How votes are converted to seats in the House of Representatives and how that has changed.

In a perfectly proportional legislature the percent of seats should equal the percent of votes received by a party. Electoral systems based on proportional representation come close to ensuring this by design.

Two-party, plurality, systems are rarely if ever proportional. They tend to reward votes disproportionately, giving more seats than votes to one party and fewer seats than votes to the other. They also often award a majority of seats for less than a majority of votes.

One measure of the bias in a system is the “representation ratio,” the percent of seats divided by percent of votes. A value over 1.0 means a party gets more seats share than votes share, and values less than 1.0 means underrepresentation.

In the US from 1942 until 1994 the Democratic party was advantaged, with a representation ratio typically around 1.1 with variation across elections. After 1994 that reversed, with the Republican party enjoying an advantage, a bit smaller than Dems had.

Part of this was the “solid South”, dominated by Democrats until the 1980s coupled with very low turnout which made winning Dem vote totals smaller than in competitive elections. The transformation of parties in the South after 1980 became a GOP advantage.

Gerrymandering also plays a role in the vote-to-seats relationship, with advantages to parties that control legislatures and governorships that create the districts. Courts imposed some limits on districting beginning in the 1960s.

From 1942 to 1994 Democrats were advantaged in all but two elections. Since 1994 Republicans have been advantaged in all but one election (2008). The advantages were persistent in each era.

The RepRatio is a simple measure of advantage, but what about how votes are converted to seats across elections? This chart shows the percent of seats won by percent of national vote won in each election. 1942-94 is different from 1996-2020.

One measure of bias is the percent of votes required to win 50 percent of seats. In 1942-94, Dems needed 48.4% of votes to reach 50% of seats. Since 1994, Dems need 51.2% of votes to reach a majority of the House. There is uncertainty but these are the expected outcomes.

Another measure is the “swing ratio”, the slope of the regression lines, measuring how much seat share changes for a 1 point change in vote share. In 1942-94 Dems got 1.80 percent more seats for a 1 percentage point increase in vote share. After 1994 it has been 1.47.

Post 1994 Republicans gained an advantage in votes required for half the seats & reduced the swing ratio to lessen the effect of votes on seats. Both eras have swing ratios over 1.0 meaning seats are more responsive to votes than pure proportionality. This is common in 2 party single-member district systems.

If we shift to the relationship between national presidential vote and seats in the House we can extend the time frame back to 1900. I divide into two partisan eras, 1932-1992 for Dems, and 1900-1928 plus 1996-2020 with a GOP House advantage.

Interestingly, the relationship of seats and votes is essentially the same for the 1900-28 and 1996-2020 eras of GOP advantage. A test of different slopes & intercepts gives p=.69 so I combine them here.

In the 1932-1992 Dem era, a Democratic presidential vote of just 36.3% was enough to expect a 50% Dem House. In the GOP eras, a Dem president needed 51.2% of the national vote to expect half of the House.

The Democratic solid South again provided a huge advantage in the 1932-92 period. In the two eras that Reps were advantaged in the House, their advantage is much smaller, requiring Dems to get 51.9% of the pres vote, 50.3 in 1900-28 & 52.7 since 1996.

The takeaway is that Republicans converted a long time disadvantage in winning House seats to a smaller but persistent advantage after 1994. Once control of the House was won in 1994, the GOP has held an advantage, despite one reversal in 2008.

The size of the current Democratic disadvantage is important, but it should be recognized that the GOP disadvantage from 1932-1994 was far greater. Changes in regional party dominance plays a big role in that and shows party advantage can be altered.