A New Proposal on Special Majority Voting

Special majority voting is usually defined in terms of the proportion of the electorate required for a positive decision. This note reassesses that definition, and proposes an alternative. The proposal is to define special majority voting in terms of the absolute margin between the majority and the minority required for a positive definition. It is shown that if we use special majority voting for “epistemic” reasons – i.e. because of a concern for reaching “correct” decisions – then the standard definition not only has the wrong focus, but may be even counterproductive, while the proposed alternative definition is “epistemically” sound. Several technical results related to the Condorcet jury theorem are adduced to back up the argument. Many decision-making bodies employ special majority voting for important decisions. In jury decisions, for example, special majorities of at least 10 out of 12 jurors are often required for a verdict leading to conviction. To change the Basic Law of the Federal Republic of Germany, two thirds majorities in both chambers of parliament, Bundestag and Bundesrat, are required. Under simple majority voting, a positive decision – for example, the accceptance of law – is reached if the decision is supported by more than 1⁄2 of the electorate. Under special majority voting, given the standard definition, a positive decision is reached if the decision is supported by a proportion of at least q of the electorate, where q is greater than 1⁄2, often substantially greater. In the examples above, q equals 5/6 and 2/3, respectively. In this note, I will reasesses the standard definition of special majority voting, and propose an alternative definition. Under the proposed alternative definition, a positive decision is reached if the absolute margin between the majority and the minority is at least m, where m is a positive integer (for example, m = 100 or m = 2). Specifically, I will show that if we use special majority voting because of a concern for reaching “correct” decisions – in short, for “epistemic” reasons –, then the standard definition not only has the wrong focus, but may be even counterproductive. I will further show that the proposed alternative definition remedies these problems, by diverging from the standard characteristic of special majority voting that the support from a certain proportion q of the electorate is required, where q may be substantially greater than /2. A concern for reaching “correct” decisions should thus lead us to adopt the alternative definition of special majority voting. If we nonetheless seek to use special majority voting under the standard definition, then we cannot justify this in terms of a concern for reaching “correct” decisions. Rather, a justification would need to appeal to certain “procedural” properties of special majority voting in its standard form which are independent from a concern for “correctness”. Amongst those procedural properties might be, for example, the property of giving veto power to minorities. 1 I am very grateful to David Estlund and Robert Goodin for inspiring my interest in this issue and for comments, and to Iain McLean for discussion. Address for correspondence: Nuffield College, Oxford OX1 1NF, U.K.; E-mail [email protected]. 2 Alternatively: greater than. 3 Alternatively: greater than.