You realize that actually the exact opposite has been shown multiple times.
People that identify as classical liberals (libertarians) and strong liberal have an average I.Q. of 106.42, whereas those that identify as conservative and strong conservative have an average I.Q. of 94.82. Meaning that actually liberals have a higher I.Q. on average than those that claim to be conservative. According to a longitudinal study completed in 2010. (In case you're wondering, those who have strong liberal and classical liberal views actually scored similarly across the board, with no statistical difference)

A 2009 study correlated cognitive capacity with political beliefs among 1,254 community college students and 1,600 foreign students seeking entry to U.S. universities, it found that conservatism is "related to low performance on cognitive ability tests." In 2012, a paper reported that people endorse more conservative views when drunk or under cognitive pressure; it concluded that "political conservatism may be a process consequence of low-effort thought."

There is some evidence that liberals have less education, because people who have no high school education are more likely to be liberal (by a small margin), than conservative. This pattern repeats with those that didn't graduate high school, those that did graduate, those that have some college, and into college graduates, but once you get into post graduate work suddenly the trend is flipped on its head, drastically. People who have postgraduate education are almost entirely liberal.

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