Probability Reversal and the Disjunction Effect in Reasoning Systems
  Data based judgments go into artificial intelligence applications but they
undergo paradoxical reversal when seemingly unnecessary additional data is
provided. Examples of this are Simpson's 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 Pearson's chi-squared or Fisher's 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.
