Decision Making Structures: Dealing with Uncertainty within by Dr. Mario S. Catalani, Dr. Giuseppe F. Clerico (auth.) PDF

By Dr. Mario S. Catalani, Dr. Giuseppe F. Clerico (auth.)

This e-book is the cuhnination of a long time' learn encouraged by way of the pioneering and seminal works of Sah and Stiglitz. We gratefully recognize the impression of those authors, whose principles and contributions have introduced us jointly in this collabo­ ration, regardless of our divergent medical backgrounds (while Catalani is drawn to quantitative equipment, Clerico is a non-quantitative economist) . We thank the Editor of the Rivista Internazionale di Scienze Economiche e Commerciali for permission to exploit a little bit converted models of papers released in that evaluate (they are the content material of Chapters I and III of half I, and of bankruptcy I of half II). We heartily thank Ms. Laura McLean for conscientiously revising our English. The ebook of this ebook has been made attainable by means of a supply from the dep. of Economics, college of Turin, Italy. Torino, July 1995 Mario S. Catalani Giuseppe F. CIeri co CONTENTS creation 1 half I a few types of choice making constructions I. How and whilst unanimity is an excellent selection rule 15 II. Majority ideas and potency of the choice strategy 31 III. crew cooperation vs. self sufficient evaluation forty-one IV. management and dependence fifty nine V. the choice making technique of political organisations seventy five half II Pyramid selection constructions I. Pyramidal buildings: a initial observe ninety one II. different homes of pyramids 103 III. Pyramids and dependence 117 IV. association, loyalty, and potency 133 Conclusions 151 References 163 Mario S.

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Then 3 apI ap' = 12p [p(1 - a2 pT ap~,3 = 12p {-2(1 = 12p(1 - p) p) 2 - r 2 (1 - r) ] , p)p + (1 - p)2 [1 - + '"'( [2r(1 - r) - r2] } 3p + 2'"'(2 - 3'"'(3(1- p)] . When p = 0 then p = 0 and the second derivative is equal to zero. The same is true when p = 1. Now consider 0 < p < 1. Set 56 Then ag ap Po O'er,co g(O) = 1 + 2'l- 3'l = (1 - 1')(1 + l' + 31'2), g(l) = -2 + 21'2 = -2(1 - 1'2). Let P < 1/2. Then 0:::; l' Let CatalAn a COOPERATION < 1, and g(O) > 0, g(l) < o. Furthermore 3 3 = -3+31' = -3(1-1' ) < O.

The firm owner has n collaborators. Let's assume that each them has the same probability of developing a good idea, called probability p. We assume that if the collaborators work together, one of them will emerge as leader. Furthermore if they are working cooperatively, the leader will influence the other collaborators, who are otherwise independent in their decision process. We model this influence as follows. Given that the leader has accepted a good project, the probability that any other collaborator will accept it is 15 > p.

I 51 COOPERATION Clerico Analogously P~n = Pr[Al n A2 n ... n A n- 1 n L] = Pr[A1 n A2 = pn-lp, n ... , For generic n and k, using the laws of probability we get P~k = L . n-l( n -)l · j=k r1(1 - J + n-l L rt- . 1- 1 ( n-l ) . n _ . P-l(1 - j=k J (1 - p)+ . pt-1p + pn-lp. Using the binomial relation and making a change of variable the former relation becomes On the other hand 52 COOPERATION For p = p, P~k r =p and L P~k = n-l . k J= ( = P~,k' Catalani as it must be. In fact, when p = p, Clerico then ) n -:- 1 p1(1 _ p)n- j J Another property of P;:, is the following: k p = 1 =?

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