What is the phrase to describe the problem of mass participation?

It sounds like you're describing the "tragedy of the commons" concept.

The tragedy of the commons is an economics theory, according to which individuals, acting independently and rationally according to each one's self-interest, behave contrary to the whole group's long-term best interests by depleting some common resource.

Thanks to Joe's answer, I was able to follow some links on Wikipedia and found the answer. This is commonly referred to as the Free Rider Problem. According to Wikipedia:

A free rider, in economics, refers to someone who benefits from resources, goods, or services without paying for the cost of the benefit. The term "free rider" was first used in economic theory of public goods, but similar concepts have been applied in to other contexts, including collective bargaining, antitrust law, psychology and political science. Free riding may be considered as a free rider problem when it leads to under-provision of goods or services, or when it leads to overuse or degradation of a common property resource.

(my emphasis as this was the specific usage I was looking for)

Just to clarify how this phrase applies to the example I gave: In the example given, the communal "service" is reduced resource usage. This is a service that everyone benefits from when there is recycling, and yet any one person can be a free rider by not recycling yet still benefit from their neighbors' recycling.