Abstentions in the German Bundesrat and ternary decision rules

Abstract

Ternary decision rules are analyzed that allow for abstentions, in addition to Yea- and Nay-votes. The German Bundesrat serves as a prime example. We show that the decision-making efficiency of the Bundesrat would increase if abstentions were allowed. Generally, a formula for the mean success margin of a ternary decision rule is derived assuming selfdual and permutationally invariant distributions. Specifically, the ternary Penrose/Banzhaf model is discussed in detail. The influence probabilities of voters, and the influence sensitivity of the rule are evaluated