Abstract
In this paper, we investigate deliberation procedures that invite citizens with contextual opinions to explore alternative thinking frames. Contextuality is captured in a simple quantum cognitive model. We show how disagreeing citizens endowed with contextual opinions can reach consensus in a binary collective decision problem with no improvement in their information. A necessary condition is that they are willing to (mentally) experience their fellow citizens' way of thinking. The diversity of thinking frames is what makes it possible to overcome initial disagreement. Consensus does not emerge spontaneously from deliberations: it requires facilitation.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.