I appreciate that you don’t want to hijack, but I think this issue gets to the heart of a representative democracy, so I’m going to reply. I think that representatives serve that broader duty that you mention, but they also have a local representative function: to represent the issues that are important to their local constituents. How far down you drill with that local function is question, of course, but I think it is one of the core functions of a representative, and therefore does play into drawing electoral boundaries.
Let’s do a thought experiment. Suppose the electoral law changes in California, and California goes to a single system of all at-large representatives, both in Sacramento and the House of Representatives. And then, due to some fluke in the system, not a single candidate from San Francisco gets elected to either Sacramento or Washington. Would you be content to have your interests represented by members elected from Los Angeles, Bakersfield and the Inland Empire?
Let’s say that there are 15 seats up, in a proportional-representation district, and the only significant parties are the Whigs and the Tories. Each of those two parties will have a list of 15 individuals, in order, to be their candidates. If the vote comes in that 2/3 of the populace prefer the Whigs, and 1/3 prefer the Tories, then the folks who get in will be the top 10 people on the Whig list, and the top 5 people on the Tory list. If the next election, the party preferences of the people change, that might instead become, say, the top 8 Whigs and the top 7 Tories. But unless the district swings so far that one party gets all of the seats, the top person on the Whig list and the top person on the Tory list are sure to get in. And the second and third on those lists nearly as guaranteed.
That is a potential problem with a body as small as congress representing so many people. It seems unlikely any state would select pure proportional representation for state congress though. But that does show that not all versions of proportional representation would be preferable to the current system. Let’s look at what you win/lose for federal elections though:
Current system:
A resident of California is represented by one single congressperson. This person is almost without exception from one of two parties, and for many residents will have political opinions completely opposite to them, even thought they’re from the same district. This person also represents a district with roughly 3/4 million people, and depending on the nature of the district, your needs may be completely different to the majority’s. Will your congressperson care? Or focus on the groups that are large enough to get them more votes than the opposition candidate?
Statewide proportional representation:
You’d be likely to get more political parties, so potentially you have multiple parties that all just list a couple of Angelenos on top and then some representatives of other cities, and somehow only these parties get votes and some regions are left without anyone being from “there”.
First of all I question whether splitting California in 53 really gives that many people a representative that is “theirs” in a meaningful sense, but if you had the situation described above and a large number of people found that undesirable, it would leave room for parties to exploit. If the main party of your choice neglects your region, start a competing party with a similar platform but listing people from “underrepresented” regions on top. Or just threaten to switch parties if the geographic distribution isn’t improved. (Not saying “just start your own party”. I meant “someone will start a new party or influence an existing one”.) And that is presuming you find it more important what region your representative is from/represents, than what their detailed position is on issues.
And then there are hybrids. Carve California into 10 congressional districts with 5 representatives each and use the remaining three as representative-at-large and elect them with “leftover votes” to get closer to true statewide proportional representation.
Ah. Well, that’s a crappy system if you’re only voting for a party and not for an individual as well. STV generally doesn’t work like that.
What the Danes basically do is count a vote twice, once for the party to determine how many seats it wins and once for the individual to determine who gets those seats. You don’t need the complication of ranked or transferable voting. If your candidate doesn’t make the cut, one or more of your preferred party will.