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With winner-take-all state elector selection plus elector counts that favor lower-population states there are huge distortionary effects on voter turnout, the actual choices a voter makes in the voting booth, and campaigning, including GOTV efforts. The nationwide popular vote therefore has little meaning, not just on the actual outcome (plainly irrelevant for that) but even as some kind of score-keeping or "what if" thought experiment.

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Your argument isn't supported by the turnout results. Average in 2016 was about 59%. Non-swing states like CT, DE, IA, MA, MD, ME, NJ, OR, NH posted 65%+ turnout. Many swing states did have solid turnout, but even among states with similar tight margins there's a wide variance, like 75% in MN vs 66% in MI.

Edit: Data from here: https://ballotpedia.org/Voter_turnout_in_United_States_elect... (notably PA and WI are missing)

Maybe you could say states that transition from being safe to swing states see a turnout boost? I haven't checked. I would expect that turnout is more determined by demographics and inertia (states with high turnout in prior elections continue to do so, etc) than whether they are swing states, though.

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