The Republican Party's Senate Advantage

The US Senate is perhaps the least democratic body in the world. And the ways in which it's undemocratic - with each state getting 2 senators regardless of population and winner take all elections - happens to create an advantage for Republicans. This advantage has been reported in several different ways such as how many people the Senators represent

Today, according to Drutman’s figures, the 47 Democratic senators represent almost 169 million people, while the 53 Republican senators represent about 158 million.

Or how many people voted for each 

In the new Senate, the 46 Democrats will have received 20 million more votes than the 54 Republicans.

Neither of these seem like the right way to demonstrate the advantage. The problem with the first method stems from the word "represent." Someone can represent you - legally - without representing you philosophically. If one party won all 100 seats by just 1 vote each, they would legally represent everyone, but not policy-wise.

The second method ignores all the people who voted against someone. 

Instead, the right way is compare everyone who voted for Democrats in the Senate's 100 races to everyone who voted for Republicans in those same races. If we do that it turns out that Republicans haven't had the advantage in votes since January 2, 2001 even though they've controlled the Senate for nearly 13 of the 20 years since then.

On the plot above, the purple line shows how many more (or fewer) people voted for Democrats in the 100 Senate elections that fill the seats at any given time The blue streaks show the periods of Democratic control of the Senate. You can see that Democrats have had a vote advantage of millions, but it has not resulted in control of the Senate. Over the past 4 years, their vote advantage was more than 10 million votes and yet they didn't control the Senate.

A few caveats about the data. 

• When a seat is filled by an appointee, it doesn't count in the total (both Democrats and Republicans get zero votes). 
• Senators are counted with the party they caucus with, unless they switch parties mid-term. So votes for Bernie Sanders count as votes for Democrats, but votes for Jim Jeffords following his 2001 switch still counted for Republicans. 
• In jungle primaries or California's top-2 system, the votes from the runoff are used, unless only one party advances and then the votes from the primary are used with each parties candidates votes added together. 

https://www.brookings.edu/experts/molly-e-reynolds/

https://www.washingtonpost.com/outlook/senate-states-republican-control/2020/11/18/571573e0-2915-11eb-92b7-6ef17b3fe3b4_story.html