Scaling Voters, Candidates, and Groups with Feeling Thermometers

Below we use Bakker and Poole’s Bayesian multidimensional scaling method to scale voters, candidates, and groups together using respondents’ feeling thermometer ratings. Specifically, the UGA module of the 2015 Cooperative Congressional Election Study asked 1,000 respondents to rate how warmly or coldly they felt about a series of candidates and groups (e.g., investment bankers, Muslims, Evangelical Christians, etc.).

Based on these thermometer ratings, we can jointly scale voters and these candidates/groups such that greater distances correspond to “colder” ratings and smaller distances correspond to “warmer” ratings. The main advantage of the Bakker-Poole method is that it avoids pushing candidates/groups too far to the edges of the space. That is, there are some voters to the left of Sanders and the right of Trump–as a general rule, candidates shouldn’t be the most extreme points in the space. As a technical matter, this is because Bakker-Poole MDS uses the log-normal distribution to model the thermometer ratings, which reflects the intuition that smaller distances should have smaller error variances.

The results are shown below. Because we are using a Bayesian approach, we can easily extract measures of uncertainty for the point locations (Jacoby and Armstrong have also developed a bootstrapping approach to estimate uncertainty intervals for MDS solutions). Accordingly, we also plot the 95% credible intervals for Donald Trump, Marco Rubio, Jeb Bush, Bernie Sanders, Hillary Clinton, and Pope Francis.

Several things stand out. First, there is a clear liberal-conservative division not only among candidates and partisans, but also social groups. There are two distinct clusters of Democratic and Republican candidates, voters, and groups.

That being said, there are also internal divisions within each of the party clusters. Both Clintons and President Obama are highest on the second dimension, while we find Sanders and several liberal groups lower on the second dimension. Socialists are placed the furthest left of all groups. On the Republican side, Trump and Jeb Bush anchor opposite ends of the second dimension. As we would expect, more Republicans have high second dimension scores (closer to Trump) than low second dimension scores (closer to Jeb Bush).

There is more uncertainty associated with the locations of the Republican candidates than with Hillary Clinton or Bernie Sanders. Hillary Clinton is also closer to the interior of the Democratic Party than Trump is to the interior of the Republican Party.

Click image to enlarge

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