Politically Polarized, Ideologically … Complicated Mapping America’s Ideological Terrain, Part 1 by Joshua Mendelsohn, Michael Pollard – “In April, the Washington Post published an article titled “The Coming Republican Demographic Disaster, in 1 Stunning Chart.” It discusses one of the most notable trends in American politics over the past decade: Republican candidates do consistently worse with people of color, and the proportion of non-white voters in the American electorate is increasing. This could be bad news for the Republican party. If its candidates do not improve their appeal among non-white voters, their chances of winning future elections will decline sharply in the coming decades. This example highlights a more general fact of electoral politics. Demographics—the personal and ideological characteristics of voters—matter. For example, Hillary Clinton polls very well with female voters, while Donald Trump has a staggering lead among voters who hold a negative view of immigration. However, no characteristic or belief accounts for 100 percent of a person’s vote; all personal characteristics and beliefs play a part in shaping a person’s choices. For example, among respondents who supported a candidate in the most recent wave of the RAND Presidential Election Panel Survey (PEPS),women were more likely to support Democratic candidates. Even so, they had only a 60-percent chance of supporting a Democrat, not a 100-percent chance. Moreover, certain subgroups of women had a very high chance of supporting Republicans. For example, women who supported building a fence along the Mexican border had only a 26-percent chance of favoring a Democratic candidate. While demographics matter, no single category is enough to describe the complexity of a person—or that person’s likely voting behavior. While demographics matter, no single category is enough to describe the complexity of a person—or that person’s likely voting behavior. To understand the complexity involved, some social scientists use the metaphor of social space. In physical space, we define the position of objects in three dimensions. In social space, scientists make inferences about people based on the intersection of their various characteristics and beliefs, where each characteristic and belief is its own dimension. For example, Table 1 charts the chance that a respondent favored Ted Cruz in the March PEPS wave, given the person’s highest educational degree and age. All values of 10 percent or more are shaded green. Based on this table, we could say that Cruz support was more likely in the right-side, middle region of the Age x Education space—that is, among voters ages 50 or above with moderate amounts of education. There are thousands of personal characteristics, each of which is potentially relevant for understanding a person’s choices. That is to say, each characteristic potentially defines a dimension of social space relevant for understanding personal choice. While scientists can use high-dimensional geometry to understand this space mathematically, it is impossible to accurately draw a thousands-dimensional space on a two-dimensional piece of paper. Fortunately, a family of mathematical procedures called multi-dimensional scaling (MDS) can tell us how an approximation of that high-dimensional space might look as a two-dimensional map….”