P.P. Wakker's Additive Representations of Preferences: A New Foundation of PDF

By P.P. Wakker

ISBN-10: 9048140366

ISBN-13: 9789048140367

ISBN-10: 940157815X

ISBN-13: 9789401578158

`This ebook represents a truly actual and significant contribution to the maths of selection thought.
The distinguishing characteristic of Wakker's technique is that he has little need of a reference experiment.
There are extra effects aplenty and lots more and plenty for the choice theorist to reflect on. those effects also will support psychologists, economists and others formulate and try types of decision-making behaviour.
by means of any criteria its book is a landmark ... first-class survey and precis of the literature on additive choice versions. every one web page represents the distillation of a lot proposal. thus, it's a booklet that rewards analyzing and rereading. Wakker's effects and techniques of evidence will enlighten study into determination conception for plenty of years.'
British magazine of Mathematical and Statistical Psychology, forty three, 1990

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Get Additive Representations of Preferences: A New Foundation of PDF

`This booklet represents a really actual and critical contribution to the math of determination concept. The distinguishing function of Wakker's technique is that he has little need of a reference test. There are extra effects aplenty and masses for the choice theorist to give some thought to. those effects also will support psychologists, economists and others formulate and try types of decision-making behaviour.

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Extra resources for Additive Representations of Preferences: A New Foundation of Decision Analysis

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Let Xj = Yj for all essential j. If no coordinate is inessential then x = y, so X Pd Y by reflexivity of Pd. Now let there be k inessential coordinates, say {l, ... ,k}, with k> O. 2Yl,y2) Pd ... •k}(yl' ... 'yk) = y. By transitivity of Pd we get x Pd y. From this also follows that ~ is trivial whenever all coordinates are inessential. Conversely, if ~ is trivial, then X_jVj Pd X_jWj for all X_jVj' X_jWj so that every coordinate j is inessential. o The above lemma shows that inessential coordinates may just as well be suppressed.

6 will show that, for a (connected-topology-) continuous weak order, the condition that no coordinate reveals contradictory tradeoffs is not only necessary for additive representability, but also sufficient. This shows that the binary relations >-~. and ~~ will primarily be of use for additively representable preference relations. 2. A final comment on our use of the term tradeoff. Say n=2, r l =r2=IR, x=(2,3), y=(l,4), and x >y. Then in multiattribute utility theory the term tradeoff is used for the exchange of the 'gain' [xI;YI] for the loss [x2;Y2]' which may be called a (favourable) tradeoff.

Xi+l for all 0 ~ i ~ m-l, so that xk ~. all 0 ~ k < t :s m, in particular x ~. y. Were now y ~. x' for all 0 :s k:s t:s m, contradicting xiPxi+l. So x >.. y, and ,... must extend P. For the demonstration of (vi) => (ii), suppose xPy. Then xPy, so by (vi) not yRx, and (ii) follows. For (i) => (vi), first note that by (i), xPy implies, by the furthermore-statement, that not yRx. Since xPy => xRy always holds true, [xPy) => [xRy and not yRx) follows. To establish the reversed implication, suppose that [xRy and not yRx).

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Additive Representations of Preferences: A New Foundation of Decision Analysis by P.P. Wakker


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