Coherent upper and lower conditional probabilities defined by Hausdorff outer and inner measures are proposed to represent respectively the unconscious and conscious activities of the human brain when information is given. In the model uncertainty measures are defined according to the complexity of the conditioning event that represents the given information. The model is applied to explain mathematically the conjunction fallacy in Linda's Problem and the bias of selective attention described in the so-called invisible Gorilla experiment, that is often taken as a characteristic example of the inescapable limitations of human perception. Once people are concentrated on doing a specific action, they do not notice unexpected events (having 0 probability) occurring in the meantime. When applying the model, selective attention is no longer a bias since it is able to explain this function of the human brain mathematically. Moreover different reactions of people to unexpected events can be represented in different metric spaces with metrics which are not bi-Lipschitz. In these metric spaces coherent upper conditional probabilities defined by Hausdorff outer measures are not mutually absolutely continuous and so they do not share the same null events.

Coherent lower and upper conditional previsions defined by Hausdorff inner and outer measures to represent the role of conscious and unconscious thought in human decision making

Serena Doria
Primo
2021-01-01

Abstract

Coherent upper and lower conditional probabilities defined by Hausdorff outer and inner measures are proposed to represent respectively the unconscious and conscious activities of the human brain when information is given. In the model uncertainty measures are defined according to the complexity of the conditioning event that represents the given information. The model is applied to explain mathematically the conjunction fallacy in Linda's Problem and the bias of selective attention described in the so-called invisible Gorilla experiment, that is often taken as a characteristic example of the inescapable limitations of human perception. Once people are concentrated on doing a specific action, they do not notice unexpected events (having 0 probability) occurring in the meantime. When applying the model, selective attention is no longer a bias since it is able to explain this function of the human brain mathematically. Moreover different reactions of people to unexpected events can be represented in different metric spaces with metrics which are not bi-Lipschitz. In these metric spaces coherent upper conditional probabilities defined by Hausdorff outer measures are not mutually absolutely continuous and so they do not share the same null events.
File in questo prodotto:
File Dimensione Formato  
IJAR2023.pdf

Solo gestori archivio

Tipologia: PDF editoriale
Dimensione 450.56 kB
Formato Adobe PDF
450.56 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11564/803771
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 1
social impact