A Simple Model of Senate Elections

Without a President seeking re-election at the top of the ticket, the Democrats face a substantial challenge if they wish to win back the Senate in 2016.

While the Presidential race gets all the media and pundit attention, the battle for control of the Senate also looms large in this election year.  Republicans enter the election holding 54 of the 100 Senate seats, so a net Republican loss of just five seats would put the Senate back in Democratic hands.  The Democrats have the advantage that many more Republican seats, twenty-four, are at risk in the 2016 election compared to only ten held by Democrats.  This lopsided margin reflects the result of the 2010 off-year election when Republicans picked up six seats from the Democrats.  In principle, some of those Republican senators may be more vulnerable in a Presidential year with higher turnouts and more visibility.  The Democrats certainly believe they can retake the Senate this November.  The Party aggressively recruited candidates for the Senate elections and had secured bids from all but one of its top-tier candidate selections by early October of 2015.

The Democrats also have the advantage that the party of the incumbent President usually wins a slim majority of the Senate vote in “on-year” elections when a Presidential election also takes place but loses in “off-year” elections.


Unfortunately for the Democrats the relationship between Senate electoral success and type of election is not so simple.  If I divide up on-year elections into ones when the President ran for re-election and ones when, like the upcoming election, he did not, a very different pattern emerges.  The President’s party fared substantially worse in the five open-seat elections since 1946 than it did in elections with the President at the top of the ticket.  While open-seat years gave the President’s party a one-percent boost compared to off-years, that difference is not statistically significant.  What matters is whether the President is running or not.


The Democrats’ optimism is also based on the much larger number of Republican seats at risk in 2016.  I find some support for the notion that a Senate “Class” with a comparatively lopsided division of the vote in one election becomes more competitive six years later.  Statisticians call this phenomenon “regression toward the mean,” where observations that were outliers at one time show more average scores when measured again. But this effect is weak, and the division of the Senate vote in 2010, 53-47 percent Republican, was not as lopsided as the margin in terms of seats, 65-35 percent Republican.  All told the estimated “rebound” effect given the Republican 2010 landslide is just 0.6%, raising the expected Democratic vote from 47.1% to 47.7%.

Where else might the Democrats gain some relief?  Perhaps the generally positive state of the economy might provide some help.  Political scientists and economists have tested many different measures of economic conditions in models of voting for President and Congress.  One simple measure that has consistently proven significant is the change in personal income, and that proves true for Senate elections as well.


This chart adds the effects of the year-on-year percent change in real disposable personal income to our simple model.  While the effect of rising incomes is positive and statistically significant, it alone cannot overcome the substantial deficit facing the Democrats in an open-seat election year.  In the six years of the Obama Administration, personal income rose by at most 2.2 percent in a single year, 2012.  With a likely figure for annual income growth in 2016 at around two percent, we should expect the Democrats to win only about 48 percent of the Senate vote in 2016.

Winning a majority of the Senate vote is not a requirement for winning a majority of the contested seats.  In 2004, and most dramatically in 1982, the Republicans managed to win a majority of the seats with a minority of the votes cast.


The high “swing ratio” of 2.4 means that a change of one percent in the percentage of votes won translates on average to a 2.4 percent increase in the percentage of seats.  So even fairly small changes in the division of the vote can have much larger effects on the composition of the United States Senate.

I tried some other possible influences like the approval rating of the President and the size of the President’s margin in on-year elections.  I found no “coattails” effect for the Presidential vote either in years when the President is running or years when he not.  Presidential approval does matter, but only in off-year elections, so I did not include it in this discussion about 2016.  That finding is consistent with a conventional view that off-year elections reflect public opinion about the President’s performance in office.