On the hardness of finding good pacts

Reaching agreements is part of the life of any human group, but it is especially important in the context of political relations. In parliamentary systems, when no party has an absolute majority, it is necessary to establish pacts with other parties to carry out as many laws as possible that fit with our ideology. However, finding the best possible deals is not an easy task. In fact, in this work we not only show that it is an NP-complete problem, but also that it is impossible to guarantee a good approximation ratio in polynomial time. Even so, we show that it is possible to use genetic algorithms to obtain reasonably satisfactory pacts, and we illustrate it for a specific case study of the Spanish parliament.