By Patrick Suppes (auth.), James Leach, Robert Butts, Glenn Pearce (eds.)
ISBN-10: 9027703272
ISBN-13: 9789027703279
ISBN-10: 9401025711
ISBN-13: 9789401025713
Read Online or Download Science, Decision and Value: Proceedings of the Fifth University of Western Ontario Philosophy Colloquium, 1969 PDF
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Extra resources for Science, Decision and Value: Proceedings of the Fifth University of Western Ontario Philosophy Colloquium, 1969
Example text
The desired positive addition to Rule A can now be given by reference to an action's optimality; and Rule AB, incorporating this addition can be stated in the form that, if Luke is certain that Matthew is playing in such a game and has such a preference system that Ms is inadmissible and M t is optimal in that game and for that preference system, then Luke must not allow for the possibility of Matthew's choosing Ms and must allow for the possibility of his choosing M t • Luke's following Rule AB instead of Rule A will not affect Luke's credal sets when only Matthew's monadic games are concerned.
So [,ul], [,u2]' ... [,urn] cannot be the fundamental 2 3 )It 1 03 02 )It D, )It 1\ .. ;j > ~ - = ~ ~ 0\ W BEHIND DECISION AND GAMES THEORY 37 credal sets in Luke's game if he is genuinely playing a game with Matthew. The fact that in Luke's game with Matthew [Jll]' for example, cannot be a fundamental credal set by no means prevents it from being a credal set. I shall be explaining two rules to be used for determining what are to be fundamental credal sets in a game with a person, and in both of these the set (Jll] will appear as the credal set of a certainty of a proposition in the relevant decomposition.
G. L l , L 2, one or other of three alternatives, taken to be exclusive and exhaustive: (1) that Luke would prefer to do Ll rather than to do L2 were ms to be true, (2) that Luke would prefer to do L2 rather than Ll were ms to be true, (3) that Luke would prefer neither action to the other were ms to be true; with the added qualification in all three cases that his preference or lack of preference would be unaffected if a conjunction of ms with any proposition logically consistent with it and satisfying two minor conditions (to exclude Jeffrey's cases and iterated credal modalities) were substituted for ms.
Science, Decision and Value: Proceedings of the Fifth University of Western Ontario Philosophy Colloquium, 1969 by Patrick Suppes (auth.), James Leach, Robert Butts, Glenn Pearce (eds.)
by Ronald
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