How many voters are needed for paradoxes?

Summary. This paper presents a general procedure for finding profiles with the minimum number of voters required for many important paradoxes. Borda's and Condorcet's classic examples are revisited as well as generalizations. Using Saari's procedure line, we obtain an upper bound for the minimum number of voters needed for a profile for which the Condorcet winner is not strictly top ranked for all weighted positional procedures. Also we give a simple upper bound on the minimum number of voters needed for a set of prescribed voting outcomes. In contrast to situations wherein small numbers of voters are needed, we consider paradoxes requiring arbitrarily large numbers of voters as well as large numbers of alternatives. Finally we indicate connections with statistical rank based tests. Received: April 18, 2001; revised version: May 25, 2001     

Improving Environmental Performance: A Challenge for Romania

The transition process in Central and Eastern Europe was associated with growing environmental awareness. This paper analyses the determinants of pollution abatement and control expenditure at plant level in the case of Romania using survey data and a multilevel regression model. Our findings suggest that, although Romania has improved its environmental performance, formal and informal regulations are still only partially developed owing to the difficulties of economic transition, and heterogeneity across regions remains considerable.     

Utility maximization under a shortfall risk constraint

The article analyzes optimal portfolio choice of utility maximizing agents in a general continuous-time financial market model under a joint budget and downside risk constraint. The risk constraint is given in terms of a class of convex risk measures. We do not impose any specific assumptions on the price processes of the underlying assets. We analyze under which circumstances the risk constraint is binding. We provide a closed-form solution to the optimization problem in a general semimartingale framework. For a complete market, the wealth maximization problem is equivalent to a dynamic portfolio optimization problem.