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Partitioneditcount: Naïve extensional reasoning in conditional probability judgment
 Journal of Experimental Psychology: General
, 2004
"... The authors provide evidence that people typically evaluate conditional probabilities by subjectively partitioning the sample space into n interchangeable events, editing out events that can be eliminated on the basis of conditioning information, counting remaining events, then reporting probabiliti ..."
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Cited by 10 (5 self)
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The authors provide evidence that people typically evaluate conditional probabilities by subjectively partitioning the sample space into n interchangeable events, editing out events that can be eliminated on the basis of conditioning information, counting remaining events, then reporting probabilities as a ratio of the number of focal to total events. Participants ’ responses to conditional probability problems were influenced by irrelevant information (Study 1), small variations in problem wording (Study 2), and grouping of events (Study 3), as predicted by the partition–edit–count model. Informal protocol analysis also supports the authors ’ interpretation. A 4th study extends this account from situations where events are treated as interchangeable (chance and ignorance) to situations where participants have information they can use to distinguish among events (uncertainty). People are often called on to make judgments of conditional likelihood. For example, a patient might try to assess the likelihood of having a disease, given a positive test result; a litigant might try to estimate the odds of prevailing in court, given a piece of damning evidence. Over the last 30 years, psychologists have shown that people typically judge conditional probabilities using a
On the Emergence of Reasons in
"... We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating finite predicate knowledge bases as potentially infinite propositional knowledge bases. It is shown that for a range of predicate knowled ..."
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We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating finite predicate knowledge bases as potentially infinite propositional knowledge bases. It is shown that for a range of predicate knowledge bases (such as those typically associated with inductive reasoning) and several key propositional inference processes (in particular the Maximum Entropy Inference Process) this procedure is well defined, and furthermore yields an explanation for the validity of the induction in terms of `reasons'. Keywords: Inductive Logic, Probabilistic Reasoning, Abduction, Maximum Entropy, Uncertain Reasoning. 1 Motivation Consider the following situation. I am sitting by a bend in a road and I start to wonder how likely it is that the next car which passes will skid on this bend. I have some knowledge which seems relevant, for example I know that if there is ice on the road then there is a good chance of a skid, and similarly if the bend is unsigned, the camber adverse, etc.. I possibly also have some knowledge of how likely it is that there is ice on the road, how likely it is that the bend is unsigned (possibly conditioned on the iciness of the road) etc.. Notice that this is generic knowledge which applies equally to any potential passing car.
Flippable Pairs and Subset Comparisons in Comparative Probability Orderings and Related Simple Games, The Centre for Interuniversity Research in Qualitative Economics (CIREQ), Cahier 152006
, 2006
"... Abstract. We show that every additively representable comparative probability order on n atoms is determined by at least n − 1 binary subset comparisons. We show that there are many orders of this kind, not just the lexicographic order. These results provide answers to two questions of Fishburn et a ..."
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Abstract. We show that every additively representable comparative probability order on n atoms is determined by at least n − 1 binary subset comparisons. We show that there are many orders of this kind, not just the lexicographic order. These results provide answers to two questions of Fishburn et al (2002). We also study the flip relation on the class of all comparative probability orders introduced by Maclagan. We generalise an important theorem of Fishburn, Pekeč and Reeds, by showing that in any minimal set of comparisons that determine a comparative probability order, all comparisons are flippable. By calculating the characteristics of the flip relation for n = 6 we discover that the polytopes associated with the regions in the corresponding hyperplane arrangement can have no more than 13 facets and that there are 20 regions whose associated polytopes have 13 facets. All the neighbours of the 20 comparative probability orders which correspond to those regions are representable. AMS classification: 60A05, 91B08 (primary), 06A07, 91A12, 91E99 (secondary)
On the Existence of Extremal Cones and Comparative Probability Orderings
"... We study the recently discovered phenomenon [1] of existence of comparative probability orderings on finite sets that violate Fishburn hypothesis [2, 3] — we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on the set ..."
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We study the recently discovered phenomenon [1] of existence of comparative probability orderings on finite sets that violate Fishburn hypothesis [2, 3] — we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on the set of n = 7 elements and showed that no extremal cones exist on the set of n ≤ 6 elements. In this paper we construct an extremal cone on a finite set of prime cardinality p if p satisfies a certain number theoretical condition. This condition has been computationally checked to hold for 1,725 of the 1,842 primes between 132 and 16,000, hence for all these primes extremal cones exist.
A Characterization of the Language Invariant Families satisfying Spectrum Exchangeability in Polyadic Inductive Logic
, 2008
"... A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap ..."
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A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and NixParis Continua.
On Probabilistic Parametric Inference
, 2008
"... An objective operational theory of probabilistic parametric inference is formulated without invoking the socalled noninformative prior probability distributions. ..."
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An objective operational theory of probabilistic parametric inference is formulated without invoking the socalled noninformative prior probability distributions.