Aggregation and Representation of Preferences: Introduction to Mathematical Theory of Democracy - Hardcover

Tanguiane, Andranick S.

Hardcover

ISBN 10: 3540538453 ISBN 13: 9783540538455

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1991

Synopsis

Aggregation is the conjunction of information, aimed at its compact represen- tation. Any time when the totality of data is described in terms of general- ized indicators, conventional counts, typical representatives and characteristic dependences, one directly or indirectly deals with aggregation. It includes revealing the most significant characteristics and distinctive features, quanti- tative and qualitative analysis. As a result, the information becomes adaptable for further processing and convenient for human perception. Aggregation is widely used in economics, statistics, management, planning, system analysis, and many other fields. That is why aggregation is so important in data pro- cessing. Aggregation of preferences is a particular case of the general problem of ag- gregation. It arises in multicriteria decision-making and collective choice, when a set of alternatives has to be ordered with respect to contradicting criteria, or various individual opinions. However, in spite of apparent similarity the problems of multicriteria decision-making and collective choice are somewhat different. Indeed, an improvement in some specifications at the cost of worsen- ing others is not the same as the satisfaction of interests of some individuals to the prejudice of the rest. In the former case the reciprocal compensations are considered within a certain entirety; in the latter we infringe upon the rights of independent individuals. Moreover, in multicriteria decision-making one usu- ally takes into account objective factors, whereas in collective choice one has to compare subjective opinions which cannot be measured properly.

About this title

Synopsis

This book is devoted to the revision of Arrow's paradox in social choice about the inconsistency of several natural assumptions. Two ways of overcoming the paradox are considered. The traditional approach, suggesting rejection of one of the axioms of social choice, is studied on two different models, and new concept of representativeness is introduced. It is shown that the concept of a dictator in Arrow's model is understood in an extended way, since certain dictators are representatives of the collective rather than dictators in a proper sense. Therefore, the prohibition of dictatorship should be refined, after which Arrow's axioms become consistent. The concept of representativeness is also applied to limited groups of individuals, making decisions on behalf of the whole collective-cabinets (multidictatorial representations with delimited competence, named by analogy with cabinets of ministers), and councils, making decisions by means of voting. The consideration has evident parallels with the three forms of political power: the president, the government, and the parliament.

The proposed approach to the problem contributes to the substantiation of such an indirect way of realizing collective will as giving powers to elected representatives, used in all democratic systems.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1991
• Language: English
• ISBN 10: 3540538453
• ISBN 13: 9783540538455
• Binding: Hardcover
• Number of pages: 331