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This paper investigates the properties of social choice functions that represent resource allocation strategies in interference coupled wireless systems. The allocated resources can be physical layer parameters such as power vectors or antenna weights. Strategy proofness and efficiency of social choice functions are used to capture the respective properties of resource allocation strategy outcomes being non-manipulable and Pareto optimal. In addition, this paper introduces and investigates the concepts of (strict) intuitive fairness and nonparticipation in interference coupled systems. The analysis indicates certain inherent limitations when designing strategy proof and efficient resource allocation strategies, if the intuitive fairness and nonparticipation are imposed. These restrictions are investigated in an analytical social choice function framework for interference coupled wireless systems. Among other results, it is shown that a strategy proof and efficient resource allocation strategy for interference coupled wireless systems cannot simultaneously satisfy continuity and the frequently encountered property of non-participation.