Decisive Rules Research Articles

Classification of windstorms over France

A method of semi-automated classification of windstorms over France is proposed, in order to provide insurance companies with meteorological statistical values, that could lead to an evaluation of storm risks. Because not all storm events have the same origins or the same features, and do not always hit the same regions, a classification is necessary in order to assemble storm events with meteorological and geographical similarities. The classification is based on the expert knowledge of a weather forecaster, who first analyses 44 storm events and draws out the meteorological features of different types of storm. Afterwards, the results of the human typology are automated by determining decisive rules with criteria, which are calculated with only observed meteorological surface data over France. The automation of the human typology is obtained by taking into account the main results of statistical methods such as objective classification or discrimination and by validating them with physical considerations. We thus succeed in formulating the reasoning of the expert. The classification is then applied to the Météo-France records since 1962. We succeed in selecting 524 storm events and in classing them into seven main types, with enough events in each class to calculate statistical values. © 1998 Royal Meteorological Society

Structural instability of decisive majority rules

We study social aggregation rules that satisfy a Pareto and a decisive majority condition. A rule satisfies the decisive majority condition if whenever the voters can be divided into two internally homogeneous groups (i.e. groups within which all individuals agree about all possible choices) and these groups have opposite preferences, then the majority's preference is respected. No assumptions are made about the outcome when the individuals have more than two different preferences even when a majority agrees on a choice x being preferable to another y. Therefore a decisive majority condition does not imply, i.e., is strictly weaker than, majority rules. The main result is that Pareto decisive majority rules are necessarily structurally unstable, in the sense that the outcome preference, which is a vector field, will undergo major changes in structure in response to small changes in the underlying parameters. The importance of structural instability derives from the fact that small errors of observation will lead to drastically different answers. An example of the result for three voters and with a two-dimensional choice space is also given.