The axiom of equivalence to individual power and the Banzhaf index

Research output: Contribution to journalArticlepeer-review


I introduce a new axiom for power indices on the domain of finite simple games that requires the total power of any given pair i,j of players in any given game v to be equivalent to some individual power, i.e., equal to the power of some single player k in some game w. I show that the Banzhaf power index is uniquely characterized by this new “equivalence to individual power” axiom in conjunction with the standard semivalue axioms: transfer (which is the version of additivity adapted for simple games), symmetry or equal treatment, positivity (which is strengthened to avoid zeroing-out of the index on some games), and dummy.

Original languageAmerican English
Pages (from-to)391-400
Number of pages10
JournalGames and Economic Behavior
StatePublished - 1 Mar 2018


  • 2-efficiency
  • Banzhaf power index
  • Dummy
  • Positivity
  • Semivalues
  • Simple games
  • Superadditivity
  • Symmetry
  • Transfer

All Science Journal Classification (ASJC) codes

  • Finance
  • Economics and Econometrics


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