The idea here is that moral theories get more influence the more probable they are; yet even a relatively weak theory can still get its way on some issues that the theory think are extremely important by sacrificing its influence on other issues that other theories deem more important. For example, suppose you assign 10% probability to total utilitarianism and 90% to moral egoism (just to illustrate the principle). Then the Parliament would mostly take actions that maximize egoistic satisfaction; however it would make some concessions to utilitarianism on issues that utilitarianism thinks is especially important. In this example, the person might donate some portion of their income to existential risks research and otherwise live completely selfishly.
As I noted, the model was proposed for dealing with a situation where you’re not sure of which ethical theory is correct. I view this somewhat differently. I lean towards the theory that the parliamentary model itself is the most correct ethical theory, as the brain seems to contain multiple different valuation systems that get activated in different situations, as well as multiple competing subsystems that feed inputs to these higher-level systems. (E.g. there exist both systems that tend to produce more deontological judgments, and systems that tend to produce more consequentialist judgments.)
Over time, I’ve settled upon something like a parliamentary model for my own decision-making. Different parts of me clearly tend towards different kinds of ethical frameworks, and rather than collapse into constant infighting, the best approach seems to go for a compromise where the most dominant parts get their desires most of the time, but less dominant parts also get their desires on issues that they care particularly strongly about. For example, a few days back I was considering the issue of whether I want to have children; several parts of my mind subscribed to various ethical theories which felt that the idea of having them felt a little iffy. But then a part of my mind piped up that clearly cared very strongly about the issue, and which had a strong position of “YES. KIDS”. Given that the remaining parts of my mind only had ambivalent or weak preferences on the issue, they decided to let the part with the strongest preference to have its way, in order to get its support on other issues.
There was a time when I had a strong utilitarian faction in my mind which did not want to follow a democratic process and tried to force its will on all the other factions. This did not work very well, and I’ve felt much better after it was eventually overthrown.