Representing complete and incomplete subjective linear preferences on random numbers. (English) Zbl 1064.91031
Summary: We show that preferences on random numbers which satisfy certain natural properties can be represented, in the setting of topological vector spaces, by a suitable family of continuous previsions which is, in a sense, unique. Moreover, for most commonly used spaces of random numbers, we establish that one can derive these preferences, via an expectation operator, from a suitable family of probabilities (whether or not finitely additive).
MSC:
| 91B06 | Decision theory |
| 06A06 | Partial orders, general |
| 62C05 | General considerations in statistical decision theory |
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