Maybe, but not necessarily.

Let's imagine a hypothetical piece of research that every single person wants, and wants enough to willingly contribute their share (per capita, or wealth/income adjusted, whatever) if that is required in order to have the research done. However, if they value the money they would be contributing more than the marginal change in the research for lack of their funding, they might rationally choose still not to contribute unless coerced to do their part.