On June 5, 2017, the data journalism website fivethirtyeight.com introduced its new yardstick to assess which political party is winning the battle to control the U.S. House of Representatives (House) after the 2018 midterm elections. This tool is a weighted average of “generic ballot polls,” polls that ask respondents some variant of the question “If the election were held today, would you vote for the Democratic or Republican House candidate in your Congressional district.”

For reference, Democrats lost the total of all votes cast for the House in 2016 by 1.1 percentage points, 47.6% – 48.7%, despite netting six seats.

As of 10:12 am on June 7, fivethirtyeight.com had the Democrats winning the House vote by 6.1 percentage points, 44.5% -38.4% (with 17.1% undecided/choosing another party). If the Democrats won the House vote by 6.1 percentage points in 2018, that would mark a 7.2 percentage shift in the Democrats’ direction since 2016.

To regain control of the House, Democrats need to add 24 seats to their post-2016-election tally of 194.

Here is the question, then.

What change in Democratic seats would historically be associated with a 7.2 pro-Democratic percentage point shift?

To answer this question, I first compared the change in Democratic margin (Democratic percentage minus Republican percentage, total House vote) from the previous election year (“margin change”) to the change in the number of House seats held by Democrats[1] from the previous election (“seat change”) for the 24 House elections from 1970 to 2016[2].

**Figure 1: Change in Democratic minus Republican Margin of Total House Vote vs. Change in Democratic House Seats, 1970-2016**

Change in Democratic House Vote Margin vs. Change in Democratic House Seats, 1970-2016

For example, in 2006, when Democrats netted 31 seats to recapture the House, they also increased their margin over Republicans by 10.5 percentage points, from -2.6 percentage points in 2004 to +7.9 percentage points in 2006 (Figure 1).

The relationship between margin change and seat change is strong and linear: the Pearson correlation (R) between the two measures is +0.91, meaning the two values nearly always rise or fall in tandem.

The next step was to run an ordinary least squares (OLS) linear regression on these data. An OLS regression yields the average change in one variable given an n-unit change in another variable, analogous to calculating the slope of a line (y=mx+b). According to this OLS regression[3], a 7.2 percentage point margin change would, on average, result in a 20.8 seat change, just shy of the 24 seats Democrats need.

Knowing that the party in the White House often loses seats in midterm elections, I tested whether the relationship between margin change and seat change differed between midterm and presidential elections by adding a “product term” to the regression.

The short answer is yes: the relationship between margin change and seat change is higher in a midterm year[4]. According to this second OLS regression, a 7.2 percentage point margin change is associated with, on average, a 25.3 seat change, slightly more than the Democrats need to recapture the House in 2018. Moreover, for every 1.0 percentage point increase in margin change, average seat change increases 3.4.

Despite the possible Republican House advantage from gerrymandering, I found no change over time in the association between margin change and seat change[5].

I will close this remarkably short (for me) post by showing the average seat change associated with a range of margin changes (Table 1):

**Table 1: Estimated Average Change in Democratic House Seats Resulting From Various Changes in %Democratic-%Republican Margin in Total House Votes, 2016 to 2018**

Margin Change, 2018 |
Seat Change, 2018 |

-3 | -9.4 |

-2 | -6.0 |

-1 | -2.6 |

0 | 0.8 |

1 | 4.2 |

2 | 7.6 |

3 | 11.0 |

4 | 14.4 |

5 | 17.8 |

6 | 21.3 |

6.8 |
24.0 |

7 |
24.7 |

8 |
28.1 |

9 |
31.5 |

10 |
34.9 |

11 |
38.3 |

12 |
41.7 |

According to this model, Democrats need to win the House vote in 2018 by around 5.7 percentage points (*i.e.*, a 6.8 percentage point margin change) to recapture the House.

Until next time…

[1] Sidestepping, for now, *net* seat change, which only differs from actual seat change if the number of seats held by Independents changes.

[2] The selection of years is solely because I have been collecting data on all elections (president, Senate, House, governor, state legislative seats) since 1968 for a much larger project. Sneak preview: I observe a fundamental shift in party “focus” between Executive and Legislative in 1992-94. Stay tuned.

[3] Average seat change = 3.112 * margin change – 1.627

[4] The new formula for midterm elections, if you must know, is Average Seat Change = 3.408 * Margin Change + 2.433 -2.770. The coefficients for Margin Change, Election Type (1=Midterm, 0= Election), Margin Change times Election Type were 2.076, 2.433 and 1.332, respectively. The adjusted r-squared was 0.831.

[5] In fact, the product term year*margin change was perfectly collinear with margin change, preventing me from running the OLS regression.

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