  The 'conjunction fallacy' has been extensively debated by scholars in
cognitive science and, in recent times, the discussion has been enriched by the
proposal of modeling the fallacy using the quantum formalism. Two major quantum
approaches have been put forward: the first assumes that respondents use a
two-step sequential reasoning and that the fallacy results from the presence of
'question order effects'; the second assumes that respondents evaluate the
cognitive situation as a whole and that the fallacy results from the 'emergence
of new meanings', as an 'effect of overextension' in the conceptual
conjunction. Thus, the question arises as to determine whether and to what
extent conjunction fallacies would result from 'order effects' or, instead,
from 'emergence effects'. To help clarify this situation, we propose to use the
World Wide Web as an 'information space' that can be interrogated both in a
sequential and non-sequential way, to test these two quantum approaches. We
find that 'emergence effects', and not 'order effects', should be considered
the main cognitive mechanism producing the observed conjunction fallacies.
