Independence, Additivity, Uncertainty

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Springer Science & Business Media, Jan 17, 2003 - Business & Economics - 277 pages
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The work on this book started many years ago as an attempt to simplify and unify some results usually taught in courses in mathematical economics. The economic interpretation of the re sults were representations of preferences as sums or integrals and the decomposition of preferences into utilities and probabilities. It later turned out that t.he approach taken in the earlier versions were also the proper approach in generalizing from preferences which were total preorders to preferences which were not total or tran sitive. The same mathematics would even in that situation give representations which were additive. It would also give decomposi tions where concepts of uncertainty appeared. Early versions of some of the results appeared as Working Pa pers No. 135, 140, 150, and 176 from The Center for Research in Management Science, Berkeley. A first version of chapters 2, 4, 6, 7, and 8 appeared 1969 with the title" Mean Groupoids" [177]. They are essentially unchanged -except for some notes especially in chapter 6. Another version appeared 1990 as [178]. Chapter 10 contains results from the same versions and from [181]. Chapter 11 by Birgit Grodal is based on [91] by Grodal and Jp,an-Francois Mertens. Chapters 11 and 12 - also by Birgit Gro dal -contains the results from the earlier versions, but have been extended (by Karl Vind) to take into account the new corollaries of the results in the other chapters.
 

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Contents

I
1
II
2
III
4
IV
6
V
7
VI
9
VII
14
VIII
16
LXXIV
123
LXXV
124
LXXVI
126
LXXVIII
128
LXXIX
131
LXXX
133
LXXXI
135
LXXXII
136

IX
18
X
20
XI
23
XIII
24
XVI
25
XIX
27
XX
29
XXI
31
XXII
33
XXIII
37
XXIV
38
XXV
39
XXVI
40
XXVIII
43
XXIX
45
XXX
49
XXXI
52
XXXII
54
XXXIII
57
XXXIV
59
XXXV
60
XXXVI
61
XXXIX
62
XLII
63
XLIV
65
XLV
69
XLVI
70
XLVII
73
XLVIII
77
L
78
LI
81
LII
83
LIII
85
LIV
87
LV
88
LVI
91
LVII
95
LVIII
97
LIX
98
LXI
102
LXII
103
LXIII
106
LXIV
107
LXV
108
LXVI
113
LXVII
115
LXVIII
116
LXIX
117
LXX
118
LXXI
119
LXXII
120
LXXIII
121
LXXXIII
137
LXXXIV
138
LXXXV
140
LXXXVI
144
LXXXVII
147
LXXXVIII
149
LXXXIX
152
XC
159
XCI
164
XCII
165
XCIII
169
XCIV
170
XCV
174
XCVI
177
XCVII
183
XCVIII
187
XCIX
189
C
190
CI
192
CII
193
CIII
194
CIV
195
CVII
196
CVIII
197
CX
198
CXII
199
CXIII
201
CXIV
203
CXV
206
CXVI
213
CXVII
215
CXVIII
220
CXX
221
CXXI
222
CXXII
223
CXXIII
225
CXXIV
227
CXXV
228
CXXVII
229
CXXVIII
231
CXXIX
232
CXXX
235
CXXXI
237
CXXXII
240
CXXXIII
243
CXXXIV
244
CXXXV
247
CXXXVIII
248
CXXXIX
252
CXL
253
CXLI
269
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Page iv - grant from the Ford Foundation to the Graduate School of Business Administration, University of California, Berkeley, and

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