While often seen as an elitist practice found only in artistic and academic circles, speculative design has grown in popularity and is now practiced in more diverse contexts and with a variety of participants. In order to gain a better understanding of this ostensible 'participatory turn', this paper presents an initial exploration of participatory speculative design based on a pilot survey of recent projects. Using a sample of projects we develop an 8-step hierarchical taxonomy of participation in speculative design that moves from 'spectatorship' to 'reflection', 'inspiration', 'generative reflection', 'shared creativity', 'shared authorship', 'initiative' and, finally, 'ownership'. The taxonomy helps to raise important questions about the character and outcomes of participatory speculative design processes and the role played by designers as agents of the public imagination.