By Andranick S. Tanguiane

ISBN-10: 3642765165

ISBN-13: 9783642765162

ISBN-10: 3642765181

ISBN-13: 9783642765186

Aggregation is the conjunction of data, aimed toward its compact represen tation. Any time while the totality of information is defined when it comes to normal ized symptoms, traditional counts, commonplace representatives and attribute dependences, one without delay or in a roundabout way offers with aggregation. It contains revealing the main major features and targeted positive aspects, quanti tative and qualitative research. consequently, the knowledge turns into adaptable for additional processing and handy for human conception. Aggregation is regularly occurring in economics, information, administration, making plans, approach research, and plenty of different fields. because of this aggregation is so very important in info professional cessing. Aggregation of personal tastes is a specific case of the overall challenge of ag gregation. It arises in multicriteria decision-making and collective selection, while a suite of choices needs to be ordered with admire to contradicting standards, or numerous person critiques. besides the fact that, despite obvious similarity the issues of multicriteria decision-making and collective selection are a bit diverse. certainly, an development in a few requirements on the price of aggravate ing others isn't the comparable because the pride of pursuits of a few participants to the unfairness of the remaining. within the former case the reciprocal compensations are thought of inside a definite entirety; within the latter we infringe upon the rights of autonomous participants. furthermore, in multicriteria decision-making one usu best friend takes under consideration aim elements, while in collective selection one has to check subjective reviews which can't be measured properly.

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**Additional resources for Aggregation and Representation of Preferences: Introduction to Mathematical Theory of Democracy**

**Example text**

Since axiom A4 supposes the existence of at least two situations, it is meaningless for fixed preferences. Axiom A5 implies that at least two arguments U;, Uj of the function f( Ut, ••. e. an increment of each implies the increment of the function. Since our consideration turns out to be trivial, we need additional assumptions for the analysis of the given model. We shall strengthen axiom A3 up to the Pareto principle, whence we shall deduce the strict monotonicy of the goal function f( Ul, ...

The interdependence of different properties of alternatives, caused by physical, econimical, or other constraints is also represented by restrictions. We can say that the desire is opposed to the reality-the goal function to the restrictions, and their interaction determines the optimal decision. Thus the problem of numerical representation of orderings is of considerable importance for practical purposes. On the other hand, numerical representations allow us to study preferences in habitual functional terms.

Y X3 {x: x E X,(y,x) E R} Fig. 27 which is obviously indifferent to y. The following propositions, proving the analogy between continuous orders and functions, are valid for weak orders only. 5. PROPOSITION (On Attaining Maxima and Minima on a Compactum). Let P be a continuous weak order on a compactum X and let R be dual to P. e. m,M E X such that (x,m) E Rand (M,x) E R for any x EX. e. PROOF. M(x) = {x': x' E X, (x', x) E R}, which is closed by continuity of P. We shall show that the family of sets M(x) has the finite intersection property.

### Aggregation and Representation of Preferences: Introduction to Mathematical Theory of Democracy by Andranick S. Tanguiane

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