Approaches to Cybernetics

I see you're already familiar with Paul's work, but if you haven't already I'd definitely recommend reading the book Classical Econophysics and Towards a New Socialism. 

And it's true that not all methods use the input/output planning methods. The Cybersyn experiment in chile did not, for example, I'd read The Brain of the Firm for more information about that, although keep in mind that it was still much more dependent on market prices and money than the planning model put forth by Cockshott and Cottrell. More than simply dictating inputs and outputs, cybernetics tells us a lot about how information feedback loops between planners, managers and workers can be structured. The idea of input/output planning is in some ways far older than cybernetics itself, with its origins placed either with the french physiocrats before the time of adam smith, or with alternative planning methods suggested in the soviet union as far back as the 20s and 30s. It makes sense that the two go together, however, as an IO table is essentially the product of taking inputs and applying some transformation to them to get the outputs, in computer science and mathematics this would be some formula or set of instructions, versus the real world transformation occurring in production. Pre-digital computers, economic models like Marx's department model in Vol 2, as well as social reproduction theory (which also relied on IO Anylsis in its quantitative form), would work with input and outputs iteratively, in the kind of feedback loops which cybernetics concerns itself with. 

A lot of the current socialist cybernetic crowd is very heavily indebted to cocckshott, and because of that there is a focus on the calculation of production ratios. I'm skeptical of this focus, for reasons I might elaborate later when I have more time in it's own post. I think there is a lot of work involving the rigorous study of bidirectional relationships between systems and controllers. Brain of the firm is probably a good place to start, and I also think some of the stuff I posted over here is worth checking out. https://casperforum.org/community/cyber/categorical-cybernetics/

It depends on what aspect you are talking about; I/O analysis is kind of the mathematical linchpin of planning because it allows you to compute the necessary inputs exactly.

Here is Tomas' intro: https://www.haerdin.se/blog/2021/02/08/some-example-economic-linear-programs/

And here is Cibcom's intro: https://cibcom.org/mathematics-to-plan-an-economy-an-introduction-to-cyber-socialist-calculation/

As you'll see from the above the next step is mathematical optimization which allows you to incorporate real world constraints into the model.

From an engineering standpoint I/O analysis + mathematical optimization is the way to go.

That being said planning is not the only aspect of cybernetics; I/O analysis and mathematical optimization are techniques to calculate inputs which are only useful if the information provided is accurate. 

The most sophisticated planning software is useless without being embedded in an effective organizational framework for managing changes in production, resources, and demand. This is where the Beer's viable systems model comes in.

The VSM is a neurophysiology-inspired form of organization designed to dynamically adapt to circumstance.

CyberSyn was a social technology in the most literal sense in that it technologically mediated effective organization. It's means of computing inputs and economic simulation was actually it's weak point since it relied on statistical inference; it's success is a result of the fact it was a really good management system implemented through a proto-internet.

Here is a video about the VSM: https://www.youtube.com/watch?v=Y76o0GU1s5c&t=4822s

I can imagine a future cybernetic planning system would be something like a CyberSyn but using I/O optimization instead of Bayesian inference.