It seems that specifying the delegates’ informational situation creates a dilemma.
As you write above, we should take the delegates to think that Parliament’s decision is a stochastic variable such that the probability of the Parliament taking action A is proportional to the fraction of votes for A, to avoid giving the majority bloc absolute power.
However, your suggestion generates its own problems (as long as we take the parliament to go with the option with the most votes):
Suppose an issue The Parliament votes on involves options A1, A2, …, An and an additional option X. Suppose further that the great majority of theories in which the agent has credence agree that it is very important to perform one of A1, A2, …, An rather than X. Although all these theories have a different favourite option, which of A1, A2, …, An is performed makes little difference to them.
Now suppose that according to an additional hypothesis in which the agent has relatively little credence, it is best to perform X.
Because the delegates who favour A1, A2, …, An do not know that what matters is getting the majority, they see no value in coordinating themselves and concentrating their votes on one or a few options to make sure X will not end up getting the most votes. Accordingly, they will all vote for different options. X may then end up being the option with most votes if the agent has slightly more credence in the hypothesis which favours X than in any other individual theory, despite the fact that the agent is almost sure that this option is grossly suboptimal.
It looks like this problem is assuming that Parliament uses plurality voting with more than 2 options. It seems like it shouldn’t be a problem if all votes involve only 2 options (an up-or-down vote on a single bill). If we want the rules to allow votes between more than 2 options, it seems fixable by using a different voting system such as approval voting.
Given delegates with a certain type of amnesia (i.e. they should not remember to have voted on an issue before, although they might have to remember some binding agreements (I am not sure about that)), we could replace a plurality vote with an elimination runoff, where at each step of elimination delegates think that this is the only vote on that issue (which is thought to be affected by randomization) and they are not allowed to introduce new options.
Well, this system might have its own disadvantages, possibly similar to these (however, at each step negotiations are allowed), although delegates wouldn’t know how to actually game it.
Harras:
It looks like this problem is assuming that Parliament uses plurality voting with more than 2 options. It seems like it shouldn’t be a problem if all votes involve only 2 options (an up-or-down vote on a single bill). If we want the rules to allow votes between more than 2 options, it seems fixable by using a different voting system such as approval voting.
Given delegates with a certain type of amnesia (i.e. they should not remember to have voted on an issue before, although they might have to remember some binding agreements (I am not sure about that)), we could replace a plurality vote with an elimination runoff, where at each step of elimination delegates think that this is the only vote on that issue (which is thought to be affected by randomization) and they are not allowed to introduce new options.
Well, this system might have its own disadvantages, possibly similar to these (however, at each step negotiations are allowed), although delegates wouldn’t know how to actually game it.