"Recall that" [if one can pardon that expression] the Constitution of the United States provides that
(1) the president is elected by a college of electors, and that
(2) there are as many of those from each state as there are senators and representatives in Congress, and that
(3) there are two senators from each state and a number of representatives from each state approximately proportional to the state's population, and that
(4) the legislature in each state decides how the electors are chosen.
All but two of the 50 states give all of their seats in the electoral college to the candidate winning a majority of the votes in that state. The other two, Maine and Nebraska, elect one elector in each congressional constituency (or "district") separately and the other two electors are chosen by a vote of the people of the whole state.
The legislature of Maryland has passed a law saying all of its electors will be of the party that wins a majority of the popular vote across the whole country, provided a specified number of other states pass the same law. This law is supported by Democrats.
Now in one or more states, Republicans in the legislature have introduced bills to adopt the system used in Maine and Nebraska.
It seems to me that the Maryland bill goes all the way in a certain direction, but this last noted bill goes only part-way in the same direction; it's the same thing but less extreme. They're both moving in the direction of making the electoral college vote more likely to agree with the popular vote, but the Republican bill doesn't go as far.
But some Democrats have bitterly accused the authors of the Republican bill of trying to "rig" the electoral college's vote. I haven't seen any specificity about their rationale.
Is there some mathematical reason to view the Republican bill as other than something between the current system and the system proposed by the Maryland legistlature?
Mathematically, there does not appear to be any reason for the Republican-supported bill. The reason these bills have been adopted & proposed is based in how Congressional seats are selected. Each state, of course has two Senators. Since the ratification of the Seventeenth Amendment (1913), these Senators have been directly elected by a majority vote of the people of the respective state.
So having two electors elected statewide by a majority vote is basically mirroring the election of the Congressional offices those electors "correspond" to. As for Representatives, each Representative in the U.S. House is elected directly by the people of their district. In the two states you mentioned (Maine and Nebraska), again, the electors are elected in a way that mimicks the way the corresponding Congressional members are elected.
A further discussion of the failings and benefits of the "Electoral College" is not on-topic for this site, but you can read here for a overview why is it beneficial and the logic behind its initial adoption.