While 'Winner Takes All' is one way to do representative voting and checking that item off the list, it's one of the worst ways to be representative. CGP Grey has a series of videos on different voting systems and their pros and cons on youtube - start with this one, which goes through the ways 'winner takes all' drives towards worse representation: https://www.youtube.com/watch?v=s7tWHJfhiyo

Another issue that Grey doesn't mention is that electioneering in the US is so constant and expensive, that politicians can rarely afford to speak in-depth to people without money to donate. It's a subtle effect and not really corruption, but a result of having to endlessly chase the dollars in order to electioneer.

The US has a representative system, no-one's arguing against that. But is it satisfactory or unsatisfactory?

State and local elections are often not winner takes all, but two-round voting. (Really, more than that, if you want to cheat and count the primary election and possible run-offs there.)

Because it produces outcomes where the distribution of power in government does not follow the distribution in the preferences of the electorate (even the distribution as expressed in voting, which is already distorted by tactical accommodation to the known features of the electoral system.)

This is problem stemming largely from the use of single-member winner-take-all elections by majority/runoff or plurality rules, as is the case for most legislative (and many other) elections, and which is compounded, at the federal level, by distribution of representation disproportionately to population (obviously in the Senate, but granularity results in significant variance in district size for House seats, as well.)

Arend Lijphart's Patterns of Democracy provides pretty good coverage of both the degree to which various modern democracies have representative government, the structural features that are associated with effective representation, and the effects that those variations in effectiveness of representation have.

> People freely choosing to vote for people that you don't consider to be in their best interests does not make a government unrepresentative.

True, but America, nevertheless, among modern democracies has a notably poorly representative government.

> There are a few factors that impact representativeness - gerrymandering and the ineligibility of felons and illegal immigrants, for instance, but all-in-all that impact is pretty minor.

Gerrymandering actually has a lot less impact on representativeness than it gets credit for (but it having any significant effect is a product of single-member, winner-take-all districts, which have a very large effect on representativeness, even outside of gerrymandering.)

> In particular, of course, at a local and state level, those impacts are reduced along with the scale.

No, the scale might be reduced, but the effects of gerrymandering and disenfranchisement, such as they are, are not reduced at local scale (and may actually be exacerbated, depending on the locale -- there are locales above and below the national average for distortion from any of those sources.)

Additionally, there are systems used at local scale (such as multiseat elections on a Vote for N system, with N winners) that are frequently used in local elections that are more hostile to effective representation than single-member, winner-take-all districts.

OTOH, the effects of unequal allocation (at least for legislative districts) are reduced at the state level.

> If Americans have a divisive, gridlocked federal government that produces results nobody likes, that's the natural consequence of a divisive, gridlocked populace that doesn't know what it wants (lower taxes! more social security! balance the budget!), not un-representative government.

Well, no, its a product of a combination of unrepresentative government and a Constitutional system deliberately made to have many veto points, which means if the distortions that effect different institutions work in different directions, the result is gridlock.