---
_id: '63731'
abstract:
- lang: eng
  text: The Banzhaf power index can be used to quantify the explanatory power of single
    conditions in a configurational analysis that aims at identifying whether combinations
    of conditions are sufficient for an outcome. The latter method is an integral
    part of the Qualitative Comparative Analysis (QCA) approach. It is widely used
    in the literature, e.g., in the field of International Management. Haake and Schneider
    (2023) give a rigorous description of the connection between the empirical and
    game theoretic modeling. To justify that the Banzhaf index is an appropriate tool
    to measure the influence of a condition, this paper discusses a novel axiomatization
    of the Banzhaf index that uses axioms that are directly linked to the QCA methodology.
    As a side result, we demonstrate that in our model the Banzhaf index can be reinterpreted
    as an average of Shapley-Shubik indices.
author:
- first_name: Claus-Jochen
  full_name: Haake, Claus-Jochen
  id: '20801'
  last_name: Haake
- first_name: Martin
  full_name: Schneider, Martin
  id: '471'
  last_name: Schneider
  orcid: https://orcid.org/0000-0002-6961-3716
citation:
  ama: Haake C-J, Schneider M. An Axiomatization of the Banzhaf Index to Measure Influence
    in Qualitative Comparative Analysis. <i>International Journal of Game Theory</i>.
    2026;55. doi:<a href="https://doi.org/10.1007/s00182-026-00978-2">10.1007/s00182-026-00978-2</a>
  apa: Haake, C.-J., &#38; Schneider, M. (2026). An Axiomatization of the Banzhaf
    Index to Measure Influence in Qualitative Comparative Analysis. <i>International
    Journal of Game Theory</i>, <i>55</i>. <a href="https://doi.org/10.1007/s00182-026-00978-2">https://doi.org/10.1007/s00182-026-00978-2</a>
  bibtex: '@article{Haake_Schneider_2026, title={An Axiomatization of the Banzhaf
    Index to Measure Influence in Qualitative Comparative Analysis}, volume={55},
    DOI={<a href="https://doi.org/10.1007/s00182-026-00978-2">10.1007/s00182-026-00978-2</a>},
    journal={International Journal of Game Theory}, publisher={Springer}, author={Haake,
    Claus-Jochen and Schneider, Martin}, year={2026} }'
  chicago: Haake, Claus-Jochen, and Martin Schneider. “An Axiomatization of the Banzhaf
    Index to Measure Influence in Qualitative Comparative Analysis.” <i>International
    Journal of Game Theory</i> 55 (2026). <a href="https://doi.org/10.1007/s00182-026-00978-2">https://doi.org/10.1007/s00182-026-00978-2</a>.
  ieee: 'C.-J. Haake and M. Schneider, “An Axiomatization of the Banzhaf Index to
    Measure Influence in Qualitative Comparative Analysis,” <i>International Journal
    of Game Theory</i>, vol. 55, 2026, doi: <a href="https://doi.org/10.1007/s00182-026-00978-2">10.1007/s00182-026-00978-2</a>.'
  mla: Haake, Claus-Jochen, and Martin Schneider. “An Axiomatization of the Banzhaf
    Index to Measure Influence in Qualitative Comparative Analysis.” <i>International
    Journal of Game Theory</i>, vol. 55, Springer, 2026, doi:<a href="https://doi.org/10.1007/s00182-026-00978-2">10.1007/s00182-026-00978-2</a>.
  short: C.-J. Haake, M. Schneider, International Journal of Game Theory 55 (2026).
date_created: 2026-01-26T12:30:50Z
date_updated: 2026-01-26T12:42:04Z
department:
- _id: '205'
- _id: '475'
- _id: '185'
doi: 10.1007/s00182-026-00978-2
intvolume: '        55'
keyword:
- Banzhaf index
- axiomatization
- QCA
- explanatory power
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://link.springer.com/article/10.1007/s00182-026-00978-2#citeas
oa: '1'
publication: International Journal of Game Theory
publisher: Springer
quality_controlled: '1'
status: public
title: An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative
  Comparative Analysis
type: journal_article
user_id: '20801'
volume: 55
year: '2026'
...