Fairly recently there have been discussions about the link between inequality and inequality of opportunity. Alan Krueger has introduced the "Great Gatsby Curve," which is represented below.
Inequality, measured by the gini coefficient (a leading measure of inequality, 1 representing perfect inequality and 0 representing perfect equality) is compared to the "intergenerational earnings elasticity," which measures the degree to which one's economic position early in life is a predictor of income later in life. The Scandinavian Social Democracies are highly equal societies with considerable class mobility, while the United States is less equal and its people are more likely to be in the class in which they started life.
This graph seems to be a pretty indication of the degree to which a society provides equality of opportunity and a reasonable degree of equality of outcomes. Since there seems to be such a strong relationship, these two are clearly linked. A more equal society provides more equality of opportunity. This has been remarked many times before, especially by social democrats, who may seek to increase the services available to lower income individuals both to provide support in the here and now and to help the poor to improve their chances of economic success in the long run.
One question that I have about this information is where would the developing nations lie on this graph? Let me throw some cold water on the projection of U.S. inequality of opportunity. I think it's very problematic to make a projection based merely on available data because there may be institutional factors that may change radically enough to affect the result. For example, the quasi-universal health care program enacted by the Democrats and Obama may boost equality of opportunity in the future. Further, if a big enough change in taxes and benefits were to occur within the intervening years between 2010 and the future date being measured (which I believe is more than a decade away), then it may dampen the movement along the curve, or a combination of factors may reverse it. After all, the results of the graph are not immutable.