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)….