7 research outputs found
A Computational Theory of Subjective Probability
In this article we demonstrate how algorithmic probability theory is applied
to situations that involve uncertainty. When people are unsure of their model
of reality, then the outcome they observe will cause them to update their
beliefs. We argue that classical probability cannot be applied in such cases,
and that subjective probability must instead be used. In Experiment 1 we show
that, when judging the probability of lottery number sequences, people apply
subjective rather than classical probability. In Experiment 2 we examine the
conjunction fallacy and demonstrate that the materials used by Tversky and
Kahneman (1983) involve model uncertainty. We then provide a formal
mathematical proof that, for every uncertain model, there exists a conjunction
of outcomes which is more subjectively probable than either of its constituents
in isolation.Comment: Maguire, P., Moser, P. Maguire, R. & Keane, M.T. (2013) "A
computational theory of subjective probability." In M. Knauff, M. Pauen, N.
Sebanz, & I. Wachsmuth (Eds.), Proceedings of the 35th Annual Conference of
the Cognitive Science Society (pp. 960-965). Austin, TX: Cognitive Science
Societ
Understanding Consciousness as Data Compression
In this article we explore the idea that consciousness is a language-complete
phenomenon, that is, one which is as difficult to formalise as the foundations
of language itself. We posit that the reason consciousness resists scientific
description is because the language of science is too weak; its power to
render phenomena objective is exhausted by the sophistication of the brain’s
architecture. However, this does not mean that there is nothing to say about
consciousness. We propose that the phenomenon can be expressed in terms of
data compression, a well-defined concept from theoretical computer science
which acknowledges and formalises the limits of objective representation. Data
compression focuses on the intersection between the uncomputable and the finite.
It has a number of fundamental theoretical applications, giving rise, for example,
to a universal definition of intelligence (Hutter, 2004), a universal theory of prior
probability, as well as a universal theory of inductive inference (Solomonoff,
1964). Here we explore the merits of considering consciousness in such terms,
showing how the data compression approach can provide new perspectives
on intelligent behaviour, the combination problem, and the hard problem of
subjective experience. In particular, we use the tools of algorithmic information
theory to prove that integrated experience cannot be achieved by a computable
process
Seeing Patterns in Randomness: A Computational Model of Surprise.
While seemingly a ubiquitous cognitive process, the precise definition and function of surprise remains elusive. Surprise is often conceptualized as being related to improbability or to contrasts with higher probability expectations. In contrast to this probabilistic view, we argue that surprising observations are those that undermine an existing model, implying an alternative causal origin. Surprises are not merely improbable events; instead, they indicate a breakdown in the model being used to quantify probability. We suggest that the heuristic people rely on to detect such anomalous events is randomness deficiency. Specifically, people experience surprise when they identify patterns where their model implies there should only be random noise. Using algorithmic information theory, we present a novel computational theory which formalizes this notion of surprise as randomness deficiency. We also present empirical evidence that people respond to randomness deficiency in their environment and use it to adjust their beliefs about the causal origins of events. The connection between this pattern-detection view of surprise and the literature on learning and interestingness is discussed
A Computational Theory of Subjective Probability [Featuring a Proof that the Conjunction Effect is not a Fallacy]
35th Annual Conference of the Cognitive Science Society, Berlin, Germany, 31 July - 3 August 2013In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We argue that classical probability cannot be applied in such cases, and that subjective probability must instead be used. In Experiment 1 we show that, when judging the probability of lottery number sequences, people apply subjective rather than classical probability. In Experiment 2 we examine the conjunction fallacy and demonstrate that the materials used by Tverksy and Kahneman(1983) involve model uncertainty. We then provide a formal mathematical proof that, for every uncertain model, there exists a conjunction of outcomes which is more subjectively probable than either of its constituents in isolation
A Computational Theory of Subjective Probability : [Featuring a Proof that the Conjunction Effect is not a Fallacy]
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We argue that classical probability cannot be applied in such cases, and that subjective probability must instead be used. In Experiment 1 we show that, when judging the probability of lottery number sequences, people apply subjective rather than classical probability. In Experiment 2 we examine the conjunction fallacy and demonstrate that the materials used by Tverksy and Kahneman (1983) involve model uncertainty. We then provide a formal mathematical proof that, for every uncertain model, there exists a conjunction of outcomes which is more subjectively probable than either of its constituents in isolation
A computational theory of subjective probability [Featuring a proof that the conjunction effect is not a fallacy
Abstract In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We argue that classical probability cannot be applied in such cases, and that subjective probability must instead be used. In Experiment 1 we show that, when judging the probability of lottery number sequences, people apply subjective rather than classical probability. In Experiment 2 we examine the conjunction fallacy and demonstrate that the materials used by Tverksy and Kahneman (1983) involve model uncertainty. We then provide a formal mathematical proof that, for every uncertain model, there exists a conjunction of outcomes which is more subjectively probable than either of its constituents in isolation
A Computational Theory of Subjective Probability [Featuring a Proof that the Conjunction Effect is not a Fallacy]
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We argue that classical probability cannot be applied in such cases, and that subjective probability must instead be used. In Experiment 1 we show that, when judging the probability of lottery number sequences, people apply subjective rather than classical probability. In Experiment 2 we examine the conjunction fallacy and demonstrate that the materials used by Tverksy and Kahneman (1983) involve model uncertainty. We then provide a formal mathematical proof that, for every uncertain model, there exists a conjunction of outcomes which is more subjectively probable than either of its constituents in isolation