What Do You Do With Your Ranked Choice Data?

Once our data is on the permutahedron, we need to figure out some methods to analyze it. One method is to look at the eigenvectors of this data. These eigenvectors make up a basis for the data space, so we can write our total data as a linear combination of these eigenvectors, each of which can also be represented on a permutahedron.

Once again we can look for particular trends. For example, the eigenvectors with the smallest eigenvalues are always the smoothest, that is, there is the least change from node to node. This can tell us a little about the uniformity of the data.

We can also group these eigenvectors by symmetry type. This gives some insight into clustering of the data. If there is a strong signal on a certain shape, we can hypothesize that there may be some grouping of that shape. For example, if the 2-2 shape has a strong signal, we may be looking at 2 parties of 2 candidates.

However the structure of these eigenvectors is messy and largely uninterpretable, so we will next seek out a dictionary of vectors that spans the space, but is more interpretable.