Monday, March 5, 2018

Visualizing U.S. gun laws

The Founding Fathers of the USA made the decision to explicitly insist on the right of all US citizens to bear arms, because they felt that to do otherwise could be the foundation of what we would now call a Police State. The right was granted in the well-known 2nd Amendment, along with the right form a militia (to fend off the British, among others). This may have been a reasonable way to achieve freedom in the 1700s; and it was certainly the basis of the reputation of the Wild West in the 1800s.

However, increasingly during the 1900s, and especially now, in the 2000s, the practical consequences of this part of the US Constitution have come into question. Indeed, due to recent events in some states, this facet of the United States has come to world-wide attention, because it is a quite unique gun legislation. However, this is an over-simplification, because there are substantial differences between the fifty states (and the District of Columbia). This blog post provides a practical look at the similarities and differences in these gun laws.

The 2nd Amendment of the U.S. Constitution, the Bill of Rights:
"A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."

Gun legislation in the United States

Gun legislation is not a federal business, as one may think when following the news. The USA is a union of states, rather than a federation, with the states retaining all political rights that they have not delegated to the federal government (ie. inter-state laws and inter-nation laws). This differs from almost all other countries, in which the federal government retains all political rights that it does not delegate to the states or counties.

In particular, the US state legislations are highly diverse regarding how to exercise the basic (constitutional) right to bear arms. Some states retain the original 1700s interpretation while others have made it rather hard to carry guns, either openly or concealed.

The web site GunsToCarry, for example, breaks the legislation down to five general points:
  • Does one need a permit?
  • Does one need a permit to purchase a gun?
  • Does one need to register an owned gun?
  • Is it allowed to carry the gun in the open?
  • Are there background checks when one privately sells or buys a gun?
For each state, each of these questions can be answered by 'Yes' or 'No', for both hand guns (pistols, revolvers, etc) and long guns (rifles) separately.

In addition, further restrictions/modifications are listed. For instance, there are variations regarding the general policy regarding getting a permit for a gun ("Unrestricted"; "Shall Issue"; "May Issue") and how it's done. Hawaii, to take one example, requires permits, and the general policy is "May Issue", meaning that the state may issue a permit or decide not to, on a case-to-case basis. In reality, the bars to getting a permit are so high in Hawaii that normally people don't get one. The other "May Issue" exercised as "No Issue" state is New Jersey. Another characteristic is that some states, such as California, do not allow private sales unless they are done via a licensed dealer or state law enforcement department.

This all leads to 17 characters that can contribute to differences between states. These can be illustrated in a simple network. The outcome is shown below, after some technical details about how to produce the picture.

Technical details

To provide a pictorial overview of these differences, we can use a particular type of network, called a phylogenetic network. We first calculate pairwise distances between the states, quantifying their differences, and then use a neighbor-net to create the picture as a single graph.

The five main questions provide ten binary (2-state) characters (No = 0, Yes = 1), but I chose an ordered ternary character (3-state) for open carry, to account for local variation (open carry allowed in general = 0, not state-wide = 1, not-at-all = 2). For the ordered ternary characters, the change from e.g. "Unrestricted" (0) to "May Issue" (2) counts as two differences. To even out the impact of binary and ternary characters, all binary characters have the weight two. Hence, a distance of 0 (between any given pair of states) means that the two states have the same legislation in all scored characters; and a distance of 2 would mean that two states differ completely in their legislation.

I excluded one character (the maximum number of rounds allowed per magazine) that provides little discriminatory signal, since it can only be scored for the rather few states that have a magazine size restriction (either 10 or 15 rounds) for hand or long guns (or both).

Gun legislation in the states of the U.S.A.

The interpretation of the network is straightforward. States that are closely connected in the network are similar to each other based on their gun laws, and those that are further apart are progressively more different from each other. Find your own state, and you can immediately see which states are similar to it. (For more details, see: How to interpret splits graphs)

Figure 1 A neighbour-net visualizing the differences in gun legislation in the U.S.A. Blue stars indicate states where guns have to be registered.

The graph well captures the differences in the state legislations. States without gun control, i.e. no permits needed, no registration, free-to-carry, no limitation of magazine sizes, form one endpoint of the network (highlighted in red).

At the opposite end of the graph, highlighted in green, are those states requiring permits for having, buying or selling a gun, that don't endorse open carry, and limit the size of magazines to 10/15 rounds. This part of the network is spread out because each state shows a different combination of controls. The most restrictive states are the right-most ones (Hawaii, Connecticut, California and District of Columbia).

In between these two endpoints, come the states that exercise some control (e.g. on handguns only). These are generally more similar to the no-control states, in that they may require one or another permit, but otherwise have no or few restrictions.

You will note the position of both Texas and Florida (states that joined the Union in the 19th century and were part of the Confederacy) in the network — they are both down the end with the fewest gun controls. You will also note the position of the most densely populated states, which are mostly down the other end.

Finally, here is the same graph with two historical groups of states highlighted, representing two phases of the development of the modern USA. The nature of modern gun laws is not randomly distributed among these groups.

Figure 2 Same graph as in Fig. 1, showing the original Thirteen Colonies (1700s) and the states of the Confederacy (1800s).


Clearly, the United States provides a variety of gun legislation, from strong control to almost none. This inevitably leads to strongly opposing opinions among the public when it comes to guns, although this calls into question a basic constitutional right.

The network also provides a guide-graph for any tourists who might be concerned about U.S. gun legislation. They should visit states such as California if they wish to feel safer, or Alaska if they are searching for a little wild-west feeling.

More plots, links, etc can be found in the related long-read. It includes mapping results of recent and earlier tight presidential elections, population density, real GDP, and number of firearm-related deaths per 100,000 inhabitants; links for further reading and some thoughts on the issue.


I have provided fileset on Figshare, including the matrix used (annotated NEXUS, generated with and optimized for Mesquite; "simple" NEXUS with set-up details for PAUP*), the resultant distance matrices (raw, PHYLIP-formatted; analyzed, Splits-NEXUS-formatted), and the figures (for this post an the related long-read)

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