Equitable Representation in the Councils of the United Nations: Theory and Application

We develop a theoretical framework for equity in council voting games (CVGs). In a CVG, a fully representative voting body delegates decision-making to a subset of the members, as describes, e.g., the United Nations Security Council (UNSC). Three equity concepts are proposed, ex-ante (procedural) equity, ex-post (outcome) equity and regional equity. The last two concepts are consistent with a new square-root rule on the probability of council membership, but no CVG can meet all three concepts. We apply our framework to evaluate the equitability of the UNSC, and the claims of those who seek to reform it.