By P.P. Wakker
`This ebook represents a truly actual and critical contribution to the maths of determination thought.
The distinguishing function of Wakker's procedure is that he has little need of a reference experiment.
There are additional effects aplenty and lots more and plenty for the choice theorist to think of. those effects also will support psychologists, economists and others formulate and attempt versions of decision-making behaviour.
via any criteria its e-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 idea. accordingly, it's a publication that rewards analyzing and rereading. Wakker's effects and techniques of evidence will enlighten examine into choice concept for plenty of years.'
British magazine of Mathematical and Statistical Psychology, forty three, 1990
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Additional resources for Additive Representations of Preferences: A New Foundation of Decision Analysis
7. Let ~ ~i' ~i ~ is weakly separable. Yi if there exists an alternative v such Rli the symmetric part, and ~i and -< i be a weakly separable weak order. Then lor all i, Xi' Yi: Yi] <=> [v-iXi ):: V -iYi lor lill. alternatives v] . [Xi ~i ~i is a weak order. [Xi >1 Yi] <=> [there exists an alternative v such that v_ixi > v-iYi] <=> [v-ixi > V -iYi lor all alternatives v] . [Xi Rli Yi] <=> [there exists an alternative v such that v -ixi [v-ixi RI V -iYi lor all alternatives v] . ~ is weakly and strongly monotonic with respect to (~J')' n J=l RI v -iYi] <=> • o The derivation of these results is straightforward, and left to the reader.
1. CARTESIAN PRODUCT STRUCTURE, EXAMPLES In this section we introduce on X, the set of alternatives, the main structure of interest in this monograph. We shall assume throughout the sequel that X is a Cartesian product njdrj, with I an index set. We shall nearly always, with Chapter V excepted, assume that I is a finite set (l, ... ,n}, for n E IN. Many definitions and results of this chapter are as well applicable to infinite index sets I. The idea is that every alternative is described by a list of properties, indexed by I.
An example of an act is x = (5,-3,-1), indicating an act (or 'gamble', as the usual term in this context is) which will leave the decision maker with xl = $5 if the first horse will win, x2 = $-3 if the second horse will win, and Xs = $-1 if the third horse will win. , which state is true). See Savage(1954}, or Dreze(l987,Chapter I}. 2. , the decision maker) thinks x is at least as good as y. See Katzner(l970}. 3. Producers theory Here x is an input vector, i indicates a production (actor, Xj is the input (rate) of production factor LV: Hdrj -+ IR is a production function, assigning to every x the (maximally attainable, one-dimensional) output V(x}.