AI 中文总结
本文研究客观概率下的WTA-WTP差距，提出弱秩依赖效用模型，刻画其结构与影响因素，对禀赋效应楔形给出决策论解释，结果不同于Rabin校准含义。
AI 中文摘要
本文研究客观概率下的接受意愿/支付意愿（WTA-WTP）差距。有限彩票上的偏好满足完备性、传递性、连续性、弱独立性、参考划分和范围依赖。弱独立性仅对保持参考点且不跨诱导的损益划分移动结果的混合，要求冯·诺依曼-摩根斯坦独立性。其表示为弱秩依赖效用（WRDU），通过锚定参考点的独立子效用评估收益与损失，并通过损失侧分量上的范围依赖拉格朗日惩罚系数ρ重组。倒数指数λ=1/ρ表示WTA-WTP损失厌恶惯例。主要结果刻画了标准化可容许交易类，其中WTA-WTP差距源于不对称的买卖无差异方程。在该类中，λ>1会压低WTP并抬高WTA，而ρ>1对应收益寻求或损失衰减。固定的倒数损失厌恶指数没有内在机制使楔形随交易规模变化收敛到零；衰减需要一条交易路径，其中ρ>1且λ收敛到其共同中性值1。该分析基于弱化的独立性、参考锚定、半仿射子效用标准化和范围依赖惩罚，对禀赋效应楔形给出了决策论解释，该结果不同于Rabin校准含义，且不依赖常相对风险厌恶效用或概率加权。
英文摘要
This paper studies the willingness-to-accept/willingness-to-pay (WTA-WTP) gap under objective probabilities. Preferences over finite lotteries satisfy completeness, transitivity, continuity, weak independence, reference partition, and range dependence. Weak independence requires von Neumann-Morgenstern independence only for mixtures that preserve the reference point and do not move outcomes across the induced gain-loss partition. The representation, weak rank-dependent utility (WRDU), evaluates gains and losses by separate subutilities anchored at the reference point and recombines them through a range-dependent Lagrangian penalty coefficient \r{ho} on the loss-side component. The reciprocal index ${λ= 1/ρ}$ reports the WTA-WTP loss-aversion convention. The main result characterizes a normalized admissible transaction class in which the WTA-WTP gap follows from the asymmetric buying and selling indifference equations. In this class, $λ > 1$ suppresses WTP and elevates WTA, while $ρ> 1$ corresponds to gain seeking or loss attenuation. A fixed reciprocal loss-aversion index has no internal mechanism that makes the wedge converge to zero as transaction scale changes; attenuation requires a transaction path on which $ρ> 1$ and $λ$ converge to their common neutral value one. The analysis gives a decision-theoretic account of the endowment-effect wedge based on weakened independence, reference anchoring, semi-affine subutility normalization, and range-dependent penalization. The result is distinct from the Rabin calibration implication and does not rely on constant-relative-risk-aversion utility or probability weighting.
