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Classical probability model that reproduces the disjunction effect via expectation-parameter partitioning, proving classical and quantum-like models have equivalent expressiveness for decision rates.
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| name | classical-disjunction-effect-model |
| description | Classical probability model that reproduces the disjunction effect via expectation-parameter partitioning, proving classical and quantum-like models have equivalent expressiveness for decision rates. |
Methodology for modeling the disjunction effect in human decision making within classical probability theory, by introducing a continuous expectation parameter that partitions the participant pool by ambiguity level. Proves that classical and quantum-like models have equivalent observable expressiveness — their difference lies only in how ambiguity is represented. Based on arXiv:2603.23233.
The disjunction effect violates the classical law of total probability in human decision making: people's choices differ when they know the outcome vs. when they don't. Classically, P(defect) should equal P(defect|coop)×P(coop) + P(defect|defect)×P(defect), but empirically it doesn't.
Instead of the binary certainty assumption (opponent will definitely cooperate or definitely defect), introduce a continuous expectation parameter θ ∈ [0,1] representing the anticipated likelihood of opponent defection. The participant pool is partitioned by expectation level, and the ambiguity set is the union of interior expectation bins.
Proved: Any triple of defection rates (cooperate-known, defect-known, unknown) achievable by a quantum-like model can be reproduced exactly by a classical instance of the expectation-parameter model. Both frameworks have identical expressive power for observable rates.
The difference is NOT in probability theory breaking down, but in:
Given empirical defection rates across three conditions:
For any quantum-like model producing rates (r_coop, r_defect, r_unknown):
If d_U ≈ d_C×P(C) + d_D×P(D), the disjunction effect is absent. The model reduces to standard classical decision theory — no special modeling needed.
If solving produces negative weights, increase the number of bins or relax the constraint. This indicates the data cannot be fit with the current granularity.
With too many bins, the model becomes unidentifiable. Use minimum bins (typically 3-5) that reproduce the data. Apply regularization to prefer smoother distributions.
Empirical rates: P(defect|coop) = 0.3, P(defect|defect) = 0.7, P(defect|unknown) = 0.55 Classical prediction: 0.3×0.5 + 0.7×0.5 = 0.5 ≠ 0.55 (disjunction effect!) Expectation model: Partition population into low/high/medium expectation bins to reproduce 0.55 while maintaining LOTP within each bin.
