The name is absent



unique prior μ on the full state space, incorporating implicit probabilities for
unconsidered propositions. To generate a multiple priors model, it is natural
to suppose that there may be more than one such measure. An obvious way
to do this is to look at the measures induced conditional on the possible truth
values for one or more unconsidered propositions.

Considering any p' E P-, there are two induced measures on P'i. namely

and


μ+ (E (p))


μ (E (p)) =


μ (E (p Λ p'Y)
μ (E (p'))

.p E Pi


μ (E (p λ^√))     p

μ (E ⅛')) 'p E

For a proposition p' that is independent of Pг in the sense that, for all p E Pг

μ (E (p λ p')) = μ (E (p)) μ (E (p')) .

we have μ+ = μ since, for all p E Pг

μ+ (E (p))


μ (E (p λ p')) = μ (E (p)) μ (E (p'))

μ(E (p'))            μ(E (p'))

μ(E (p)) μ(E (^p')) = μ(E (p λ +'л = e
μ(E (^p'))           μ(E (^p'))      μ

In general, however, μ+E (p) = μ-E (p) . and consideration of probability
values for
p' in the range [0.1] gives rise to probabilities for p in the range
-E (p) . μ+E (p)] . Thus, we can define a set of priors

M (p') = {Λμ+ + (1 - - :0 A 1} .

The natural interpretation here is that each element of the set of multiple pri-
ors may be derived as a conditional probability measure, given a probability
number for the unconsidered proposition
p'. Thus p' has a status interme-
diate between propositions in
Pг that are under active consideration, and
unconsidered propositions in the case of restricted Bayesianism. Although
the decision-maker does not explicitly consider
p'. the range of multiple priors
corresponds to the probability measure that would arise if
p' were a consid-
ered proposition with probability
A.

For a more general version of the multiple priors model, let P* be a
set of unconsidered propositions, closed under
^ and Λ. and let Δ be the
unit simplex with dimension equal to
K = card (P*) . having typical element
λ=(A1..... Aκ) such that J^fe A= 1. For each pE P*. we have, as described

11



More intriguing information

1. Tariff Escalation and Invasive Species Risk
2. Licensing Schemes in Endogenous Entry
3. New urban settlements in Belarus: some trends and changes
4. WP 48 - Population ageing in the Netherlands: Demographic and financial arguments for a balanced approach
5. The Effects of Attendance on Academic Performance: Panel Data Evidence for Introductory Microeconomics
6. How to do things without words: Infants, utterance-activity and distributed cognition.
7. An Efficient Circulant MIMO Equalizer for CDMA Downlink: Algorithm and VLSI Architecture
8. A Unified Model For Developmental Robotics
9. Multifunctionality of Agriculture: An Inquiry Into the Complementarity Between Landscape Preservation and Food Security
10. Special and Differential Treatment in the WTO Agricultural Negotiations
11. ‘I’m so much more myself now, coming back to work’ - working class mothers, paid work and childcare.
12. The name is absent
13. Regional Intergration and Migration: An Economic Geography Model with Hetergenous Labour Force
14. The name is absent
15. Modelling Transport in an Interregional General Equilibrium Model with Externalities
16. Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment
17. The name is absent
18. Word searches: on the use of verbal and non-verbal resources during classroom talk
19. What Contribution Can Residential Field Courses Make to the Education of 11-14 Year-olds?
20. CREDIT SCORING, LOAN PRICING, AND FARM BUSINESS PERFORMANCE