Posted by Nicholas Beaudrot of Electoral Math
Tony Vila has helpfully pointed out that I gave too much credit to Democratic leaning gerrymandering leading to the domination of the House of Representatives up until 1994. Remember, in the 1980s, Reagan Democrats were, well, Reagan Democrats. Today, they're registered Republicans, or their children are. So up until that time Democrats regularly won at least a small majority of the popular vote. Winner-take all elections, rather than proportional representation will always exaggerate the dominance of the majority party.
Vila points out that if, say, 52% of the population nationwide votes for the Republican candidate, an even distribution of voters would mean that 52% of every district votes for the Republican candidate, which would mean we'd live in a one-party state! In practice, this never happens, since party identity has since time immemorial been linked to regional, ethnic, cultural, or ideological identity, for better or worse.
So, it's harder to estimate the impact of gerrymandering, except in clear cases such as 1996, where Democrats couldn't produce a majority in the house despite a majority in the popular vote, and 2004, where Democrats lost seats despite gaining ground in the popular vote.