I find it amusing in the Business Insider version [1] of this article "managing others" features at the least-susceptible to automation end of the chart. This appears to belie an oversight, that automation job loss is not just about jobs directly replaced by robots, but the jobs (like managing the to-be-automated workers) that simply become irrelevant.
You obviously need many fewer managers in that scenario. But I think you would need humans to decide that a business should exist and start it, and to continually set direction and goals (beyond mere financial goals).
It will be interesting to see the first businesses that are run almost entirely by algorithms. If that becomes common, or the norm, why would we even need separate companies? Maybe the algorithms will merge their "businesses." Maybe Skynet starts not via military algorithms but business algorithms.
EDIT: I recently left a medical device company, whose products without a doubt save and improve lives. This business was started decades ago, with two obvious goals: make money, and improving lives. Part of the direction and goals for that company has always been service to society (humans), and I know that many or most of the people working there think of it in exactly that way: they're serving society (and happily making money while doing it). That's how I felt about it.
What incentive would an algorithm have for starting and running a business like that? Particularly as fewer humans are required to serve that and other "businesses" (processes?), might such a company be seen as a waste of resources? Why not just let most of the humans die?
But then, following that thought to its sci-fi conclusion, once human civilization has all but disappeared, what would the purpose of any Skynet-like business algorithm be? Would it start shutting itself off, business/process by business/process?
"Algorithms" don't have incentives. "Algorithms" do not seek to conserve resources. "Algorithms" do not seek to shut down purposeless activity, or indeed determine what activity is purposeless.
An algorithm might do some of those things, if the human that created it wanted that to be the case, or they didn't but the implementation was buggy.
A human writing an algorithm to run an automated medical device company would presumably include some terms which would ensure that the company's resources were used in a way that served the public good, to the extent that that was compatible with whatever other objectives that human had for the algorithm, such as making profit, or avoiding kinds of research that human considered immoral.
A human who writes an algorithm to run a company which prioritises "something" over the survival of human civilisation and resists any attempt to adjust its priorities once the error is obvious enough to be noticed, and then runs that algorithm on a system with the capability to actually cause the end of human civilization, is a super-villain or a super-idiot.
Services such as Google search probably already have enough information to infer by ML that there is a demand for products in a certain area that is being underserved.
But a successful algorithm wouldn't start businesses that aren't needed. Which means that there's a "needed" parameter. Which algorithmically begs the question "am 'I' (the algorithm/business) needed?"
No, not really. Taking a current example, Kubernetes includes an algorithm that decides which processes are to be run and which aren't. That doesn't mean it will suddenly decide to apply that algorithm and kill itself!
[1] http://www.businessinsider.com/jobs-that-robots-will-take-20...