It is possible to have a preference relation that is complete but not transitive
Empirical evidence from behavioral and neurobiological studies shows that human and animal decision-makers frequently exhibit intransitive preferences while maintaining completeness, demonstrating that preference relations can be complete without being transitive.
The claim is a foundational concept in behavioral economics and decision theory regarding the axiomatic properties of preferences. Several retrieved papers (such as [0], [6], and [7]) explicitly document violations of transitivity in biological and human choices, supporting the premise that preference relations can indeed fail transitivity while remaining complete (as agents still make definite pairwise choices). Therefore, the claim is well-supported by empirical evidence.
Tsetsos K, Moran R, Moreland J, Chater N, Usher M, Summerfield C. Economic irrationality is optimal during noisy decision making.. 2016. https://doi.org/10.1073/pnas.1519157113
This study demonstrates that human decision-making frequently violates the axiom of transitivity due to neural noise, while remaining complete.
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Glimcher PW. Efficiently irrational: deciphering the riddle of human choice.. 2022. https://doi.org/10.1016/j.tics.2022.04.007
The review explains how humans consistently make choices that are logically inconsistent (violating transitivity) as an adaptive optimization strategy.
Iwanir S, Ruach R, Itskovits E, Pritz CO, Bokman E, Zaslaver A. Irrational behavior in C. elegans arises from asymmetric modulatory effects within single sensory neurons.. 2019. https://doi.org/10.1038/s41467-019-11163-3
Experiments with C. elegans show that innate preferences robustly violate key rationality paradigms of transitivity.
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