MediaWiki is the software Consumerium uses on its R&D wiki which you are using right now. It is one of several wiki code options, seemingly the one that has a wikitext standard suitable for large numbers of people to collaborate on in many languages. http://mediawiki.org
It is not however ideal as a piece of code to work with our hardware requirements or protocol requirements, e.g. it does not currently integrate with any mobile device code, chat code otherwise then that the people using the Wikis might also be using IM, such as irc or email to communicate with each other. Nor does it implement some features of the content wiki or opinion wiki that will be needed eventually to deliver Consumerium Services such as signing versions of articles, which is needed for non-centralized integrity burden of proof.
Therefore its use at present is really just a test, and to make it easier to collate text from other GFDL services, most of which also use mediawiki. Consumerium developers will have to make their choices based also on the constraints the Consumerium License might place on using GPL'd code. This might not be an issue, or it might be a huge issue, we just don't know. The MediaWiki 1.3 release is now available and should be compared to GetWiki.
The long term choices of wiki code and its integration with other code are things the Consumerium Governance Organization will decide, and this Development Wiki is here to discuss. As part of reflexive design, we will generally use the tools we are trying to test, before deciding to use them. This will often bias sysops and others in favour of what is in use now! We should be very aware of this systemic bias.