This appeared in the news yesterday.
http://www.alternet.org/media/most-depressing-discovery-about-brain-ever?paging=off
It turns out that in the public realm, a lack of information isn’t the real problem. The hurdle is how our minds work, no matter how smart we think we are. We want to believe we’re rational, but reason turns out to be the ex post facto way we rationalize what our emotions already want to believe.
...
The bleakest finding was that the more advanced that people’s math skills were, the more likely it was that their political views, whether liberal or conservative, made them less able to solve the math problem. [...] what these studies of how our minds work suggest is that the political judgments we’ve already made are impervious to facts that contradict us.
...
Denial is business-as-usual for our brains. More and better facts don’t turn low-information voters into well-equipped citizens. It just makes them more committed to their misperceptions.
...
When there’s a conflict between partisan beliefs and plain evidence, it’s the beliefs that win. The power of emotion over reason isn’t a bug in our human operating systems, it’s a feature.
So, my first thought was that this might be a trivial statement. If any person is 30% likely to give the wrong answer for partisan reasons, but the chance of getting it wrong depends on innumeracy, then partisanship will be the dominant reason for error among highly numerate people, because it's basically the only source of error, even though total error is lower.
But turns out this is a rather meaningful statement (as shown by Figure 6 of the paper). Among liberals, numeracy has basically no impact on whether or not they correctly answered the political question when it disagreed with their priors (which is, frankly, horrifying). Conservatives who scored 8 or 9 (the max score) on numeracy were slightly better at giving the answer that went against their political position than less numerate conservatives, but only slightly. When the answer supported by the data supports the expected preconceived notion, both conservatives and liberals saw a positive relationship between numeracy and giving the correct answer. (Oddly, for conservatives the relationship looks linear, but for liberals it's flat-ish then sharply positive.)
That seems odd. What's the difference between being handed a a list of numbers that support gun control being useless and being handed a list of numbers that you misinterpret as supporting gun control being useless?
I would have expected numeracy to be completely independent of the answer....