Will a Democrat have the Electoral College advantage in any of the next three elections (2024, 2028, or 2032)?
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A candidate has the Electoral College advantage if their margin in the tipping point state is greater than their margin in the popular vote. So, for example, if the two major party candidates win 47% (R) and 51% (D) of the popular vote, but in the tipping-point state, they win 49% (R) and 50% (D) of the votes, then the Republican has an Electoral College advantage of 3%, since they lost the popular vote by 4% (i.e., their margin was -4%) but only lost the tipping point state by 1%.

The tipping point state is the state that gives a candidate the decisive 270th electoral vote, if you give the candidate their electoral votes starting from the state where their margin was largest and continuing in order. It is possible for there to be two tipping point states (this happened in 2020, see here for details), and in that case, the margins of the two will be averaged when determining the Electoral College advantage.

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Probability is higher given that Trump's EC advantage this year appears to have been only around 0.3% or so.

Historically, the advantage in the Electoral College alternates, with Democrats having the advantage in 2004, 2008, & 2012 and Republicans having the advantage in 2000, 2016, & 2020.
https://fivethirtyeight.com/features/even-though-biden-won-republicans-enjoyed-the-largest-electoral-college-edge-in-70-years-will-that-last/

I don't think that these are completely uncorrelated (or this market should be at 1 - (.5)^3 = 87.5%), but I think it is not unlikely for the advantage to reverse.