difficult problem of understanding when a local optimum is an u-local or a global one. In the former section we will give an algorithm that computes the universal basin of attraction of a given social outcome in $O(M^3\log M)$ time, where $M$ is the number of social outcomes. We point out that this problem deals with both object constructions and agendas. Since there could be infinitely many agendas, the problem it is not finite [*a priori*]{}. It is not difficult to reduce the problem to a finite one, but a simple brute-force algorithm would take far more than exponential time. This algorithm has been implemented by the first author who has written the computer program [FOSoR]{} [@FOSoR]. In Section \[sec:numerical\] we will give numerical data obtained by means of the computer program [FOSoRStat]{} [@FOSoRStat] (created by first author) that computes statistics on the number of social rules with a given number of (u-)local optima.

The last section is devoted to one example. It is treated in some detail because it is the smallest in which all kinds of optima (local, u-local and global) appear.

#### Acknowledgements

The authors are grateful to Prof. Luigi Marengo for his useful comments and corrections.

