EconPapers    
Economics at your fingertips  
 

Inferring probability comparisons

Matthew Harrison-Trainor, Wesley H. Holliday and Thomas F. Icard

Mathematical Social Sciences, 2018, vol. 91, issue C, 62-70

Abstract: The problem of inferring probability comparisons between events from an initial set of comparisons arises in several contexts, ranging from decision theory to artificial intelligence to formal semantics. In this paper, we treat the problem as follows: beginning with a binary relation ≿ on events that does not preclude a probabilistic interpretation, in the sense that ≿ has extensions that are probabilistically representable, we characterize the extension ≿+ of ≿ that is exactly the intersection of all probabilistically representable extensions of ≿. This extension ≿+ gives us all the additional comparisons that we are entitled to infer from ≿, based on the assumption that there is some probability measure of which ≿ gives us partial qualitative information. We pay special attention to the problem of extending an order on states to an order on events. In addition to the probabilistic interpretation, this problem has a more general interpretation involving measurement of any additive quantity: e.g., given comparisons between the weights of individual objects, what comparisons between the weights of groups of objects can we infer?

Keywords: Qualitative probability; Comparative probability; Imprecise representability; Sets of probability measures; Additive measurement (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0165489617301154
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:91:y:2018:i:c:p:62-70

Access Statistics for this article

Mathematical Social Sciences is currently edited by J.-F. Laslier

More articles in Mathematical Social Sciences from Elsevier
Series data maintained by Dana Niculescu ().

 
Page updated 2018-02-24
Handle: RePEc:eee:matsoc:v:91:y:2018:i:c:p:62-70