Controversial public debates driven by incomplete scientific data where nobody can claim absolute certainty, due to the current state of scientific knowledge, are studied. To adopt a cautious balanced attitude based on clear but inconclusive data appears to be a lose-out strategy. In contrast overstating arguments with incorrect claims which cannot be scientifically refuted appears to be necessary but not sufficient to eventually win a public debate. The underlying key mechanisms of these puzzling and unfortunate conclusions are identified using the Galam Unifying Frame (GUF) of opinion dynamics. It reveals that the existence of inflexible agents and their respective proportions are the instrumental parameters to determine the faith of incomplete scientific data in public debates. Acting on one’s own inflexible proportion modifies the topology of the flow diagram, which in turn can make irrelevant the value of initial support. On the contrary focusing on open-minded agents may be useless given some topologies. Accordingly, the inflexibles rather than the data are found to drive the opinion of the population. The results shed a new but disturbing light on designing adequate strategies to win a public debate. The cases of global warming is briefly discussed.
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