Some examples from 2018 of the problems with single seat districts.
As I have often written, the electoral system we use to elect the House of Representatives (and most other legislative bodies across the country) is antiquated and flawed. It privileges the container (the district) over that which is in the container (citizens).
Representative democracy, wherein citizens vote, votes are tallied, and votes are then translated into offices in government, ought to produce a result that is reasonably representative of the population. That is to say, an underlying assumption is that those who govern should reflect, to some reasonable degree, the views of the governed. I note “to some reasonable degree” because perfect representation is impossible save in a direct democracy in which we all participate.
Just having elections is not enough, the way the votes are cast, counted, and applied, matters greatly.
The Electoral College, by way of example, is a system in which voters vote, but then those votes are translated by a process that means that the person with less popular support can win the office. That is not a representative outcome. (And yes, clearly one’s mileage may vary as to whether one is bothered by that fact or not).
As a side note, I would note that while the notion of representativeness is not one we talk about in regards to our elections (though we should, and appear to be starting to do so), we fully understand it because we talk about it all the time when we discuss polls. The whole idea of polling is to take a representative sample of a target population. Good polling requires good sampling. So, too, good representative democracy require good electoral rules which will create an actual reflection of the population. Any of us who know even a modicum about polling knows that if one’s goal is to find out a state’s presidential preferences, how one polls matters. If one attempts a statewide poll in Alabama but only in the Black Belt, the western side of Montgomery, and the core of Birmingham, one would find (incorrectly) that the Democrats are going to dominate (all of those areas are heavily populated by African-Americans). The problem with that sampling process is that is it decidedly not representative of the state as a whole. We know this is problematic for opinion polls, and we should understand that systems that likewise bias outcomes is a bad way to elect “representatives” (scare quotes to make a symbolic point).
