"Fairness" being seen as the same as to majority > all would just result in what we've seen happen with our democracy experiments in places like the Mideast. The majority group just ends up using democracy as a cudgel against minority groups. Those minority groups of course don't just stand idly by and next thing you know the entire system is in meltdown and beelining right towards the next iron fist.

But in general this cost pales in comparison to the alternative system where by merit of having a simple majority, a majority group can impose their every whim and desire on the every minority group with absolutely no restraint. If you can solve both problems in some way, do feel free to share - and not only here. You'd have solved a core problem of political science!

Yes, they can, especially where the combination of FPTP with gerrymandered districts, unequal allocation (by population) of seats (in all three of the Senate and, because of granularity limits, the House and, as a consequence of both of those, in the Electoral College) makes it possible for a minority with the right geographic distribution to have majority control of political institutions.

Should each district be as competitive as the state, so each district roughly works out to be 55% - 44%, knowing that by definition the state's districts would be 9-0 for one party?

Should you instead have five districts clearly for one party, and four districts clearly for the other, knowing that by definition each district would have a huge incumbency advantage?

A lot of people would say they want the districts to be both representative of the state's population, and competitive, without realizing those two principles are in tension.

Each state has x districts drawn by an independent third party which must pass a certain threshold for compactness, and y seats not associated with a district.

Via any mechanism you choose (preference, ranked choice, FPP with parties, whatever) votes are assigned. Any voter in one of the x districts that does not get representation from their local member has their vote flow to one of the y seats.

The exact implementations have tradeoffs, but all are far better.

If you look at the journey from citizen opinion to passed bill, there's a reconciliation process, where those opinions are sorted and filtered to consensus and final vote.

Without proportional representation, more of that process happens earlier. More responsibility given to voters to burden some of that compromise process. When people complain about "lesser of two evils" when thinking of candidates in primaries, or doing calculus on who has a better chance in the general election, that's an expression of that process.

With proportional representation, voters have less of that burden, and have a better chance of electing someone that is closer to exactly what they want. But the burden doesn't go away - instead, that burden increases in the deliberative body itself. More factions and more division in the House.

I'm not trying to represent one approach as better or worse - just saying it's a trade-off, and it isn't the case that proportional representation is "better". From the citizen voter's perspective, maybe, but from the citizen that cares about the final outcome via House bills, it's not so clear.

"Yeah sure, your representatives will be more aligned, but then the outcomes won't be along strict two party lines and will be more aligned with those representatives".