## Program ipnice

This page enables you to run the program called ipnice to find power indices for member countries in the EU Council of Ministers using the rules for Qualified Majority Voting agreed in the Treaty of Nice. The power indices are evaluated exactly using the triple-majority rule; a decision requires each of the following:
(i) qualified majority of weighted votes, (ii) a minimum percentage of the EU population, (iii) a simple majority of member countries, all in favour.

The program computes the following power indices with respect to this decision rule for each member country:
Penrose index or Absolute Banzhaf index:  the number of swings divided by the number of possible voting outcomes among the other members.

Normalised Banzhaf index:  the number of swings as a proportion of the total number of swings for all members. The indices sum to 1 over all members.

Power to Prevent Action (Coleman):  the number of swings divided by the number of voting outcomes that lead to a decision. A measure of a member's  blocking power.

Power to Initiate Action (Coleman):  the number of swings divided by the number of outcomes that do not produce a decision. A measure of the member's power to get its way within the voting body.
References: Penrose (1946), Banzhaf (1965), Coleman (1971), Leech (2002d).

This algorithm ipnice has the advantages of being simple, since it is a direct application of the fundamental definitions of the indices, and of giving exact values. Its disadvantage is that it has exponential time complexity because the computing time required doubles each time an extra member is added. In practice this means that it works well for small voting bodies but is practically infeasible for a number of countries much in excess of 30.

## Data Input for ipnice

Enter your data in the boxes below. Two quotas must be entered: Quota 1 is the threshold for QMV, Quota 2 is the population threshold (as a proportion). For each country enter its QMV weight under the Nice Treaty and its population as a proportion of the EU.

Number of Member Countries

Quota 1

Quota 2:

Weights:

Populations: