In Ideal Advisor Theories and Personal CEV, my co-author and I describe a particular (but still imprecisely specified) version of the parliamentary approach:

we determine the personal CEV of an agent by simulating multiple versions of them, extrapolated from various starting times and along different developmental paths. Some of these versions are then assigned to a parliament where they vote on various choices and make trades with one another.

We then very briefly argue that this kind of approach can overcome some objections to parliamentary models (and similar theories) made by philosopher David Sobel.

The paper is short and non-technical, but still manages to summarize some concerns that we'll likely want a formalized parliamentary model to overcome or sidestep.