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Register a new userProbability Reversal and the Disjunction Effect in Reasoning Systems
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Added by
Subhash Kak
Publication date
2017
fields
Informatics Engineering
and research's language is
English
Authors
Subhash Kak
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Data based judgments go into artificial intelligence applications but they undergo paradoxical reversal when seemingly unnecessary additional data is provided. Examples of this are Simpsons reversal and the disjunction effect where the beliefs about the data change once it is presented or aggregated differently. Sometimes the significance of the difference can be evaluated using statistical tests such as Pearsons chi-squared or Fishers exact test, but this may not be helpful in threshold-based decision systems that operate with incomplete information. To mitigate risks in the use of algorithms in decision-making, we consider the question of modeling of beliefs. We argue that evidence supports that beliefs are not classical statistical variables and they should, in the general case, be considered as superposition states of disjoint or polar outcomes. We analyze the disjunction effect from the perspective of the belief as a quantum vector.
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Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere. W.S. Anglin, the Mathematical Intelligencer, 4 (4), 1982.
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