This does not establish causality - which way does the influence flow - from economic institutionalized freedom to political or vice versa?
But, in a very important assertion in the same chapter:
The existence of a free market does not of course eliminate the need for government. On the contrary, government is essential both as a forum for determining the "rules of the game" and as an umpire to interpret and enforce the rules decided on.
So, regardless of the causality, Acemoglu and Robinson may well be on to something in their exploration of the relationship between economic and political institutions.
Friedman's well founded advocacy of free markets supported by a political framework designed to support individualism and liberty follows the above support of limited government:
What the market does is to reduce greatly the range of issues that must be decided through political means, and thereby to minimize the extent to which government need participate directly in the game. The characteristic feature of action through political channels is that it tends to require or enforce substantial conformity. The great advantage of the market, on the other hand, is that it permits wide diversity. It is, in political terms, a system of proportional representation. Each man can vote, as it were, for the color of tie he wants and get it; he does not have to see what color-the majority wants and then, if he is in the minority, submit.
At our July bookclub a member of our group expressed both admiration and appreciation for the manner in which Friedman articulates and advocates for individualism, liberty and free market structures.
In the video below, Friedman clarifies the relationship between economic and political freedom.
He makes the important observation that the relationship is a complex one and that there are any number of possible outcomes from the interaction between economic and political institutions.
A younger Friedman discusses the nature of economic systems and this video references Leonard Reed's famous I, Pencil essay.