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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. ; info:eu-repo/semantics/published

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.

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. ; info:eu-repo/semantics/published

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. ; info:eu-repo/semantics/published

From the literature on decentralization, it appears that the fiscal vertical imbalance (i.e. the dependence of sub-national governments on national government revenues to support their expenditures) is somehow inherent to multi-level governments. Using a stylized model we show that this leads to a reduction of the extent of redistributive fiscal policies if the maximal size of government has been reached. To test for this empirically, we use some high quality data from the LIS dataset on individual incomes. The results are highly significant and point in the direction of our theoretical predictions. [Copyright 2008 Elsevier B.V.]

From the literature on decentralization, it appears that the fiscal vertical imbalance is somehow inherent to multi-level governments. Using a stylized model we show that this leads to a reduction in the extent of redistributive fiscal policies if the maximal tolerable size of government has been reached. To test for this empirically we use some high quality data, from the LIS dataset, on individual incomes. The results are highly significant and point in the direction of our theoretical predictions.

This paper shows how decentralized election results can be used to understand patterns of electoral volatility. Comparing two elections, the model provides a lower bound of the share of voters lost by a party, and of the number of new voters that it managed to convince. The paper proposes a typology of electoral results based on the estimated parameters of the model. We argue that the model can be used to better understand the local specificities linked to the personalization of politics, to avoid errors linked to omitting the role of abstention, and that it also provides a simple tool for better during the fact prediction of electoral results. ; info:eu-repo/semantics/nonPublished