By Andranick S. Tanguiane
ISBN-10: 3642765165
ISBN-13: 9783642765162
ISBN-10: 3642765181
ISBN-13: 9783642765186
Aggregation is the conjunction of knowledge, aimed toward its compact represen tation. Any time whilst the totality of knowledge is defined by way of basic ized signs, traditional counts, regular representatives and attribute dependences, one at once or in a roundabout way bargains with aggregation. It comprises revealing the main major features and particular gains, quanti tative and qualitative research. accordingly, the data turns into adaptable for additional processing and handy for human belief. Aggregation is regularly occurring in economics, facts, administration, making plans, process research, and plenty of different fields. this is the reason aggregation is so very important in facts seasoned cessing. Aggregation of personal tastes is a specific case of the final challenge of ag gregation. It arises in multicriteria decision-making and collective selection, whilst a collection of possible choices needs to be ordered with recognize to contradicting standards, or a number of person critiques. even though, even with obvious similarity the issues of multicriteria decision-making and collective selection are just a little varied. certainly, an development in a few requirements on the expense of aggravate ing others isn't the related because the pride of pursuits of a few members to the bias 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 self reliant participants. additionally, in multicriteria decision-making one usu best friend takes under consideration goal components, while in collective selection one has to check subjective evaluations 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
This implies that the number of jumps cannot exceed the cardinality of the base. We show that condition 4 implies condition 2. Define 5 to consist of the points of a dense countable subset of X, the endpoints of empty intervals, and also the first and the last elements of X, if there are any in X. By condition 4 set 5 is countable, and we can index it by positive integers: 5= {Sl,S2, •• • }. We shall construct a mapping f(d) of some subset D of dyadic rational points in the interval (0; 1) onto the set 5.
M - 1 we proceed as follows. If there is that S E S such then we choose it to have the minimal index in S and put otherwise we exclude from DnH all the points between dm and dmH . If there is S E S such that f(d M ) -< s, then we choose it to have the minimal index in S and put otherwise exclude from Dn+1 all the points greater than dM. We form Dn+1 from the points of the DnH left after these exclusions together with the points of Dno The order-preserving mapping f : DnH --t S is defined at the present and all previous inductive steps.
With regard to the limited accuracy of measurement and perception, only partial orders meet the idea of preference in a strict sense, whereas weak and strict orders should be regarded as certain idealizations of real preferences. However, the use of weak and strict orders is justified by the fact that they can be represented by goal functions, in contrast to partial orders, whose numerical representations are much more complex (Fishburn 1970b). When a preference order is represented by a goal function, decision-making becomes an optimization problem-the search for maxima of the given goal function under the restrictions, corresponding to budget, resources, technology, etc.
Aggregation and Representation of Preferences: Introduction to Mathematical Theory of Democracy by Andranick S. Tanguiane
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