This really comes down to the CAP theorem whereby it is stated that if there are equal number of servers on either side of the partition the database cannot maintain CAP (Consistency, Availability, and Partition tolerance). An Arbiter is specifically designed to create an "imbalance" or majority on one side so that a primary can be elected in this case.
If you get an even number of nodes on either side MongoDB will not elect a primary and your set will not accept writes.
Edit
By either side I mean, for example, 2 on one side and 2 on the other. My English wasn't easy to understand there.
So really what I mean is both sides.
Edit
Wikipedia presents quite a good case for explaining CAP: http://en.wikipedia.org/wiki/CAP_theorem