Holism has its value in complexity of analysis, not dividing and not being reductionist. But how would You explain public and private sectors and the interaction between them by holistic approach?
Methodological holism assumes that social institutions and organizations are prior to and independent from individuals. This presents that they can serve as primary independent variables determining individual and collective behavior and outcomes. It maintains that the society in its certain aspects is not reducible to the individuals that comprise it. Structures are placed at the forefront of explanation (Halperin & Heath, 2012). In an attempt to study the interaction among and between the public and private sectors, methodological holism will prescribe to look at the elements of the sectors as "social wholes". As holism argues, there are some terms not reducible to the individual such as class or revolution. The interactions between the sectors could be understood by what Emile Durkheim presents as 'social facts', which includes social organizations and social currents, and has the power of coercion.
I hope this response helped though it did not really answer your question directly. This response is highly subject to criticism and review. Good Day!
Well, I would recommend not to take holism as if there was symmetry - or asymmetry between the components, here the public and the private sector. Properly speaking, a good complexity approach does not focus so much in holism as in networks, fluctuations or non-linear dynamics. Systems theory is much more concerned with holism, as such.
The interactions between the private and the public sector depend on each country. In one cases the private sector is larger and stronger. In some others, quite the opposite happens. Still, in some other cases, there is a sort of evenness between both sectors.
Furthermore, I would suggest to take always into account the weight of the so-called third sector, i.e. the civil society. You cannot not discharge it - here or there.
Holism - briefly, it instructs us to avoid being narrow and overly presumptive. Embrace complexity: Preprint Public-Private Partnerships (PPP) in Africa: Harking the Holonomic
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