Unacceptable risks and the continuity axiom
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Unacceptable risks and the continuity axiom. / Jensen, Karsten Klint.
I: Economics and Philosophy, Bind 28, Nr. 1, 2012, s. 31-42.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › fagfællebedømt
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TY - JOUR
T1 - Unacceptable risks and the continuity axiom
AU - Jensen, Karsten Klint
PY - 2012
Y1 - 2012
N2 - Consider a sequence of outcomes of descending value, A > B > C > . . . > Z. According to Larry Temkin, there are reasons to deny the continuity axiom in certain ‘extreme’ cases, i.e. cases of triplets of outcomes A, B and Z, where A and B differ little in value, but B and Z differ greatly. But, Temkin argues, if we assume continuity for ‘easy’ cases, i.e. cases where the loss is small, we can derive continuity for the ‘extreme’ case by applying the axiom of substitution and the axiom of transitivity. The rejection of continuity for ‘extreme’ cases therefore renders the triad of continuity in ‘easy’ cases, the axiom of substitution and the axiom of transitivity inconsistent. As shown by Arrhenius and Rabinowitz, Temkin's argument is flawed. I present a result which is stronger than their alternative proof of an inconsistency. However, this result is not quite what Temkin intends, because it only refers to an ordinal ranking of the outcomes in the sequence, whereas Temkin appeals to intuitions about the size of gains and losses. Against this background, it is argued that Temkin's trilemma never gets off the ground. This is because Temkin appeals to two mutually inconsistent conceptions of aggregation of value. Once these are clearly separated, it will transpire, in connection with each of them, that one of the principles to be rejected does not appear plausible. Hence, there is nothing surprising or challenging about the result; it is merely a corollary to Expected Utility Theory.
AB - Consider a sequence of outcomes of descending value, A > B > C > . . . > Z. According to Larry Temkin, there are reasons to deny the continuity axiom in certain ‘extreme’ cases, i.e. cases of triplets of outcomes A, B and Z, where A and B differ little in value, but B and Z differ greatly. But, Temkin argues, if we assume continuity for ‘easy’ cases, i.e. cases where the loss is small, we can derive continuity for the ‘extreme’ case by applying the axiom of substitution and the axiom of transitivity. The rejection of continuity for ‘extreme’ cases therefore renders the triad of continuity in ‘easy’ cases, the axiom of substitution and the axiom of transitivity inconsistent. As shown by Arrhenius and Rabinowitz, Temkin's argument is flawed. I present a result which is stronger than their alternative proof of an inconsistency. However, this result is not quite what Temkin intends, because it only refers to an ordinal ranking of the outcomes in the sequence, whereas Temkin appeals to intuitions about the size of gains and losses. Against this background, it is argued that Temkin's trilemma never gets off the ground. This is because Temkin appeals to two mutually inconsistent conceptions of aggregation of value. Once these are clearly separated, it will transpire, in connection with each of them, that one of the principles to be rejected does not appear plausible. Hence, there is nothing surprising or challenging about the result; it is merely a corollary to Expected Utility Theory.
U2 - 10.1017/S0266267112000107
DO - 10.1017/S0266267112000107
M3 - Journal article
VL - 28
SP - 31
EP - 42
JO - Economics and Philosophy
JF - Economics and Philosophy
SN - 0266-2671
IS - 1
ER -
ID: 40978275