By P.P. Wakker
`This publication represents a really genuine and demanding contribution to the maths of selection concept.
The distinguishing characteristic of Wakker's process is that he has no use of a reference experiment.
There are extra effects aplenty and masses for the choice theorist to examine. those effects also will aid psychologists, economists and others formulate and attempt versions of decision-making behaviour.
by means of any criteria its booklet is a landmark ... very good survey and precis of the literature on additive choice types. each one web page represents the distillation of a lot idea. in this case, it's a publication that rewards studying and rereading. Wakker's effects and strategies of evidence will enlighten study into choice idea for lots of years.'
British magazine of Mathematical and Statistical Psychology, forty three, 1990
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Additional info for Additive Representations of Preferences: A New Foundation of Decision Analysis
This case is somewhat outside the main interest of this monograph; hence no proof will be given rC5. 6. Let Y be a connected separable topological space. For a binary relation ~' on Y the following two statements are equivalent: (i) There exists a continuous representing function V' : Y (ii) The binary relation ~' -> IR. is a continuous weak order. 6). The function V' in (i) above is continuously ordinal. o For the sake of easy reference we write out the following corollary of the above theorem.
X ~ y: x gives at least as much output as y. See Shephard(l970}. 4. Dynamic applications Here x is a consumption/production path, stream of income, etc. Every i indicates a point of time, Xj is the consumption/production/income at point of time L See Koopmans( 1972}. 5. Welfare theory Here x is an allocation or social situation, I is a society or group of agents/players, every i E I is an agent/player, and Xj indicates the wealth or utility for agent i under allocation x. See Harsanyi(1955}. 6.
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. In the sequel we will sometimes do so. The conditions for binary relations introduced below will be assumed, or implied by other assumptions, throughout this monograph, with the exception of Chapter VI.
Additive Representations of Preferences: A New Foundation of Decision Analysis by P.P. Wakker