In this hypothetical, the rest do object to the pet issues of others in the coalition, but only weakly. Like, I personally would vote against corn subsidies by itself, for abortion rights, and for a package of (corn subsidies plus abortion rights). The exact policies I mentioned don't particularly matter, I'm sure you can find your own set of two issues that you'd vote this way on if it came down to it - the issues you have an opinion on, but you'd hold your nose and concede the issue if it was the price of something really important to you.

And when two or more minority interest groups feel this way on each other's issues, it is a failure to enact the "will of the people" if you use strict issue-by-issue majoritarianism. After all, each individual pet issue fails on its own merits - they just aren't broadly popular enough.

Fundamentally, the issue is that strengths of preferences do not show up in a referendum on a topic. Furthermore, there's no way to credibly commit to a compromise that gets you something important in exchange for a relatively unimportant concession. I'm not saying these issues outweigh the benefits of direct democracy, they're just problems that can get solved by a representative system.

Something like a policy proposal costing a low but non-zero amount of money for exactly zero benefit outside of the eyes of the 10% who really care about their pet cause. The non-packaged proposals get voted down not because the majority hates them, but because they don't care, at least not like the special interest does.

If a vector space is more your jam, imagine a six-dimensional vector space of policies, and each of these six hypothetical interest groups as voting for any combination of policies with a positive value along the axis in question, and against any combination of policies with a negative value. [100, -1, -1, -1, -1, -1], [-1, 100, -1, -1, -1, -1], etc, will each get voted down when presented individually as policies, but their sum as a package gets supported by each interest group.