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Download Aggregation and Representation of Preferences: Introduction by Andranick S. Tanguiane PDF

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By Andranick S. Tanguiane

Aggregation is the conjunction of data, geared toward its compact represen­ tation. Any time whilst the totality of knowledge is defined by way of normal­ ized signs, traditional counts, regular representatives and attribute dependences, one without delay or in a roundabout way offers with aggregation. It comprises revealing the main major features and detailed positive aspects, quanti­ tative and qualitative research. accordingly, the knowledge turns into adaptable for additional processing and handy for human notion. Aggregation is known in economics, information, administration, making plans, procedure research, and plenty of different fields. because of this aggregation is so very important in info seasoned­ cessing. Aggregation of personal tastes is a selected case of the final challenge of ag­ gregation. It arises in multicriteria decision-making and collective selection, while a collection of possible choices should be ordered with admire to contradicting standards, or numerous person evaluations. besides the fact that, despite obvious similarity the issues of multicriteria decision-making and collective selection are a little various. certainly, an development in a few requisites on the expense of aggravate­ ing others isn't the comparable because the delight of pursuits of a few contributors to the unfairness of the remainder. within the former case the reciprocal compensations are thought of inside of a definite entirety; within the latter we infringe upon the rights of self reliant members. furthermore, in multicriteria decision-making one usu­ best friend takes under consideration target components, while in collective selection one has to match subjective evaluations which can't be measured properly.

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

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7. EXAMPLE. The relation "to be greater than" on of the set of real numbers R is a strict order, consequently, a preference. In our designations it can be written down as P = {(x, y) : (x, y) E R X R, x> y}, and the dual relation "to be greater or equal" (which is a linear order) can be written down as R = {(x,y) : (x,y) E R x R, x 2: y}. This example is illustrated in fig. 22. 8. EXAMPLE. Let R be the set of real numbers and P be the relation, which distinguishes sufficiently remote points: P = {(x,y) : (x,y) E R X R, x> Y + 1} (fig.

It is easy to see that such trees always consist of n - 1 pairs. Further, every ratio G;jGj can be determined by the conditions of compensation of utilities for ith and jth individuals only. In other words, we use the indifference curves, which are the level curves of the goal function for the coalition of ith and jth individuals, given by the sum GiUi + GjUj. Similar reasons are also valid for the construction of the additive goal function, which is nothing else but a weighted sum of individual utilities with variable weight coefficients.

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