This may look like a slam against Republicans but I am >80% sure the Democrats also have done similar tactics
I was thinking of all the ways in the past that we have had rules to try to create consensus. Like the filibuster rule or lack thereof, and the whole Kavanaugh fight.
I saw a suggestion to reform the Supreme Count to mandate that a president gets to appoint to replace the judge who has been there the longest in the third year of his presidency (and presumably also other times to deal with deaths etc). The idea would be that the president’s party would be more likely to lose senate seats and there would have to be bipartisan support.
Unfortunately, that can lead to problems where the senate majority party just unilaterally stalls the nomination. Or even if the presidential party has 50-59 seats but the opposition party filibusters. Meanwhile, if the presidential party has 60+ votes (or 50+ after abolishing the filibuster) then they can put someone in without the consent of any opposition party members.
A similar idea (force or blockade) manifests in other areas as well. The standard model for independent redistricting is that you have N1 majority party people, N2 opposition party people, and (possibly zero) N3 independents (hopefully the sum of any two exceeds the third) and a plan must have majority approval plus one member of each group. But the problem is, one party could in theory agree to vote against all proposals that do not gerrymander their own party into a majority, and you get deadlock.
This led me to summarize what I believe is the fundamental inescapable problem with any desicion making process that is two party dominated:
Theorem: If a group is divided into two parties and there is some rule (which may or may not depend on party affiliation) that decides if a given action happens or not based on the members’ votes, then either (1) one party can force the action without the consent of any member of the other party, or (2) one party can prevent the action without the consent of even one member of the other party.
Trying to solve one just throws you into the other. The only real answer I see to break two party domination with a voting method like Score or STAR voting but not IRV which in practice leads to 2PD.
I guess I could write a formal mathematical statement when I have more time.