In the 1960s Mancur Olson and Samuel Huntington suggested that the positive correlation between per capita income and the level of sociopolitical destabilization that they detected for low and middle income countries might be partly accounted for by the growth of the inequality associated with the economic and technological development in these countries. The empirical tests we perform generally support this hypothesis, but they also identify certain limits for such an explanation. Our tests reveal for low and middle income countries a statistically significant correlation between GDP per capita and the economic inequality levels, but this correlation is not particularly strong. Earlier we found for the same countries significantly stronger positive correlations between GDP per capita and some important components of sociopolitical destabilization, such as the intensity of political assassinations, general strikes and anti-government demonstrations. It is quite clear that the strong association between the increase in the intensity of these components of sociopolitical destabilization and GDP per capita growth, can be explained by a much weaker tendency toward the growth of economic inequality only partly. In addition, our empirical tests suggest the presence of a certain threshold level of about 40 points on the Gini scale, after crossing which one can expect a radical increase in levels of sociopolitical destabilization in general, and the intensity of terrorist acts / guerrilla warfare and anti-government demonstrations in particular. According to the World Bank, the value of the Gini coefficient for Russia is now just in this zone, which suggests that the further growth of inequality in Russia could lead to an abrupt increase in political destabilization.