The group polarization effect is that, if people who already share similar views discuss something together in a group, then afterwards the individuals' viewpoints tend to me more extreme in the direction of whatever the group already agreed upon. It follows that if you are trying to acheive consensus in a large population, the worst thing you can do is to segment people into groups according to viewpoint and then have people discuss the issues with others who already share their views. Yet, this is exactly what happens in the current system (and in the voluntary constituency system proposed above) -- people tend to group into political factions, and most discussions about political issues are between people in the same faction.

To counteract this, it is desirable to get individuals from different factions talking to each other. In the current political system, the elected politicians (are forced to) talk to their counterparts in other factions, but ordinary citizens do not.

Solution: cross-councils

Create deliberative groups that include a representative sampling of citizens from different factions. Give these groups an incentive for reaching near-consensus on issues. The groups proposed here will be called __cross-councils__.

If a delegate pyramid (hierarchical voluntary constituencies) is used, then the following method may be used for creating small groups with a representative sampling of citizens from different factions. Let's say that the number of delegates in the legislature (the top layer of the delegate pyramid) is 11. We will create small groups, each of size 11. For each citizen, trace their representatives up through the delegate pyramid; that is, first find that citizen's constituency, then find that constituency's delegate, then find that delegate's 2nd-order constituency, then find that constituency's 2nd-order delegate, etc, until the trail stops (if some delegate is not a member of any constituency), or until you reach the top of the delgate pyramid, in which case you have associated that citizen with one of the 11 delegate legislators.

After doing this for every citizen, almost every citizen is associated with one of the 11 delegate legislators. This is like dividing the population of citizens into 11 factions. Now, all you have to do is assign the citizens into groups such that each group contains one citizen from each of these 11 factions.

You would only make cross-councils out of those citizens who are interested in serving on one. It's possible that some citizens would want to participate, but not be able to be assigned, because each group must have one citizen from each faction, and there could be a shortage of volunteers from one of the other factions.

Now, how to motivate the citizens in these groups to actually talk to and compromise with each other, and come to some sort of rough consensus? One way is to give them political power, conditional upon reaching near-consensus. So, give each 11-person cross-council one vote within some legislative chamber. Specify that a cross-council cannot cast their vote without the consent of at least 10 of the 11 people.