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The easiest way to work forward from a well-cited article is to do a forward Google Search. My answer is almost completely based on such a search and concentrates on three brain regions: amygdala, insula cortex, and the anterior cingulate cortex; note that all three regions are linked to emotion.

Keep in mind: when you take any two groups of people that differ significantly in behavior, socio-economic background, age, education-level, etc. It is not difficult to find differences between them on many fronts, and certain brain-structures is one of them. The difficulty of these studies, is two-fold: (1) the researchers have to do very good controls to make it believable that the difference loads on political ideology and not one of the many other things differences in political ideology usually correlates with, and (2) provide (or at least make believable to exist) some sort of causal relationship between the brain-structures they observe and the relevant behavior (i.e. political leaning). When you read these papers, these are the two points you should carefully check.

Oxley et al. (2008) showed that you don't need a brain scaner to observe correlations between physiological differences and political ideology:

[I]ndividuals with measurably lower physical sensitivities to sudden noises and threatening visual images were more likely to support foreign aid, liberal immigration policies, pacifism, and gun control, whereas individuals displaying measurably higher physiological reactions to those same stimuli were more likely to favor defense spending, capital punishment, patriotism, and the Iraq War.

The nice thing about these measurements, is that a mechanism for the correlation is easier to establish: if you are more likely to react strongly in your experiencing and processing environmental threats, then you are more likely to have that reflected in your political ideology.

Schreiber et al. (2009) followed a similar line of thought by studying how Republicans and Democrats perform in a risk-taking tasks. While the 54 participants were evaluating risks, the researchers used an fMRI to look at the activation in their amygdala. This is a natural brain region to look at, since it is believed to be important for emotional processing. They concluded:

a two parameter model of partisanship based on amygdala and insula activations achieves better accuracy in predicting whether someone is a Democrat or a Republican than a well established model in political science based on parental socialization of party identification.

The importance of the amygdala has also been tested across culturues. Rule et al. (2010) conducted a study in snap judgements in voting decisons of American and Japanese natives and showed analogous activation of the amygdala in both groups even though the traits that lead to judgments differ across the two cultures.

The importance of the insula is also not surprising, since this brain region is associated with processing of social emotions such as disgust (Wicker et al., 2003), reacting to norm-violation in ultimatum game (Sanfey et al., 2003), and empathy (Singer, 2006). Chiao et al. (2009) showed that activation in the left anterior insula (and anterior cingulate) cortex is linked with preference for hierarchical rather than egalitarian social relations; something of importance for differentiating the Conservative/Liberal mindset.

The anterior cingulate cortex (ACC) is involved in the experience of anxiety, and empathy (Decety & Jackson, 2004). Recently, Inzlicht et al. (2009) linked activity in the ACC to religiousness; in a behavioral task they showed:

Results showed that stronger religious zeal and greater belief in God were associated with less ﬁring of the ACC in response to error and with commission of fewer errors. These correlations remained strong even after we controlled for personality and cognitive ability. These results suggest that religious conviction provides a framework for understanding and acting within one’s environment, thereby acting as a buffer against anxiety and minimizing the experience of error.

Since religion is often an important distinguishing factor between conservatives and liberals, it is not surprising for activity in the ACC to also be distinguishing for political ideology.