We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Probabilistic Opinion Pooling with Imprecise Probabilities.
- Authors
Stewart, Rush T.; Quintana, Ignacio Ojea
- Abstract
The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution (Madansky [<xref>44</xref>]; Lehrer and Wagner [<xref>34</xref>]; McConway <italic>Journal of the American Statistical Association, 76</italic>(374), 410–414, [<xref>45</xref>]; Bordley <italic>Management Science</italic>, 28(10), 1137–1148, [<xref>5</xref>]; Genest et al. <italic>The Annals of Statistics</italic>, 487–501, [<xref>21</xref>]; Genest and Zidek <italic>Statistical Science</italic>, 114–135, [<xref>23</xref>]; Mongin <italic>Journal of Economic Theory, 66</italic>(2), 313–351, [<xref>46</xref>]; Clemen and Winkler <italic>Risk Analysis, 19</italic>(2), 187–203, [<xref>7</xref>]; Dietrich and List [<xref>14</xref>]; Herzberg <italic>Theory and Decision</italic>, 1–19, [<xref>28</xref>]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with <italic>imprecise probabilities</italic> (IP) by employing <italic>set-valued</italic> pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi (<italic>Synthese, 62</italic>(1), 3–11, [<xref>39</xref>]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus.
- Subjects
PROBABILITY theory; DISTRIBUTION (Probability theory); DATA analysis; MATHEMATICAL models; CANONICAL coordinates
- Publication
Journal of Philosophical Logic, 2018, Vol 47, Issue 1, p17
- ISSN
0022-3611
- Publication type
Article
- DOI
10.1007/s10992-016-9415-9