Thanks! Yes, I'm good friends with Nick and Toby. My view on their model is as follows. Sometimes intertheoretic value comparisons are possible: that is, we can make sense of the idea that the difference in value (or wrongness) between two options A and B one one moral theory is greater, lesser, or equal to the difference in value (or wrongness) between two options C and D on another moral theory. So, for example, you might think that killing one person in order to save a slightly less happy person is much more wrong according to a rights-based moral view than it is according to utilitarianism (even though it's wrong according to both theories). If we can make such comparisons, then we don't need the parliamentary model: we can just use expected utility theory.

Sometimes, though, it seems that such comparisons aren't possible. E.g. I add one person whose life isn't worth living to the population. Is that more wrong according to total utilitarianism or average utilitarianism? I have no idea. When such comparisons aren't possible, then I think that something like the parliamentary model is the right way to go. But, as it stands, the parliamentary model is more of a suggestion than a concrete proposal. In terms of the best specific formulation, I think that you should normalise incomparable theories at the variance of their respective utility functions, and then just maximise expected value. Owen Cotton-Barratt convinced me of that!

Sorry if that was a bit of a complex response to a simple question!