Imagine that a small democratic body (a town, a county, a college campus, whatever) is holding two referendums. The first concerns whether the institution should build a new road. Out of 10,000 eligible voters, only 10% vote -- they break down 60% in favor, 40% opposed. The referendum passes.
The second referendum asks that the body officially boycott Coke products (a hobby-horse I remember from my own undergraduate days). Again, it turns out that only 1,000 of the 10,000 voters show up at the polls, and of those voting the referendum passes by a 60/40 margin.
In either case, the lack of participation could be thought to have a negative impact of the democratic legitimacy of the referendum -- it might constrain our ability to say "this is what the people want." However, my instincts tell me there is a significant difference between the two cases above.
In the road referendum, I don't have any intuitive thoughts on the views of the non-participants -- which is to say, I have no reason to think that their distribution of views on the road differ from the voting population. That might change if the road was particularly beneficial to a specific subset of the population who was motivated to get to the polls (and it puts aside any issues about differential access to the polls by various social groups, which is no small thing), but otherwise there doesn't seem to be anything in particular that I can infer about the non-participants. And that (to me at least) dissipates a good portion of the democratic legitimacy threat.
In the boycott Coke referendum, by contrast, my intuition strongly suspects that most of the non-voters would (if pressed) vote against. It seems to me (and maybe I'm just wrong here) that if you're the sort of person who supports something like boycotting Coke, then you're the sort of person who will be sufficiently motivated to go to the polls and vote for it. Likewise, of the group who thinks this issue isn't such a big deal (not enough of a motive to go to the polls), it's hard to imagine many of them lean in favor of boycotting Coke. If I'm right, in this case we can infer opposition (albeit not passionately felt opposition) from non-participation. And in that case, the vote tally doesn't necessarily stand in for the "what the people want."
What do we make of this? I'm not sure. It is not even intuitively obvious that it is a bad thing that a passionate minority beat out a largely indifferent majority. Maybe turnout gives us a proxy for preference-intensity that is valuable. If John cares strongly about building a new bridge and Jane doesn't really care but is mildly against it, and that disjuncture causes more John-types than Jane-types to head to the polls, is it bad if the bridge gets built notwithstanding there being more Janes than Johns amongst eligible voters? On the other hand, that is really the positive way of framing special interest capture. You can tell similar stories about why all sorts of small and well-organized groups beat out diffuse majorities, and in many cases the results will feel like democratic failings rather than success stories.
I don't have any big sweeping thoughts about this. I am curious about what circumstances or conditions cause us to believe that non-voters likely would fall on a particular side of a controversy versus those where their views can be assumed to roughly mirror those of the voting population.