No contradiction. You are conflating within-group h\(^{2}\) with between-group. BG studies concern mostly exclusively the first, not the second.
You claim they are inflated. You have offered no reason for this.
I offered plenty of reason. I am not conflating anything, you and study authors are treating within-group variance as though it is the total variance. In fact, not only are they narrowly focussing on within group variance, but also only within-context variance constrained by extremely narrow timespans and within very narrow environmental conditions. Every aspect of the physical environment from weather and disasters to wildlife and technologies impact beliefs, including political beliefs. They and you are ignoring all of this variability. The denominator in their computation of % explained by heredity is a fraction of the real variance in the variable to be explained, and since much of it is variance caused by environmental variance, heredity would not explain most of the variance they are ignoring. Within and between group variance are not separate variables, just portions of the variance in the same variable that is often and this case is likely due to different sets of factors.
It would be like only observing a group of people in a sterile and unchanging room and measuring their actions and the variables they correlate with, then claiming that most variance in behavior is biologically based.
Another factor that inflates the correlation is that genetically similar people ten to not only seek out similar environments but to seek out each other which will mean they are more likely to share an environment with genetically similar others. Thus, whatever impact environment has on beliefs will also happen to indirectly make people who are more genetically similar, more similar in their beliefs.
Bottom line is that it is just false to claim heredity accounts for 50% of the variance in political beliefs. At best, it accounts for 50% of the variance of the 20%-50% of the total variance in political beliefs. But even that is likely high for the measurement reasons I discuss below.
However, it is known that political measurements are not perfectly reliable, this leads to \(^{2}\) underestimation. Generally, studies don't correct for measurement error, so most h\(^{2}\)'s reported are too low.
It is not true that unreliable measures mean underestimation of covariance. One reason for unreliability is a lack of precision and this is a major weakness of ideology measures. They are only able to place people into rather broad categories and fail to capture where exactly people are within each of those categories. Heredity is likely to impact what category a person is in or what quartile along the spectrum they fall into, but less likely to determine exactly where in that category or quartile any person is at any particular time or any particular context. If the ideology measures were more precise and could capture that more subtle variation, then heredity would not predict most of that additional variation, so it would only add to the denominator and not the numerator in the % of total variance in ideology explained by heredity.
Think about this analogy. Researchers have a measure of "health" that is very imprecise and only can put people into two general categories of alive or dead. Whether or not you have been shot in the head is another variable and it is predictive of this "health" measure to some degree. Although people who are NOT shot in the head are sometimes alive and sometimes dead, most people who are shot in the head are dead. Thus, being shot in the head will correlate with this "health" measure. Now, lets imagine the "health" measure is more precise and can pinpoint where people are within the "alive" category. The "shot in the head" variable will have a much weaker correlation with this more precise measure because whether you are shot in the head impact being in the dead or alive categories but has little impact on precisely where in the alive category you are.
