I don't think it will end anywhere that there are just one or two "representatives" for a particular geographic area with first-past-the-post voting. Here In the USA, we have 535 congressional districts, each with exactly one Representative, and 50 states, each with exactly two Senators. This makes it nearly impossible for anyone who isn't running as a candidate from one of the two main parties to get their foot in the door. It also means a goodly portion of of the population in each district -- those who voted for the loser(s) -- have no representation, at least for that term. The UK's House of Commons has the same issue; 650 single-member constituencies.
Places where there are more than two parties tend to have systems where at least some of the representation is "at large"; where candidates and/or parties with as little as a sin us gle-digit vote totals still end up as representatives. This means voters don't see it as "throwing away" their vote if they don't vote for one of the top two parties.
Some people think that preferential voting systems such as "ranked choice" would fix this, but I'm not at all convinced. If I was starting form scratch, designing a representative republic in the 21st century, I would have a fixed number of representatives, all "elected" at large, and individuals could change who is representing them at any time. Representatives would be proxies for individuals, and if you find yourself in disagreement with your representative over an issue that's important to you, you could pull your proxy from him and give it to someone else instantly. Anyone could stand for a seat in the legislative body at any time, and all they would need to be seated is a sufficient number of people to assign them their proxy.
hmm............not sure that the issue for the 2 x party system is just a matter of how members in either house are elected (in Governments that have 2 x houses)! At question also must be how the head-of-State is elected and more importantly () how the outcome of this process integrates with the relationship of the Country's leader with the members of the houses. Your system has independent processes and this results in both advantages and disadvantages - but the election of the head of State in other countries is different
I agree with your uncertainty regarding preferential voting. We have this system for our upper house and it has evolved into a farce where Senate members can be elected with a very small amount of primary votes - via the distribution of preferences of other candidates (it has even generated new enterprises called "preference whisperers")
I'm also uncertain about your proposal for a "representative republic in the 21st century". One of the must-haves in any successful government is stability between election cycles. If I understand your proposal correctly - the ability of voters to withdraw their support for a sitting member would (I suspect) wreak havoc on the normal process of law making because house members are continuously changing!
But it's easy for me to criticize any proposal - and not to suggest an alternative!
However, a far more important aspect of your reply and at the heart of my concern about your response is the part that I have bolded. , this sentiment crystallizes the fundamental problem discussed in earlier posts about the polarization of political views and the question of the usefulness of 2 x party systems in 21st century.
The idea that elected members only represent their voters is fundamentally inconsistent with the system for democratic voting which assumes that the elected member represents the entire constituency in their area. For as long as this dichotomy exists (or more importantly, for as long as the perception that the dichotomy exists amongst voters) - the democracy cannot (and must not) succeed because it fails to be representative!!
As indicated in earlier posts, this new construct is the evolutionary religion that seems to be pervading (infecting) modern democracies; and as I have said, it's driven largely by the clear message from political parties themselves.
If you and your fellow voters hold firm to your view (in the bolded bit), then the 21 century voting method has to accommodate this new democratic paradigm. Not sure how this is done - or even if it can be done (might be easier to change voter belief - perhaps?)
Don