Is Soros' theory of reflexivity aligned with normative vs positive economy dichotomy? Soros' theory of reflexivity is well known and I'll briefly summarize it below based on his Fallibility, reflexivity, and the human uncertainty principle(2013) article. He 


  proposes distinguishing between the objective and subjective aspects of reality. Thinking constitutes the subjective aspect. It takes place in the privacy of the participants’ minds and is not directly observable; only its material manifestations are. The objective aspect consists of observable events.


Soros further divides subjective aspect into two parts:


  The participants’ thinking serves two functions. One is to understand the world in which we live; I call this the cognitive function. The other is to make an impact on the world and to advance the participants’ interests; I call this the manipulative function. I use the term ‘manipulative’ to emphasize intentionality.


Soros emphasizes fallibility of human thinking:


  The complexity of the world in which we live exceeds our capacity to comprehend it.


Thus subjective attempts to comprehend reality (but can't do it perfectly due to fallibility), manipulative attempts to impact reality (but again do it imperfectly due to fallibility) so we have a reflexive loop shown below:



Soros criticizes economic theory as follows:


  .. their theories could not be falsified by testing. ... The same argument applies to the mainstream economic theory currently taught in universities. It is an axiomatic system based on deductive logic, not on empirical evidence.


And as usual remembers: 


  While I was reading Popper I was also studying economic theory, and I was struck by the contradiction between Popper’s emphasis on imperfect understanding and the theory of perfect competition in economics, which postulated perfect knowledge. This led me to start questioning the assumptions of economic theory.


But at the same time he says in the same article:


  why should social science confine itself to passively studying social phenomena when it can be used to actively change the state of affairs? The temptation to use social theories to change reality rather than to understand it is much greater than in natural science. Indeed, economists commonly talk about normative versus positive economics.


It seems to me that we can associate manipulative function with normative economics and cognitive function with positive economics. Am I right?  Has this line of thought been elaborated by someone?
I would say there is some degree of correspondence between the two dichotomies. However, in the economic side of things, there is in my opinion a much clearer relation between positive and normative economics (at least in the theoretical side), as it is through the use of positive economics that normative means are supposed to be achieved. 

The other dichotomy however seems to be less formal in this relation. Individuals or agents can have a given understanding of the world, but this might not be correct, or precise. Thus, if they base their manipulative actions based on their perceptions of the objective reality, it does not necessarily mean they are using the correct map of reality to act upon it. 

In other words, positive economics is (allegedly) science, whereas agents cognition is not necessarily (and perhaps not mainly) built upon scientific knowledge.

Now, having said this, it is also debatable that the normalite-positive dichotomy is as clear as initially theorised by Milton Friedman in his 1953 book "Essays in Positive Economics". For example, some Marxists argue that science itself (at least social sciences) is part of the tools used by the ruling/capitalist class to exert control over society.
In philosophy of science, there has been a long debate about what science is and about whether there is such thing as "scientific progress", or whether science is just ideology (for example, see here).