Skip to main content
SpringerLink
Log in

Consensus for belief functions and related uncertainty measures

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

We extend previous work of Lehrer and Wagner, and of McConway, on the consensus of probabilities, showing under axioms similar to theirs that (1) a belief function consensus of belief functions on a set with at least three members and (2) a belief function consensus of Bayesian belief functions on a set with at least four members must take the form of a weighted arithmetic mean. We observe that these results are unchanged when consensual uncertainty measures are allowed to take the form of Choquet capacities of low order monotonicity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aczel, J., Ng, C. T., and Wagner, C.: 1984, ‘Aggregation Theorems for Allocation Problems’, SIAM Journal on Algebraic and Discrete Methods 5, 1–8.

    Google Scholar 

  2. Dempster, A. P.: 1967, ‘Upper and Lower Probabilities Induced by a Multivalued Mapping’, Annals of Mathematical Statistics 38, 325–339.

    Google Scholar 

  3. Genest, C.: ‘Pooling Operators with the Marginalization Property’, Canadian Journal of Statistics 12, 153–163.

  4. Lehrer, K. and Wagner C.: 1981, Rational Consensus in Science and Society, D. Reidel Publishing Company, Boston.

    Google Scholar 

  5. McConway, K.: 1981, ‘Marginalization and Linear Opinion Pools’, Journal of the American Statistical Association 76, 410–414.

    Google Scholar 

  6. Shafer, G.: 1976, A Mathematical Theory of Evidence, Princeton University Press, Princeton.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, University of Tennessee, 37996-1300, Knoxville, TN, USA

    Carl G. Wagner

Authors
  1. Carl G. Wagner
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by a grant from the University of Tennessee Artificial Intelligence Group, and by the U.S. Naval Sea Systems Command, through a grant to Oak Ridge National Laboratory.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wagner, C.G. Consensus for belief functions and related uncertainty measures. Theor Decis 26, 295–304 (1989). https://doi.org/10.1007/BF00134110

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00134110

Keywords

Search

Navigation