I had no clue, so I googled it. Here, from (thank you!) Wikipedia.:

"Two-level utilitarianism (sometimes Government House utilitarianism) is a utilitarian theory of ethics developed by R. M. Hare.[1] According to the theory, a person's moral decisions should be based on a set of 'intuitive' moral rules, except in certain rare situations where it is more appropriate to engage in a 'critical' level of moral reasoning.

Utilitarians believe that an action is right if it produces the best possible state of affairs.[2] Traditional utilitarianism treats this as a claim that people should try to ensure that their actions maximize overall happiness or pleasure.[3]

Two-level utilitarianism is virtually a synthesis of the opposing doctrines of act utilitarianism and rule utilitarianism. Act utilitarianism states that in all cases the morally right action is the one which produces the most pleasure, whereas rule utilitarianism states that the morally right action is the one that is in accordance with a moral rule whose general observance would create the most happiness. In terms of two-level utilitarianism, act utilitarianism can be likened to the 'critical' level of moral thinking, and rule utilitarianism to the 'intuitive' level"

Why did not you do this? Now read it and if you have some question, start with that.

Two-level utilitarianism is virtually a synthesis of the opposing doctrines of act utilitarianism and rule utilitarianism. Act utilitarianism states that in all cases the morally right action is the one which produces the most pleasure, whereas rule utilitarianism states that the morally right action is the one that is in accordance with a moral rule whose general observance would create the most happiness. In terms of two-level utilitarianism, act utilitarianism can be likened to the 'critical' level of moral thinking, and rule utilitarianism to the 'intuitive' level" — tim wood

I expected "a moral rule whose general observance would create the most happiness" to be rule utilitarianism as something to be general would require it to pass the test of logical (critical) analysis AND feel that "in all cases the morally right action is the one which produces the most pleasure" to be act utilitarianism as without a general rule to guide us we must then fall back on our intuition.

Why did not you do this? Now read it and if you have some question, start with that. — tim wood

Thanks for your great copy & paste skills there Tim. I have read the literature but can't get my head around it, I need someone to 'unpack' it for me.

This is from Texas A & M University. It might help. I didn't get it either.

The basic argument:

1. The universalizability of moral judgments implies preference utilitarianism.

It is a logical feature of natural language that moral judgments (expressed in terms of "ought" claims, or claims about what is "right") are both (1) universalizable and (2) overriding.
By this he means that, in order to sincerely assent to the judgement that "A ought to do X to B and C," one must sincerely assent to the judgements that "B ought to do X to A and C" and "C ought to do X to A and B," were their various roles switched, and one must assent to this irrespective of what one's individual preferences are (that is, whether one is A rather than B or C).
And this means, according to Hare, that Kantian universalizability implies preference utilitarianism. For to sincerely assent to an ought claim is to prefer that the thing in question be done, even if one had to occupy, successively, the positions of each and every one of the persons involved.
Hare's criterion of universalizability thus combines the intuitiveness of the traditional Golden Rule (do unto others what you would have them do unto you -- you imagine yourself in the others' shoes) with the precision of the philosophers' condition of universalizability (when doing so, you are to imagine yourself having the others' preferences rather than your own). So one way to think of Hare's view is as providing a secular defense of the Golden Rule (one based on the logic of moral judgments rather than divine authority) and an argument to the conclusion that the Golden Rule, properly understood, implies preference utilitarianism.

2. However, human beings need both "intuitive level moral principles" and "critical thinking."

Humans' basic preferences are pretty uniform, but
Humans vary in their ability to think critically and to act on what they determine to be correct moral principles, and across time and varying circumstances, the same individual varies in these same ways.

C. This implies that one should embrace a two-level version of utilitarianism:

We use "intuitive level thinking"...
or Prima facie principles governing general types of cases commonly encountered by people...
when there isn't time for critical thinking, or
when one can't trust one's critical thinking.

and we use "Critical level" thinking"...
when prima facie principles conflict, in unusual cases, or
when both (a) it is clear that utility can be maximized a certain way and (b) one can trust one's judgment that this is so.

The discussion concludes with:

Three kinds of intuitive level principles:

Common morality: Insofar as members of a society face similar problems, we would expect agreement to emerge on basic standards which everyone in the society will be expected to live up to. Moreover, given the universal features of the human condition, we would expect there to be many similarities between the common moralities of various cultures at different times and places.

Professional ethics: Insofar as those in certain roles face similar kinds of situations repeatedly, we would expect agreement to emerge on basic standards for the conduct of various professionals and others in special roles.

Personal morality: And insofar as individuals differ in their abilities to reason critically under various circumstances, critical thinking will lead different individuals to train themselves to adhere to different sets of intuitive level rules, including "metaprinciples" for deciding when to engage in critical thinking and when to stick unquestioningly to one's intuitive level priniciples.

Wikipedia isn't always the best source of information.

If you want to know more, much more, about Hare, here is an article at the Stanford Encyclopedia of Philosophy.

Thanks, great post. Can you shed some light on the objection that such a society would have to run secretly? With only a few philosophers knowing of the utilitarian principle behind it?

Thank you very much. It's strange I got it backwards.

My feeling was that general rules don't get there before some amount of critical thinking and special cases had to be dealt with our intuition. Don't I make sense?

I really need some feedback on this one. So be kind.

Can you shed some light on the objection that such a society would have to run secretly? With only a few philosophers knowing of the utilitarian principle behind it? — Jamesk

I don't understand why there would be an "objection that such a society would have to run secretly". What are you referencing in the 'secret' part? It would seem like the utilitarian principle is obvious enough that many people would know of it. No?

I have read the literature but can't get my head around it, I need someone to 'unpack' it for me. — Jamesk

Having "bought" Kantian ethics, I don't pay much attention to anything called Utilitarianism. And I don't claim any facility in unpacking , but here's what I get from it in a sketch.

-Act utilitarianism: I just know in my gut that big expensive car is better for me than a Prius. I'll get a lot more pleasure out of it.

-Rule utilitarianism: I could maybe use that dinosaur of a car as an extra living room in my driveway, but there is no way I or the world around me benefits from my owning and driving that gas-guzzler around.

If this has missed the point, please let me know.