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This paper reevaluates the complementary symmetry property and the corresponding experimental evidence. Originally the property was stated for binary risky prospects. We generalize it to arbitrary state-contingent real-valued outcomes, thus extending the domain of choice from risk to uncertainty/ambiguity and allowing for multiple outcomes. We consider various observable tasks related to the elicitation of buying and selling prices. In particular, for selected reference point models, we derive relevant definitions of gains and losses, and identify pairs of prices satisfying the complementary symmetry property. We then run an experiment to test these new predictions, and find that while some reference point models can be refuted based on our data, others perform reasonably well. • We extend the complementary symmetry hypothesis to multiple outcomes and ambiguity. • We define various observable tasks related to the elicitation of buying and selling prices. • For selected reference point models, we identify the pairs of prices satisfying the complementary symmetry property. • We use the complementary symmetry to test some relevant reference point models. [ABSTRACT FROM AUTHOR]

Complementary symmetry was derived before under particular theories, and used to test those. Progressively general results were published. This paper proves the condition in full generality, providing a one-line proof, and shedding new light on its empirical implications. • This paper proves complementary symmetry in full generality. • This paper provides a one-line proof of complementary symmetry. • Violations of complementary symmetry are more fundamental than thought before. [ABSTRACT FROM AUTHOR]

Complementary symmetry has been proved to be fulfilled in Cumulative Prospect Theory with random reference, regardless of the form of the utility function. Furthermore an alternative model, in which complementary symmetry generally does not hold, is discussed. • Complementary symmetry under Cumulative Prospect Theory with random reference is investigated. • It is shown that the property is fulfilled, regardless of the form of the utility function. • An alternative model is discussed. • Complementary symmetry in the modified model is characterized. • The methods of functional equations are applied. [ABSTRACT FROM AUTHOR]