Modeling Support for the Democratic Party in

BY GRETA SCHEVE

If someone asked you to explain the American political landscape, your first instinct would probably not be to dive into differential equations. But it turns out that differential equations can be used to model support for political parties, and they can be a useful tool to explain different trends over time. Every place has a unique social and economic environment ultimately shaping the political landscape. At any given time, a maximum number of people will support a specific political party, also known as the carrying capacity of the party. In this piece, we can treat different socioeconomic characteristics of a population as different variables in order to build an equation for the carrying capacity of the Democratic Party in California. For the model we’ll look at, there are only two variables: the percentage of California voters with a bachelor’s degree or higher and the percentage of California voters who are veterans. While this article looks at the Democratic Party in California from 2000 to 2016, the same process could be applied to any political party over any time period (1).

First, we constructed an equation to represent the carrying capacity of the Democratic Party. Our function will look like

P* = c 0 + c 1 S 1 + c 2 S 2

In this equation, S 1 and S 2 are the socioeconomic variables that we previously mentioned. We’ll let S 1 be the percentage of California voters with a bachelor’s degree or higher and S 2 be the percentage of California voters who are veterans. If the c coefficients have a high value, that means that the corresponding S variable has a bigger impact on the overall support of the Democratic Party in California. The parameter c 0 is the baseline carrying capacity, which means that the support for the party will never fall below this value. The table shows all of the values of each of the variables and coefficients for each general election from 2000 to 2016.

ABOVE: Socioeconomic variables and their coefficients in each election year (2, 3, 4, 5, 6)

Using the carrying capacity function, we can construct a differential equation that uses the carrying capacity to predict whether support for the Democratic Party will go up or down over time. If support for the party is below the current carrying capacity, support would increase until the carrying capacity is reached. Similarly, if support for the party is above the carrying capacity, the party’s support would decrease until it reached the carrying capacity. We can solve the differential equation to get an equation that will tell us support for the Democratic Party in California at any given time between 2000 and 2016. This is a little harder than it looks, since the political climate is always changing. Essentially, solving our equation is like trying to reach a target that is constantly changing. We can make this easier to solve by splitting up the time into 4 year increments, which is the time between each general election in California. The graph shows actual and modeled support for the Democratic Party in California over time. The start of the x-axis is the year 2000, and every increase in time by one corresponds to a four year election cycle. The y-axis shows support for the Democratic Party as a percentage, with 1.0 meaning 100 percent of California voters voted for the Democratic candidate.

One of the most important results we can take away from our model and the graph above is whether or not the Democratic Party has reached its carrying capacity. From 2000 to 2008 support for the party increased, suggesting that actual support for the party was below its carrying capacity in California. However, from 2008 to 2012 support for the party decreased, suggesting support was above the party’s carrying capacity. From 2012 to 2016 the slope of the solution curve switched back to being positive, which means the carrying capacity had not been reached yet. This means that we can probably expect to see more support for the party if we look at data from the 2020 general election. In general, the changing slope of the graph over time suggests that either the carrying capacity has changed considerably over this 16 year period or the Democratic Party is very good at attracting short term support that is not sustainable over the long term. This might be the case if there were certain controversial issues on the ballot during a particular election cycle that caused a lot of people to vote Democratic that normally would not. Interestingly, the Democratic Party appeared to have gained more support than their carrying capacity from 2004 to 2008. This is in part likely due to the historic candidacy of Barack Obama, which turned out record numbers of voters. This trend started to correct itself from 2008 to 2012, but support either dropped lower than the carrying capacity or the carrying capacity increased between 2008 and 2012. This led to an increase in support yet again. One potential explanation for the dip in support in 2012 could be that there was an incumbent democratic president, which may have led to reduced voter turnout. A shifting carrying capacity means that the socioeconomic environment of California is also changing.

ABOVE: Modeled and actual support of the Democratic Party in California over four election cycles

Another important result from our model can be seen if we look a little closer at the values of the c coefficients from our carrying capacity function. Looking at the c 0 coefficient, we can see that there was a big jump in 2004 and then a jump back down in 2008. The c 0 coefficient represents the baseline carrying capacity of the party without taking into account any socioeconomic variables, so this jump supports the conclusion that the carrying capacity of the Democratic Party in California increased from 2000 to 2004, and then fell again in 2008. Additionally, in every year the c 1 coefficients are considerably larger than the c 2 coefficients, which means it is likely that being a college graduate is a much stronger indicator of support for the Democratic Party in California than being a veteran.

While we’ve only looked at how two socioeconomic variables influence support for the Democratic Party, there are infinitely many different variables that could be factored into the carrying capacity of a political party at any given time. These could include things like income level, which sector someone works in, or their age, to name a few. This model is especially useful because it can be adapted to virtually any political party. Even if differential equations can’t completely explain the changes in the American political landscape over the last 20 years, they can shed a little more light on these important political trends.