We report results from a laboratory experiment that allows us to test the incentive compatibility hypothesis of hypothetical referenda used in CV studies through the public or private provision of information messages. One of the main methodological issues about hypothetical markets regards whether people behave differently when bidding for a public good through casting a ballot vote than when they are privately purchasing an equivalent good. This study tried to address the core of this issue by using a good that can be traded both as private and public: information messages. This allows the elimination of confounding effects associated with the specific good employed. In our case information dispels some of the uncertainty about a potential gain from a gamble. So, the approximate value of the message can be inferred once the individual measure of risk aversion is known. Decision tasks are then framed in a systematic manner according to the hypothetical vs real nature of the decision and the public vs private nature of the message. A sample of 536 university students across three countries (I, UK and NZ) participated into this lab experiment. The chosen countries reflect diversity in exposure to the practice of advisory (NZ) and abrogative (Italy) referenda, with the UK not having any exposure to it. Under private provision the results show that the fraction of participants unwilling to buy information is slightly higher in the real treatment than in the hypothetical one. Under public provision, instead, there is no statistical difference between real and hypothetical settings, confirming in part the finding of previous researchers. A verbal protocol analysis of the thought processes during choice highlights that public provision of information systematically triggers concerns and motivations different from those arising under the private provision setting. These findings suggest that the incentive compatibility of public referenda is likely to rely more on affective and psychological factors than on the strategic behaviour assumptions theorised by economists.