The race for the control of the U.S. senate feels a lot like the race for control of the Electoral College (i.e., president), but there are a few crucial differences. First, the only thing that matters after the Electoral College convenes is who won the Electoral College, but minority party senators still get to vote for the next six years (and may tip the majority in the next election or sooner). Second, the Electoral College is 51 elections about the exact same two people, while senatorial elections are about 36 different sets of candidates. Thus, movements in the Electoral College are highly correlated, but senatorial elections are very independent.
Individual elections matter after determining the balance of power in the senate, but do not in the Electoral College. The president is only elected every four years, so it is hard to measure the impact of margin of victory, but the most powerful president in the last few decades lost the popular vote and barely won the Electoral College. In the senate, it is hard for individual senators to enact change, but it is easy for individual senators to block change. Also, looking forward to 2016, the Democrats will defend just 10 seats to the Republicans 24. If the Democrats do lose the senate in 2014, they are likely to win it back in 2016 on the strength of senators who won in 2014.
Start of campaign season to Election Day
The Electoral College elections are extremely correlated. I introduced my Electoral College predictions on February 16, 2012 and there were 26 races where between 5% and 95% for Obama. When I ranked those 26 states from most likely to least likely and compared that to the rank of percentage of votes on Election Day, the correlation was 0.93. Most of the movement was at the less identified fringe, where Arizona was slightly more Democratic than a few similar states with 45% of two-party vote share for Obama (still a landslide) and Maine was also slightly more Democratic than similarly secure states with 58%. When we lined up all of the states in February and pointed out the pivotal states in the middle they went: FL, VA, OH, NH, CO, IA, PA, in that order. Nine months later the vote share in order was: FL, OH, VA. PA, CO, NH, IA. Over the course of nine months the secure states all drifted towards their likely winners, but the true battleground states moved up and down in lock-step as videos turned to debates turned to Sandy. Assume there are three states with the probability of A, B, and C voting Democratic: 25%, 50%, and 75%. You can assume that if one state votes Democratic it will be C, if two states vote Democratic it will be B and C, and if three states vote Democratic it will be A, B, and C. If you assume the possibility of any other combinations at 0%, you are generally going to be fine.
The correlation between the senatorial elections is much less correlated. 16 of 33 elections were between 5% and 95% when I introduced my senatorial predictions in June of 2012. The third most likely for the Republicans in this group was Indiana at 82% for the GOP. The most Republican of the toss-up states was Missouri at 52% for the GOP. Indiana fell to the Democrats in a reasonably tight race and the Missouri fell in a landslide. Both candidates said questionable states on rape and their polls plummeted; their statements certainly entered the public debate, but there is little evidence that their individual falls seriously affected other candidates. Over the five month period of my data the correlations between initial rank of probability and final rank of vote share was 0.78. Assume there are three states with the probability of A, B, and C voting Democratic: 25%, 50%, and 75%. You can assume that if one state votes Democratic it will be C, if two states vote Democratic it will be B and C, and if three states vote Democratic it will be A, B, and C. If you assume the possibility of any other combinations at 0%, you are going to have a problem.
Election Day poses a different type of uncertainty than the course of the election. Election Day uncertainty can be correlated over both types of elections if polling is systematically biasing one party of the other. State-to-state polling for senatorial election is still less likely to be systematically biased than state-to-state polling for the Electoral College, as the polling itself is less correlated between companies and time. Yet, it is legitimate to assume that the uncertainty left on Election Day, unlike uncertainty during the campaign season, is relatively correlated for senatorial elections.
What does this mean for 2014?
The Democrats currently control 34 seats, the Republicans 30, and there 36 seats up for election. So, the Democrats, who need 50 seats for a majority, need to win 16 seats to control the senate and the Republicans, who need 51 seats for a majority, need to win 21 seats.
If this was the Electoral College, I would be comfortable lining up the states from most likely Democratic to least likely Democratic. In that list, Georgia is the swing state (if Orman goes Democratic at 49) or Colorado (if Orman goes Democratic at 50). Thus, I could say the likelihood of the Democrats controlling the senate was 35% or 27%, depending on your Orman assumption. Or 31% if you assume Orman flips a coin (50% to causus with either party) in the scenario that the Democrats hold 49 other seats and he wins. This ranking method can be attributed to Ray Fair and talked about extensively in 2012.
But, the senate is different, in that North Carolina is 72% likely to go Democratic and Alaska is 15% likely to go Democratic. If this was the Electoral College, I would say that the possibility of the Alaska going Democratic and North Carolina Republican was about 0%. States just do not leapfrog like that when the movement is so correlated. But, the possibility of the Alaska senatorial election going Democratic and the North Carolina going Republican is about 15%*28% = 4% (maybe a little less, due to some correlation).
In practice, this does not change the answer that much; assuming near independence (and 50% likelihood Orman goes Democratic if they control 49 seats) we get a probability of 27% that the Democrats control the senate. Near independence versus near perfect correlation lowers the probability just a few percentage points. But, it does dramatically alter the possible coalition that the Democrats or Republicans bring to the next senate; Begich from Alaska may toil in the minority and Hagan from North Carolina could lose, even if the Democrats hold the senate.