I am not sure abut flattening... Here is an example I just rolled for six character versus eight enemies of irrelevant nature with a +1 initiative bonus.
Us: 7, 18, 17, 22, 6, 10, Avg 13 1/3. Them: 11, 12, 14, 9, 2, 14, 10, 11, Avg 10.375. One roll each is 9 vs 11. Majoritarian is them.
Us: 1, 11, 22, 15, 10, 6, Avg. 10.83->. Them: 8, 2, 3, 12, 18, 14, 12, 15, Avg. 10.5. One roll each is 1 vs 8. Majoritarian is them.
Us: 18, 8, 4, 20, 10, 8, Avg. 11 1/3. Them: 12, 21, 13, 3, 6, 9, 8, 12, Avg. 10.5. One roll each is 18 vs 12. Majoritarian is them.
Us: 6, 11, 20, 22, 14, 17, Avg. 15. Them: 2, 12, 18, 16, 9, 21, 16, 14, Avg. 13.5. One roll each is 6 vs. 2. Majoritarian is us?
So by roll average we would win four. On bonus average we would win two. And on majoritarian we would win one, with those rolls.
I think the lesson here may definitely be: Do not do roll for everyone and then average it, hehehe... That definitely seems to flatten the math. I am not sure if those numbers suggest majoritarian favours the side with more people, or if it was just a fluke that they won that way. I guess bonus averaging is probably the simple solution then. And does not involve a ton of adding, heheh...