What's a Vote Worth? (a.k.a., The Importance of the Quantitative Liberal Arts)

DTLT is sponsoring a design sprint on The Quantitative Liberal Arts on Wednesday, March 22, at 12pm, in HCC 407. Bring your lunch if you like (we’ll provide dessert!), and come ready to discuss and assemble resources for helping our students think deeply and critically about the relationship of data and narrative. In this post, Kris Shaffer unpacks one area in which the synthesis of data and critical thought is essential to finding meaning and directing action in our current political system.

 Frederick Gibbs and Dan Cohen write:

Any robust digital research methodology must allow the scholar to move easily between distant and close reading, between the bird’s eye view and the ground level.

But this isn’t just for scholars. Merging quantitative and qualitative reasoning, applying critical thought to data, synthesizing the arts, sciences, and humanities, … these are essential elements of modern education. In fact, I’d argue that they are among the most important elements of modern education, if for no other reason than they are really hard to do well. They are also nearly absent from the information being circulated widely in our culture.

And how do we help our students develop these abilities?

Let’s take the presidential election as an example: How much is a vote worth?

Whenever there is a discrepancy between the electoral college and the popular vote in a US presidential election, this question resurfaces. Few things are more quantified in US culture than election data, and yet few things are more contested than the meaning of election data. There are a number of ways to count the value of a vote, and underlying each is a narrative, a set of values. And it’s at the intersection of data analysis and the unpacking of those values where we find meaning. So let’s explore a few of the common narratives surrounding the value of a vote and see what we can find.

When we use a system like the electoral college, citizen votes in smaller states correspond to a larger share of the electoral votes. This is because each state’s number of electors is the sum of its representatives in the House and the Senate (with the District of Columbia receiving an amount equal to the smallest state). Since the House is already determined in proportion to population, when we add two electors to each state, it messes with the proportional system, disproportionately affecting small states. (This is why opposition to the Electoral College is often encapsulated in the phrase, “One person, one vote” ― every vote counts the same.)

So in what states are individual votes worth the greatest share of the electoral college? Here is a chart, based on 2016 election results and the 2010 census (download the data here).

While most states have about 1.5–2.0 electors per million citizens, the 15 smallest states and districts show a precipitous rise in electors per citizen as population gets smaller, with the result that a citizen in Wyoming holds more than three times the share of the electoral college than a citizen in California.

Now this is citizens, not voters. Things are a little different when we look at the ratio of electors to votes.

Interestingly, Wyoming votes are still worth about three times of the electoral college than they are in California. But when we look at votes instead of citizens, we see a swing-state effect. There are a number of states where the election was closer than in California, and as a result had a higher voter turnout, giving each individual vote less of a share of the electoral college than in a state where fewer citizens turn out to vote. Notably, votes in the perennial swing state of Florida are worth about one-fourth of a Wyoming vote’s share of the Electoral College.

But this brings up a second narrative about the value of a vote: how likely is it that a changed vote will change the election results? Most states have a winner-take-all model, where the state’s winner gets all of the electoral votes. So if you want to influence the outcome of the election, this narrative says you shouldn’t move to a state where your vote is worth a large share of the electoral college. Instead, you should move to a state where the election is regularly a tight race. Which states are those?

2016 election data: margin of victory for each state and DC

The closest races in 2016 were New Hampshire, Michigan, Maine, Wisconsin, Nevada, and Pennsylvania. These are the states in 2016 where your vote was most likely to change the election results. In California, New York, Illinois, Massachusetts, and Texas, not so much.

But these aren’t the swing states we heard about constantly during the election. Where are Florida? North Carolina?

As usual, a single statistic isn’t enough to capture the complexity of the issue. If I simply want my vote to count for more of the electoral college, I move to a small state like Wyoming. If I want a high likelihood that my vote will change the Electoral College tally, I move to a close state like New Hampshire.

But if I want my vote to change the winner of the election, I want to move to a large, winner-take-all state with consistently close results. This is a state where my vote is both likely to change who my state’s electors vote for and a state with a lot of electors, and therefore a large impact on the final election result.

Which states fit that bill?

2016 election data: state margin of victory plotted against number of electors

This is kind of hard to read, so let’s take out the three states with both a large margin of victory and a large number of electors (California, Texas, and New York) and zoom in on the others (click the image to enlarge).

2016 election data: state margin of victory plotted against number of electors

Now we can readily visualize the states with a small margin of victory and a high number of electors ― they are in the upper-left of the chart: Michigan, Wisconsin, Pennsylvania, Minnesota, Arizona, and Florida. These are the states where close race intersects with high impact. (Note that North Carolina is still not in this group. While it was considered a close race going into the election, it turned out to be more firmly red than pollsters and pundits expected.)

The three states the media paid the most attention to into the wee hours of election night, also the three states whose results were contested by the Stein campaign, are in this list: Pennsylvania, Michigan, and Wisconsin. While New Hampshire was closer than all three of these, and while it was a very politically active state (with the highest voter turnout by percentage of 2010 population), it isn’t a very big prize, and thus wasn’t a big story in the media, even on election night.

There are a number of different narratives that can be spun with this data, including some I didn’t discuss here (where did candidates invest the most money? buy the most TV ads?). And it is all too easy to dismiss a narrative by countering it with other data. Data alone isn’t sufficient to answer the question how much is a vote worth? In fact, data alone is insufficient to most questions we care about. But the same is true for narrative. We need both data and narrative, and the critical abilities to combine them in appropriately nuanced ways. That’s why we need the quantitative liberal arts.

On Wednesday, March 22, at noon in HCC 407, we’ll have a brown-bag design sprint where we explore the quantitative liberal arts. We’ll unpack and critique some common data-driven narratives we engage in our culture, discuss how the issues of data needing critique and narrative needing data come up in our classes, and construct a concrete set of resources and tasks we can use to help our students (and ourselves!) bring data and narrative together in critical and meaningful ways.

So please join us! Feel free to bring a lunch. We’ll provide dessert! And we’ll hopefully all leave at least a little better equipped to help our students engage these important issues.

Header image by Mike Wilson (CC0).