David Boies is leading an effort to challenge the winner-take-all method that most states use when awarding presidential electors. There are different ways states might award electors (which I used to project alternative electoral outcomes in 2016).
Brenden Cline in 2017 nicely summarized the series of major problems with this litigation. It's been argued and rejected before. Simply put, states have essentially plenary authority to choose the method of appointing electors, and the winner-take-all method has been around for 200 years, and used basically everywhere since the Civil War--with brief exceptions in Colorado in 1876 (legislative selection), Michigan in 1892 (district method), and Nebraska and Maine (district method) in recent years. (I discuss this plenary authority in 2007 and 2008 Election Law Journal pieces, which conclude that that plenary authority does not extend to states entering into interstate compacts with one another concerning the award of electors--at least not without congressional consent. I also discuss it as an element of federalism in Invisible Federalism and the Electoral College, 44 Arizona State Law Journal 1237 (2012).)
Since Election Day, a number of litigants--admittedly, mostly (if not all!) pro se--have attempted to file just such challenges. They've lost every time (0-6 by my count).
Schweikert v. Herring (W.D. Va. 2016): "The precise issue contained in Plaintiff’s complaint was previously litigated, dismissed, and affirmed summarily by the Supreme Court. Williams v. Virginia State Bd. of Elections, 288 F. Supp. 622 (E.D. Va. 1968) (3 judge court), aff’d per curiam, 393 U.S. 320 (1969), reh’g denied, 393 U.S. 1112 (1969) . This Court lacks the authority to reach a conclusion that directly contradicts the Supreme Court’s own jurisprudence—which is precisely what Plaintiff’s complaint would ask this Court to do. Accordingly the case must be dismissed."
Birke v.The 538 Individual Members of the Electoral College (C.D. Cal. 2016): "to the extent Plaintiff challenges some states' 'winner-take-all' procedures . . . Plaintiff's challenges similarly lack merit. . . . Williams v. Virginia State Bd. of Elections, 288 F. Supp. 622 (E.D. Va. 1986), aff'd, 393 U.S. 320 (1969) (per curiam) (upholding 'winner-take-all' procedure for choosing electors)."
Conant v. Brown (D. Or. 2017), appeal pending (9th Cir. No. 17-35349): "Plaintiff's arguments are foreclosed by Supreme Court precedent. In a 1969 case, the Supreme Court summarily affirmed, per curiam, the district court's rejection of constitutional challenges to Virginia's method of providing electors to the electoral college based on a plurality vote in a statewide election. Williams v. Va. St. Bd. of Elections, 393 U.S. 320 (1969) (per curiam)."
Schultz v. Roberts (S.D. Cal. 2017): "The Electoral College system is specifically provided for by the Twelfth Amendment. Gray v. Sanders, 372 U.S. 368, 380 (1963) (“The only weighting of votes sanctioned by the Constitution concerns matters of representation, such as . . . the use of the electoral college in the choice of a President.”). Schwartz does not allege any facts to support his claim that the Electoral College system violates his constitutional right to equal protection."
Williams v. North Carolina (W.D.N.C. 2017): "Defendants conclude that Plaintiff’s claims in this matter regarding the winner-take-all method of appointing electors do not differ significantly, if at all, from those asserted in McPherson, Delaware, Penton, Williams, Schweikert, Hitson, Conant, or Birke. The opinions in these cases, particularly the Supreme Court’s opinion in Blacker and summary affirmation of Williams, apply herein."
Gordon v. Nat'l Archives & Records Admin. (D.D.C. 2017): standing
Of course, part of litigation like this is theatrical. Another part of litigation like this is to get the Supreme Court to address the merits of the dispute, even if lower courts ought, under existing precedent, summarily dismiss such claims. But, time will tell whether this effort is any more successful than the many, many failed efforts that have gone before.