There was some discussion about heroic responsibility here not too long ago. One aspect / behavior that some people (incorrectly IMO) attribute to heroic responsibility is that it is a justification for deontology violations in order to accomplish whatever goal you have.

My take is that it is more like the opposite: the thing you're describing here is mostly just ordinary high-agency behavior / executive responsibility. Where heroic responsibility comes in is that it says that you're supposed to wield that agency and level of execution continuously and at all levels of meta (using comprehensive / non-naive consequentialism) until the job is actually done. It also includes tracking and recognizing when to give up, and making that call - in your example, maybe this means stepping back and realizing that actually running the kind of ads you were trying to run are not effective or not worth the cost in the first place, or that your car dealership is headed for bankruptcy regardless of what happens with the ads. Furthermore, taking heroic responsibility means that you're obligated to do all this without stepping outside the bounds of deontology or slipping into invalid / motivated reasoning.

The entire thing about heroic responsibility, as I understand it, and as is apparent in the original HPMOR context, is that feeling responsibility for outcomes specifically when social expectations do not hold you responsible for them. I think the type of responsibility that the owner of a car ownership has for the profitability of said car dealership is called "responsibility."

For future readers of this post and other writings on heroic responsibility who feel a bit amiss, Miranda Dixon-Luinenburg's The Importance of Sidekicks may be for you (as it was for me). Think Samwise to Frodo or Robin to Batman, or if you know investing Charlie Munger to Warren Buffett, or if you like team sports Scottie Pippen to Michael Jordan. There's probably a gradient from "assistant" to "second-in-command"; I lean more towards the latter. Miranda:

I suspect that the rationality community, with its “hero” focus, drives away many people who are like me in this sense. I’ve thought about walking away from it, for basically that reason. I could stay in Ottawa and be a nurse for forty years; it would fulfil all my most basic emotional needs, and no one would try to change me. Because oh boy, have people tried to do that. It’s really hard to be someone who just wants to please others, and to be told, basically, that you’re not good enough–and that you owe it to the world to turn yourself ambitious, strategic, Slytherin.

Firstly, this is mean regardless. Secondly, it’s not true.

Samwise was important. So was Frodo, of course. But Frodo needed Samwise. Heroes need sidekicks. They can function without them, but function a lot better with them. Maybe it’s true that there aren’t enough heroes trying to save the world. But there sure as hell aren’t enough sidekicks trying to help them. And there especially aren’t enough talented, competent, awesome sidekicks.

Miranda's post clearly struck a chord as it generated 200+ comments back in the days when LW was smaller, including an endorsement and apology from Eliezer, but the one I personally found most memorable was this one because it seemed so counterintuitive:

I am male. I have high testosterone. I love competing and winning. I am ambitious and driven. I like to make a lot of money. I make a lot of money. I prefer the sidekick role.

If someone asks me "King or Prince?" I will respond with Prince every time. Hey, you can still be royalty without the weight of the world on your shoulders. I would still be a hard working Prince, too. If some asks me "Candidate or Campaign Manager?" I'll take Campaign Manager, thank you. If someone asks me "President or Chief of Staff?" well, you know the answer by now.

The more money I make and the more wisdom and experience I acquire, the more people naturally turn to me to lead. And I do it when necessary. I'm even pretty good at it. But, I don't love it. I don't require it. I don't see myself as growing more in that direction.

The same consept where independently invented by a larp organsier I know. Unfortunatly I stronly dislike the words they chose, so I will not repeat them. But it occurs to me that the consept of "final responsibility", or "the buck stops here", is so universaly usefull, that it's wierd that there isn't some more common term for it.

OK so I don't love this term. I think there's three cases:

• it's your responsibility because of a rule about an action you take.
• it's your responsibility because the outcome is your responsibility.
• it's not your responsibility but you can impact the outcome anyway and maybe you should.

The problem seems to be that responsibility does this language-decay (like "literally" -> "figuratively") from "outcome-based" to "rules-based." Maybe "heroic" is a strong enough support to prop up the "outcomes" version, but imagine this: Hooli rolls out its new corporate value, "heroic responsibility" to replace its old value of "ownership," and employees think they're basically bullshitting and trying to make them do more work for less pay, so they ignore it. So yeah, it's euphemism treadmill if it gets overused. Which it probably is, among us, by now.

So I don't love the term because it's more like a prop to educate, but in the long run we don't communicate better by diluting what responsibility is in the first place. Like I think we all need to understand that sometimes what we think of as the bare minimum is just failing, and what feels like going above and beyond is the bare minimum, not heroic.

For the 3rd category, it's just hard for me to think of this as "heroic." 

• If you're antisocial in your heroic responsibility, then we really need to be careful: antisocial is negative utility points. It deducts from the score you get for the moral outcome you're seeking. Simply put, people will think you're an asshole, not a hero, and you're morally responsible for that too. I would avoid calling people heroes for the times when they think they're right but haven't convinced anyone else.
• Either way, it probably derives from "responsible for your life" or "morally responsible." For instance going above and beyond to get promoted is the bare minimum to be employable when you're 10 years older. But these things just aren't heroic? It's just really hard for me to think of an example here that matches the connotation of "heroic" without simply being a case of taking responsibility that was already yours.

As several commenters here have said, the business owner example isn't a great fit for heroic responsibility. The core is taking responsibility for things that aren't your job, that you are not socially expected to be responsible for, because you have decided that the thing needs to be done.

The archetypal fictional example is the hero who raises the rebellion that overthrows the Evil Empire. A normal sensible peasant whose home has just been burned doesn't do that, he just tries to survive the winter. The hero decides to do more than that, even though it's not their job and they're not (at the start of the book/movie/whatever) distinguished from all the other thousands of people in the same position. That choice is why we call them the hero.

Or, for a real-life example, a factory-owner in 1940s Germany might reasonably feel that he has quite enough to do trying to keep his business running in a war zone. It's not his job to save Jewish lives, they're not his relatives or anything. And even trying to save them could be very hazardous. Nevertheless, Oskar Schindler decided he was going save as many lives as he could anyway, and saved about 1,200 people. That's what heroic responsibility looks like.

And, the most obvious example to anyone on LessWrong: there is no social expectation that a normal citizen who is not a senior government official will decide that it's up to him to save the world from the risk that Unfriendly AI kills us all, but Eliezer Yudkowsky saw that no one else was going to do the job, and he wants the world to be saved, so he's spent his career trying.

The heroic responsibility described by OP, the determination to focus on whether [goal] is actually happening or whether people are buck-passing or symbolically pretending to do the thing, or whatever other failure mode -- all that is downstream of the heroic decision to take responsibility for [goal] in the first place.

I am reminded of the quote by Adm. Rickover, the "Father of the [American] Nuclear Navy":

“Responsibility is a unique concept... You may share it with others, but your portion is not diminished. You may delegate it, but it is still with you... If responsibility is rightfully yours, no evasion, or ignorance or passing the blame can shift the burden to someone else. Unless you can point your finger at the man who is responsible when something goes wrong, then you have never had anyone really responsible.”

Rickover is famous for his focus on responsibility, accountability, and quality. Here is e.g. his essay on "Doing a Job".

It's worth distinguishing between epistemic and instrumental forms of heroic responsibility. Shapley values are the mathematically precise way of apportioning credit or blame for an outcome among a group of people. Heroic responsibility as a belief about one's own share of credit or blame is a dark art of rationality, since it involves explicitly deviating from the Shapley value assignment in one's beliefs about credit or blame. But taking heroic responsibility as an action, while acknowledging that you're not trying to be mathematically precise in your credit assignment, can still be useful as a way of solving coordination problems.

Reminds me of one of my favourite essays, Software engineers solve problems (Drew DeVault, 2020).