Modeling Support for the Democratic Party in California 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* = c0 + c1S1 + c2S2 . In this equation, S1 and S2 are the socioeconomic variables that we previously mentioned. We’ll let S1 be the percentage of California voters with a bachelor’s degree or higher and S2 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 c0 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. 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
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ABOVE: Socioeconomic variables and their coefficients in each election year (2, 3, 4, 5, 6) 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
