:p:329-343
    DOI: 10.1007/BF00118940
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF00118940
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF00118940?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Nitzan, Shmuel & Paroush, Jacob, 1980. "Investment in Human Capital and Social Self Protection under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(3), pages 547-557, October.
    2. Bernard Grofman, 1975. "A comment on ‘democratic theory: A preliminary mathematical model.’," Public Choice, Springer, vol. 21(1), pages 99-103, March.
    3. Owen, Guillermo, 1975. "Evaluation of a Presidential Election Game," American Political Science Review, Cambridge University Press, vol. 69(3), pages 947-953, September.
    4. Roberts, Blaine, 1973. "An Extension of Optimality Criteria: An Axiomatic Approach to Institutional Choice," Journal of Political Economy, University of Chicago Press, vol. 81(2), pages 386-400, Part I, M.
    5. Shmuel Nitzan & Jacob Paroush, 1984. "Are qualified majority rules special?," Public Choice, Springer, vol. 42(3), pages 257-272, January.
    6. Dreyer, Jacob S & Schotter, Andrew, 1980. "Power Relationships in the International Monetary Fund: The Consequences of Quota Changes," The Review of Economics and Statistics, MIT Press, vol. 62(1), pages 97-106, February.
    7. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    8. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    9. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    10. Howard Margolis, 1976. "A note on incompetence," Public Choice, Springer, vol. 26(1), pages 119-127, June.
    11. Nitzan, Shmuel & Paroush, Jacob, 1982. "Optimal Decision Rules in Uncertain Dichotomous Choice Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 289-297, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Scott Feld & Bernard Grofman, 1984. "The accuracy of group majority decisions in groups with added members," Public Choice, Springer, vol. 42(3), pages 273-285, January.
    2. Bryan C. McCannon & Paul Walker, 2016. "Endogenous competence and a limit to the Condorcet Jury Theorem," Public Choice, Springer, vol. 169(1), pages 1-18, October.
    3. Karotkin, Drora & Nitzan, Shmuel, 1995. "The effect of expansions and substitutions on group decision-making," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 263-271, December.
    4. Baharad, Eyal & Ben-Yashar, Ruth & Patal, Tal, 2020. "On the merit of non-specialization in the context of majority voting," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 128-133.
    5. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    6. Imma Curiel, 2014. "A multifaceted analysis of the electoral system of the Republic of Suriname," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(4), pages 29-49.
    7. Laruelle, Annick & Widgren, Mika, 1998. "Is the Allocation of Voting Power among EU States Fair?," Public Choice, Springer, vol. 94(3-4), pages 317-339, March.
    8. Barr, Jason & Passarelli, Francesco, 2009. "Who has the power in the EU?," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 339-366, May.
    9. Boratyn, Daria & Kirsch, Werner & Słomczyński, Wojciech & Stolicki, Dariusz & Życzkowski, Karol, 2020. "Average weights and power in weighted voting games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 90-99.
    10. Crama, Yves & Leruth, Luc, 2007. "Control and voting power in corporate networks: Concepts and computational aspects," European Journal of Operational Research, Elsevier, vol. 178(3), pages 879-893, May.
    11. Ruth Ben‐Yashar & Jacob Paroush, 2003. "Investment in Human Capital in Team Members Who Are Involved in Collective Decision Making," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 5(3), pages 527-539, July.
    12. Artyom Jelnov & Yair Tauman, 2014. "Voting power and proportional representation of voters," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 747-766, November.
    13. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    14. Vitaly Malyshev, 2021. "Optimal majority threshold in a stochastic environment," Group Decision and Negotiation, Springer, vol. 30(2), pages 427-446, April.
    15. Jonathan R. Strand & David P. Rapkin, 2011. "Weighted Voting in the United Nations Security Council," Simulation & Gaming, , vol. 42(6), pages 772-802, December.
    16. Muto, S., 1993. "Voters' Power in Indirect Voting Systems with Political Parties : the Square Root Effect," Discussion Paper 1993-72, Tilburg University, Center for Economic Research.
    17. Carreras, Francesc & Giménez, José Miguel, 2011. "Power and potential maps induced by any semivalue: Some algebraic properties and computation by multilinear extensions," European Journal of Operational Research, Elsevier, vol. 211(1), pages 148-159, May.
    18. Eyal Baharad & Ruth Ben-Yashar, 2009. "The robustness of the optimal weighted majority rule to probability distortion," Public Choice, Springer, vol. 139(1), pages 53-59, April.
    19. Ruth Ben-Yashar, 2014. "The generalized homogeneity assumption and the Condorcet jury theorem," Theory and Decision, Springer, vol. 77(2), pages 237-241, August.
    20. Karotkin, Drora & Paroush, Jacob, 1995. "Incentive schemes for investment in human capital by members of a team of decision makers," Labour Economics, Elsevier, vol. 2(1), pages 41-51, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:pubcho:v:43:y:1984:i:3:p:329-343. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.