Marjorie Gassner

Extending the Hausman Test to Check for the presence of Outliers

In this paper, we follow the same logic as in Hausman (1978) to create a testing procedure that checks for the presence of outliers by comparing a regression estimator that is robust to outliers (S-estimator), with another that is more e¢ cient but a¤ected by them. Some simulations are presented to illustrate the good behavior of the test for both its size and its power.

Biproportional Delegations A Solution for Two-Dimensional Proportional Representation

This paper deals with the problem of two-dimensional proportional representation most commonly encountered when seats are to be allocated in a region where voters are classified according to the double cleavage of the constituency in which they vote and the party of their choice. A priority is set here on marginal proportionality: seats are dealt out to constituencies and to parties at the global level first. It is proven that, under a very weak condition, a biproportional delegation always exists, i.e. a representation matrix matching imposed margins and which is a controlled rounding of the corresponding solution to the well-known biproportional problem. Two versions of a construction process for such a biproportional delegation are proposed and they are simulated on Belgian electoral data covering the last four general elections. Though no perfect system exists for this type of representation, comparisons with the current system plead in favor of the use of biproportional delegations.

An impossibility theorem for fair bidimensional representation: Towards a biproportional solution

This paper concerns fair (proportional) representation of a population which is divided into categories according to two criteria as is the case, for example, when an electoral system takes into account the geographical as well as the political group of the elector. Our first model leads us to the conclusion that, on the one hand, there can be no fair representation — under our very weak conditions — as soon there are more than two constituencies or more than two parties, but on the other hand, a two by two situation can always be fairly represented. As these results are mainly negative, we go on to a second model and we give a necessary and sufficient condition for the existence of a biproportional delegation.

The Problem of Representation Based Upon two Criteria

Abstract The problem considered here is that of electing a delegation when the population of electors is separated into categories, the division being based uoon one or several criteria. A two criteria-based situation currently exists in the Netherlands. Using a slightly more general version of this system, we proved that the only tyne of situation avoiding imDossibi lities is one where each criterion only presents two alternatives. Furthermore, setting a number of conditions, as weak as possible, which must be respected in order to ensure fair representation, the same result remains - which is not so surprising as it could have been suggested by Arrows famous theorem.

Problems of equity in political representation (what we want and why we can't.)

In the frame of social choice, in the aggregation of preferences and more particularly in voting theory, we present two approaches of mathematical modelisation towards political representation. Together they lead, in Section 4, to a sketch of what is, in our sense, the nature, the ideal shape and the most common misuses of real-world modelisation, in particular, its mathematical modelisation.