The study showing a correlation between "IQ" and quality of government (reference 3) estimated IQ based on the performance of public school 4th and 8th graders on standardized tests in math and reading. With that measure, the opposite causal direction seems far more likely: high quality state government leads to better public schools and thus higher test scores (which the author uses as a proxy for IQ).

State IQ was estimated from the National Assessment of Educational Progress (NAEP) standardized tests for reading and math that are administered to a sample of public school children in each of the 50 states. ... State data were available for grades 4 and 8. ... For each year, for each test, the national mean and standard deviation was used to standardize the test to have a mean of 100 and a standard deviation of 15. This standardization places the scores on the typical metric for IQ tests. The means of the standardized reading scores for grades 4 and 8 were averaged across years as were the means of the standardized math scores. State IQ was defined as the average of mean reading and mean math scores.