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. 2 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. Collections: Mathematics