I don't see how defining morality as the popular vote doesn't entail moral progress being a random walk

You imply that the empirically observed ("popular") morality of different societies at different times is a random walk. Is that a bullet you wish to bite?

The point I had in mind, though, wasn't defining morality through democracy. If you think that your moral opinions about cats on fire are better than those of some fellows a century or two ago, you have a couple of ways to argue for this.

One would be to claim that moral progress exists and is largely montonic and inescapable, thus your morality is better just because it comes later in time. Another would be to claim that you are in some way exceptional (in terms of your position in space and/or time), for example you can see the Truth better than those other folks because they were deficient in some way.

As you are probably well aware of, such claims tend to be controversial and have issues. I was wondering which path do you want to take. I'm guessing the moral progress path, am I right?

There's implicit uncertainty about ... other intuitions that implicitly affect the judgment, like pleasure ...

Sure, but what has been explicitly stipulated away?

I don't see how being able to save a life for $4,000 instead of $100,000 ... is counterintuitive, unpragmatic, or morally indefensible.

That's not what we are talking about, is it? We are talking more about immediate, visceral-reaction kinds of actions versus far-off, unconnected, and statistical-averages kinds. In some way it's an emotion vs intellect sort of a conflict, or, put in different terms, hardwired biological imperatives vs abstract calculations.

You are saying that abstract calculations provide the right answer, but I don't see it as self-evident: see my post above about putting all your trust into a single maximization.