Template-type: ReDif-Paper 1.0
Author-Name: Mackenzie, Andrew
Author-workplace-name: Microeconomics & Public Economics, RS: GSBE ETBC
Title: A foundation for probabilistic beliefs with or without atoms
Abstract: We provide sufficient conditions for a qualitative probability (Bernstein, 1917; de Finetti, 1937; Koopman, 1940; Savage, 1954) that satisfies monotone continuity (Villegas, 1964; Arrow, 1970) to have a unique countably additive measure representation, generalizing Villegas (1964) to allow atoms. Unlike previous contributions, we do so without a cancellation or solvability axiom.<br/>First, we establish that when atoms contain singleton cores, unlikely cores—the requirement that the union of all cores is not more likely than its complement—is sufficient (Theorem 3). Second, we establish that strict third-order atom-swarming—the requirement that for each atom A, the less likely non-null events are (in an ordinal sense) more than three times as likely as A—is also sufficient (Theorem 5). This latter result applies to intertemporal preferences over streams of indivisible objects.<br/>
Classification-JEL: d83,d81
Series: GSBE Research Memoranda
Creation-Date: 20180508
Number: 013
File-URL: https://cris.maastrichtuniversity.nl/ws/files/26038116/RM18013.pdf
File-Format: application/pdf
File-Size: 7985165
Handle: Repec:unm:umagsb:2018013
DOI: 10.26481/umagsb.2018013