I don't have a lot of personal exposure to how policy is made at high levels, in legislatures and executive boards and the like. I'm sure that what makes it down to the press releases and news interviews is simplified a lot. Maybe this fallacy is something that the decision-makers always have in mind, and we just don't hear about it. But I bet it's not always. In the ever-churning cycle of influences that is society, even if the bigwigs started out with these things in mind, I bet they still soak up some of the general public's way of thinking and fall prey to the same fallacies.
The fallacy I have in mind is the idea of applying cost-benefit analysis in isolation. It's best explained with an example. "If everyone in the town paid an extra $5 in their property taxes next year, we could buy a new piece of medical equipment. There isn't one like it in the area, and there's a 15% chance you or someone in your family will contract the ailment that it is used for, and having it nearby will make treatment safer, more comfortable, and more effective. Is it worth it?" Naturally, we need more information about how bad this ailment is and how much more effective the device will be than the alternatives, but let's say for the sake of argument that the ailment is bad, and the device will make a big difference.
Most people would conclude, sure, $5 for a single year isn't much, it's worth it for that benefit. And it might well be worth it. (We're ignoring the cost of powering, maintaining, and eventually replacing that device, but that's not the fallacy I'm looking for.)
But we don't have anywhere near enough information to decide that yet. The problem is that we're taking this in isolation, ignoring the fact that the cost of buying this isn't $5; it's all the possible benefits of all the other things we might have spent that $5 on. If you sit around all day listening to proposals that are just as compelling as this one, you'll end up with a lot more Yes answers than dollars. Ultimately, you can't budget everything that deserves funding; you have to prioritize.
And we're used to the idea of prioritization as a given in most venues, we almost take it for granted. Duh! Of course you have to prioritize! And yet we seem to put that idea aside so often when talking about funding projects. Time and again the justifications given -- even by national legislators speaking in Congress -- for a project come down to a simple cost-benefit analysis in isolation, as if we had a limitless pool of funds and it's just a matter of being sure we're getting our value for it.
That's why I would hate to be in that job. There's no good way to say to someone, "Yes, your proposal has merit. Yes, it's definitely worth the cost. Nevertheless, we can't afford it, because other proposals for things wholly unrelated, which are nowhere near as important to you personally, are even more important, or give even more benefit for their costs." But that's precisely what the job of budgeting really is. Or at least should be.