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Three contrasts between two senses of coherence Teddy Seidenfeld

Summary: 1
Three contrasts between two senses of coherence
Teddy Seidenfeld
joint work with M.J.Schervish and J.B.Kadane Statistics, CMU
Call an agent's choices coherent when they respect simple dominance
relative to a (finite) partition.
= { 1, ..., n} is a finite partition of the sure event: a set of states.
Consider two acts A1, A2 defined by the their outcomes relative to .
1 2 3 ... n
A1 o11 o12 o13 ... o1n
A2 o21 o22 o23 ... o2n
Suppose the agent can compare the desirability of different outcomes at least
within each state, and, for each state j, outcome o2j is (strictly) preferred to
outcome o1j, j = 1, ..., n. Then A2 simply dominates A1 with respect to .
Coherence: When A2 simply dominates A1 in some finite partition, then A1
is inadmissible in any choice problem where A2 is feasible.
Background on de Finetti's two senses of coherence
De Finetti (1937, 1974) developed two senses of coherence (coherence1 and
coherence2), which he extended also to infinite partitions.


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics