Probability Reversal and the Disjunction Effect in Reasoning Systems
This addresses a foundational issue in AI reasoning systems that could impact decision-making applications, though it appears incremental by applying quantum concepts to known paradoxes.
The paper tackles the problem of paradoxical probability reversals, such as Simpson's reversal and the disjunction effect, in AI decision systems when additional data is provided, and argues that beliefs should be modeled as quantum superposition states rather than classical statistical variables to mitigate risks.
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.