We show that every additively representable comparative probability ordering is determined by at least n-1 binary subset comparisons. We show that there are many orderings of this kind, not just the lexicographic ordering. These provide answers to two questions of Fishburn.
Keywords. Additively representable linear orders, comparative probability, subjective probability, subset comparisons
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Authors addresses:
Robin Christian
Deoartment of Mathematics
The University of Auckland
Private Bag 92019
Auckland
Arkadii Slinko
Deoartment of Mathematics
The University of Auckland
Private Bag 92019
Auckland
E-mail addresses:
| Robin Christian | rchr019@math.auckland.ac.nz |
| Arkadii Slinko | slinko@math.auckland.ac.nz |