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The vast quantity of data contributed and consumed via the internet provides an environment where Collective Intelligence (CI) can emerge. This paper considers CI in relation to the Peer-to-Peer (P2P) paradigm, an environment that has the necessary conditions for the generation of large data sets through frequent peer interactions. We then examine the characteristics of agency and relate agent computing to the conditions required to facilitate CI in P2P systems. Furthermore, we present a key research challenge for the community and propose an approach to scrutinise CI in a P2P scenario that makes use of critical dimensions as a basis to classify the likely collective emergent behaviours.