Optimal lobbying pricing

We study a game with two candidates and two interest groups. The groups offer two kinds of costly contributions to achieve political influence: (a) pre-election campaign contributions to their favourite candidates that increase their probability of winning the election and (b) post-election lobbying contributions to the winning candidate to affect the implemented policy. The candidates are the first to act by strategically choosing the lobbying prices they will charge the groups if they are elected. We characterise the equilibrium values of the lobbying prices set by the candidates as well as the equilibrium levels of the campaign and lobbying contributions chosen by the groups. We show, endogenously, that in the case with symmetric groups and symmetric politicians, a candidate announces to charge the group that supports her in the election a lower lobbying price, justifying this way the preferential treatment to certain groups from the politicians in office. We also consider two extensions (asymmetric groups and politicians who do not commit to the announced prices) and show that the results of the benchmark model hold under specific conditions.

The doctrinal paradox: comparison of decision rules in a probabilistic framework

The doctrinal paradox is analysed from a probabilistic point of view assuming a simple parametric model for the committee’s behaviour. The well known premise-based and conclusion-based majority rules are compared in this model, by means of the concepts of false positive rate (FPR), false negative rate (FNR) and Receiver Operating Characteristics (ROC) space. We introduce also a new rule that we call path-based, which is somehow halfway between the other two. Under our model assumptions, the premise-based rule is shown to be the best of the three according to an optimality criterion based in ROC maps, for all values of the model parameters (committee size and competence of its members), when equal weight is given to FPR and FNR. We extend this result to prove that, for unequal weights of FNR and FPR, the relative goodness of the rules depends on the values of the competence and the weights, in a way which is precisely described. The results are illustrated with some numerical examples.