The Wikipedia page for “Royals”:

• Lorde – Royals (wikipedia)
• Lorde – Royals (video)

…currently has this self-conflicting (and grammatically incorrect) statement:

“It follows a V-IV-I chord progression, D-C-G, and is written in the key of D Mixolydian mode (scale)”.

I intend to rectify this obscenity, but want to first small-group consensus on which of the two options are preferred. Chords:

   [D]
...gold teeth, grey goose, trippin' in the bathroom
   [D]
Blood stains, ball gowns, trashin' the hotel room,
[C]                          [G]
We don't care, we're driving Cadillacs in our dreams.

I strongly lean toward:

“It follows a I-bVII-IV chord progression, D-C-G, and is written in the D Mixolydian mode”.

…but in the score-with-minimum-accidentals sense, I would probably let it slide with:

“It follows a V-IV-I chord progression, D-C-G, and is written in the key of G”.

I remember once in high school having an argument with the rest of my band about the same question in the context of “Sweet Child o’ Mine“, where I was – because I was a dolt – arguing that it was in G, because I believe in the “score with minimum accidentals” principle. We all have high school transgressions that we regret, right?

[D]
She's got a smile that it seems to me 
  [C]
Reminds me of childhood memories where
[G]                                        [D]
Everything was as fresh as the bright blue sky.

(Note it's tuned-down a half-step, of course, since it was the '80s...)

Royals is clearly I bVII IV. Incidentally, your favorite song – Werewolves of London – is also V IV I.

[D]     [C]    [G]
     Ah-ooooo, werewolves of London

Can D Mixolydian also be a key signature? Maybe say "it follows a I bVII IV chord progression, D C G, and is in D Mixolydian."

Note, removing "the key of" and "written" I think would help avoid some ambiguity. Does "written" mean "put to paper" or "composed"? And what exactly is a key? Both questions that get in the way of understanding why the song sounds the way it does.

Re: Royals. Done. Worded exactly as Jeff suggested.

Ian: good call on "Werewolves of London". I mean, mentioning "Werewolves of London" is always a bad idea on some level, but it's interesting how "Royals" (or "Sweet Child O' Mine") is clearly I bVII IV, and "Werewolves" (or "Sweet Home Alabama") is V IV I, even though they're the same chords. In all cases the melodies leave some ambiguity too. My dream is that it's not possibly explained by the melody, but a subtlety in the bass part explains it in at least one of these songs.

Also, Jeff, this is why Ian correctly assumed I disdain "Werewolves of London":

The WoL Index: Quantifying Incomprehensibly Bad Popular Music

I think Sweet Home Alabama might be I bVII IV. But I'll have to think about it some more. It's not obvious to me, and I think I'm leaning slightly toward V IV I but I'm torn...

[D]   [C]     [G]
Sweet home Alabama
[D]       [C]          [G]
Where the skies are so blue

Fuck, now I can't decide either (re: Sweet Home Alabama). If anything, the melody resolves to D (weak argument for I bVII IV, i.e. D mixolydian). There's the little turnaround after the chorus, with the big BAM BAM on F → C, between the usual D C G phrases, which I stared at for a while and decided was mostly uninformative, but maybe argues weakly for V IV I, i.e. G major. That is, F as a bVII in G might be slightly more probable than F as a III in D. But then I thought that C serves as a nice bVII resolving to D there, which points back to D mixolydian.

Let's just agree that it's in B phrygian.

"Centerfold" is also I bVII IV IV (G F C C) IMO, so it goes into the same heuristic-breaking gray area as "Sweet Home Alabama". Although it's interesting that on the IV (C), the guitar is doing the usual Keith-Richards-esque suspension pattern that goes between C and F, which would suggest "we're home now, in C, dancing between the I and the V".

[G]            [F]            [C]               [F]  [C]
Does she walk? Does she talk? Does she come complete?

But still, I say it's I bVII IV.

I think Centerfold is more clearly I bVII IV. The prechorus especially sells it as such, with a nice V → I cadence going back into the chorus.

Here's a song that breaks my heuristics but has an obvious key:

Foster The People – Pumped up Kicks

The tonic is the third chord in the chorus progression. But I guess if you call this progression subdominant → tonic → turnaround it doesn't seem that weird, and I'd have to think there are tons of songs that do something like this, though I can't think of any off the top of my head.

I just listened to this song (Pumped Up Kicks), which remarkably I had never heard before. At first I thought¹ you were insane to suggest that “the tonic is the third chord in the progression”:

Foster The People – Pumped up Kicks (verse)

[Fm]                       [Ab]
Robert's got a quick hand
      [Eb]                        [Bb]
He'll look around the room, won't tell you his plan.

To me, everything about this progression is in Fm. It wants to resolve to Fm, and the only chord that's sort of non-diatonic is the Bb, which is just the major IV in Fm, and as per other threads I loves me some IV in minor keys (i.e., I loves me some Dorian mode).

Then after thinking you were a maniac for a bit¹, I finally listened to the chorus, which has the same chords, but I agree totally feels like it resolves to Eb:

Foster The People – Pumped up Kicks (chorus)

[Fm]                        [Ab]
All the other kids with the pumped up kicks
       [Eb]            [Bb]
Better run better run, outrun my gun

¹Eds. note: I'm correcting the historical record in writing this post. I didn't just "think" Ian was insane for thinking "Pumped Up Kicks" was in Eb, I called him out on it (all before I listened to the chorus). I believe I used the words "fucking sociopath". I may have rushed to judgement.

Incidentally if that progression (Pumped Up Kicks) had an F major instead of an F minor, it would be the same progression as “Alive”, which is yet another slightly-ambiguous case. I also say has the tonic at the first chord, where one likes the tonic to be (I bIII bVII IV):

[E]  [G]  [D]       [A]
I,   oh,  I'm still alive.

Technically you could score this in A to have one fewer accidental, but that would be almost as insane as high school me suggesting that Sweet Child o' Mine is in G.