The 2016 election has usually been described as a contest between red and blue America, but that isn’t the whole picture. My analysis of survey data collected by nonpartisan organizations suggests that this year’s voters can be broken down into not two main groups, but three.

First there are the angry “dismantlers,” who favor smaller government and support major political reform, such as term limits, constitutional limits on campaign spending, and a lifetime ban on lobbying by former members of Congress. These are the voters...