There's been a lot of discussion recently about replacing the US Electoral College with a national popular vote. As an alternative, I was thinking about how Approval voting might be used with the electoral college as it stands, but combined with some form of proportional representation. For example, if a state has M delegates, and the AV winner A receives X out of N votes, A would receive (X/N) * M delegates, rounded to the nearest integer. For remaining delegates, any ballots approving A would be removed (i.e. reweighted to zero), and the approval winner B on the remaining ballots, receiving an approval score of Y, would receive (Y/N) * M electors, rounded to the nearest integer, or the next lower integer if the sum of delegates would be greater than M. If any delegates remain after highest remnant approval drops below 1/(2N), those remaining should be given to A, the original approval winner. This process could be used in the Democratic primary or in the general election. For US presidential elections, there would be no incentive to allocate electors proportionally until a certain threshold of other states did so also. However, if such an agreement was successful, candidates would have a chance of winning (or losing) delegates in every state, making a full 50-state campaign necessary.