2.1 The state and social democracy

Following the second world war, a large effort to direct the output of national economies was set in motion. Social democratic and labour parties, reinvigorated in popularity by the horrors of war, set ambitious programmes of state provision, commonly referred to as “democratic economic planning”. To quote Sir Stafford Cripps, in his position as the UK’s Chancellor of Exchequer, who, when discussing democratic planning claimed that [16] “…we are out after something a great deal more important than a good piece of planning machinery or even than a particular way of organising our industries and services. Our aim is to create a Happy Country in which there is equality of opportunity…”. A set of industries was nationalised (including the banks, coal, telecommunications, gas, electricity, public health etc)—for the case of the UK see [17]. This was roughly the consensus, respected by conservative governments worldwide, that most of the world has followed until almost the 1980s. From that point onward we see a reversal of the state intervention trend and widespread privatisation. Though there is still a debate as to why this happened, from the electoral perspective one can observe the collapse of social democratic parties owing to the breaking down of the electoral coalitions between liberal elements and the working class (see [18] for a thorough discussion). The reversal of the trend brought widespread privatisation and the re-introduction of the market. This process of “re-marketisation” went by different speeds in different countries and different economic sectors, but arguably the process is still ongoing. Even when certain services are still nominally free at the point of use (mostly in healthcare), the vast majority of utilities (including education) is slowly moving to fee-paying models and internal markets. The victory of the market is so absolute that certain authors complain in the popular imagination: “it is easier to envision the end of the world than the end of capitalism” [19].

2.2 Socialist planning in actually existing socialism

While capitalist counties were moving away from the social-democratic model, the end of historically existing socialism lead to the introduction of “shock therapies”[20] and widespread, fast, privatisation, with at the very least questionable results. When privatisation did take a more structured form, as in the case of China, state planning was replaced due to associations with poverty. Quoting [21]“…one of our shortcomings after the founding of the People’s Republic was that we didn’t pay enough attention to developing the productive forces. Socialism means eliminating poverty. Pauperism is not socialism, still less communism.” The state took a back sit into acting as planner and started using financial means to measure (and drive) success. Fiver-year plans no longer meant exact outputs, but rather strategic visions [22], with specific GDP per capita’s aims, akin to industrial strategies elsewhere. This failure of planning, can, at least partially, be attributed to practical factors. Computers and algorithms of the scale required to plan effectively did not exist a the time, and when the first thoughts of such projects where entertained (e.g. see [23]) they were not supported adequately. Indeed, if there is anything to be said is that it is almost a miracle that any form of state planning was attempted given the means available.

2.3 Why planning?

Von Mises and Hayek [1], writing in the height of socialist revolutions, started putting together a critique of socialism, and more specifically (economic) planning. Parts of their critique (and this of their successors) sound still valid—for example same of their points on Marx’s treatment of skilled vs unskilled labour. Here we will concentrate on the arguments of planning using products and services (i.e. 10 kilos of rice, 20 pounds of flesh, 10 hours of electric supply) vs a market price allocation mechanism. Whether an optimal (automated or not) planner of such type could even exist is termed the calculation debate. Arguments against the existence of an optimal planning mechanism fall into different camps, with some being aligned to moral questions (“it is unfair to just allocate goods” or “it is undemocratic”), computational (“you can’t compute the intermediate goods to produce”) or epistemic (“there is no way for the planner to know what to produce”). We will not discuss the democratic issue in this paper, though we strongly feel that the market is exceptionally undemocratic. It is now accepted by even the opponents of planning that computation should not be an issue [24]. The epistemic argument, which is still very valid, entails that an optimal planner would not know what to compute. A price mechanism would allow whoever is engaged with the market to express their preferences of goods in terms of how much they would be willing to pay, i.e. a very subjective preference function. Prices that (for producers) might, for example, depend on the availability of goods [25]. In its extreme this holds true for consumers, as we have seen examples of iPad-for-kidney selling [26], though we think it is safe to class such behaviours as pathological. If one makes the assumption of truly subjective values that vary continuously and are also widely different from person to person, then indeed a market might be able to allocate surpluses somewhat better than a plan. However, if you do accept that the majority of the population shares some similar preference function, at least in their top priorities (e.g. food, shelter, basic communication devices, electricity, health), the argument is nonsensical and applies only to incorporeal beings. Insofar as there are relatively slow changing patterns in consumption, standard machine learning models, combined with one’s own predictions can be used to forecast demand.

2.4 Why not alternative forms of market organisation?

A popular counterargument against planning is one of efficiency, quite often expressed in macro-economic aggregates (e.g. GDP growth, the gini coefficient). These tend to hide vast complexities of the underlying tendencies of the system. In the game-theoretic literature (which is closely aligned to economic models), different notions of where a system should equilibrate in terms of specific agent rewards have been explored and unpacked. In effect, these try to predict where a large population of agents would end up, if left to explore and learn freely, given imposed game rules. For example, [27] provide four types of correlated equlibria: utilitarian (which maximise the sum of rewards for all agents), plutocratic (which maximise the maximum reward for all agents), dictatorial (which maximise the maximum reward of a specific agent) and egalitarian (which maximise the minimum reward for all agents). Instead of planning, the state could play the role of “traffic lights”, and try to stabilise the whole system by favouring certain equilbria. Arguably, and almost by definition, once a system stabilises to one set of equilibria it is hard for it to move another, as unilateral movement by any agent would is strongly disincentivised. Historically, examples like anti-monopoly laws, taxation, demurrage and the welfare state point to a countermovement towards plutocratic and dictatorial equilibria, as it looks like markets tend to generate pareto distributions [28], i.e. very few individuals tend to accumulate overwhelmingly. Monopolies, as explained by their proponents [29] allow for both innovation and “concentrated application of force”, something that would not be feasible if one a business is surviving day-to-day due to heavy taxation and competition. A modern version of planning should not be seen as a fully centralised top-down-controlled structure, but rather as a game that has egalitarianism baked in and not as an afterthought; alternatively one can see the whole edifice as a decentralised democratic monopoly.

2.5 Input-output economics and planning

The problem of planning has been formally defined in [30]. Per unit of time t, a set of demands d for certain goods (e.g, products, services) are to be satisfied for c citizens. The planner’s goal is to satisfy the demand of each citizen. In AI terms, we have something akin to a Markov Decision Process (MDP), with an agent (the planner) receiving information (the state) on the plan and a set of rewards related as to how closely the demand is met.

The parent of modern mechanisms for planning (in this context) is what is termed the input-output model, which is thoroughly reviewed by [31]. The model comprises of an nxn Matrix A of technical coefficients, a vector x of production level (i.e. how much we should produce for each product) and a demand vector d. The columns of the coefficient matrix conceptually ask the question “how many units of each good to produce a single good of the type portrayed in this column do we need?”. The dot product of each row with the technical coefficients represents the consumption of a specific good. The demand vector d represents how much external demand there is, i.e. that Eq 1 holds: (1) In matrix notation, we have Eq 2: (2)

Something to note here is that traditional input-output models have no notion of time—all production is taking place within the same temporal unit. This is somewhat counterintuitive (and problematic for actual planning), but it allows a first easy approximation. It is the model proposed by [32], covered by [33] and, with further additions (based on linear optimisation) discussed in [9]. Very similar concepts, without a specific target but with the goal of directly maximising output are also discussion by in [23]. With no time element, the model remains suitable for very high level strategic planning—and indeed such models are widely used currently (e.g. most states publish input-output tables using monetary prices). There is also very widespread literature on input-output models, but not with state planning in mind.

3.1 The model

We adapt a number of innovations to the standard input-output models, by changing the way we position the plan within the economy. As discussed before, the goal of an input-output matrix is to plan for demand at the end of a time period. Since our goal is to provide necessities to sustain humans, we set all “external” demand to zero, and introduce a set of profiles combined with the number of citizens attached to each profile. You can see an example in Table 1. Our input-output matrix describes the interactions between consumption profiles, a set of industrial goods, and a set of final goods. Profiles are columns that describe the allocation of final goods to each citizen that has been assigned this specific profile.

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Table 1. Our example input-output matrix, for a society of 1300 citizens.

Two of the IO-coeffs vary with production levels—as there are three production units (see Fig 1)—the rest are constant. Labour columns are omitted, as all values are zero. There is one industrial good Butter churn and two final goods (Milk and Butter). Demand now just signifies the number of individuals in each profile. Lb is short form for Labour and Prof for profile.

https://doi.org/10.1371/journal.pone.0257399.t001

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Fig 1. f₀₁(x₀) and f₁₂(x₁) derivation from production outputs.

There are three fictional production units that follow very different curves in their models. (a) An example of how many units of Milk and Butter churn are needed to create units Butter and Butter churn units as portrayed in the y axis, i.e. f_ij(x_i)x_i. (b) The derivation of quantities from the left to forms that we can put in the matrix, i.e. f_ij(x_i).

https://doi.org/10.1371/journal.pone.0257399.g001

3.2 Nonlinearities and learning

The plan formulation we described above inherits a number of limitations from the standard input-output model; the first one we will build upon is model linearity. The default model linearity is tremendously problematic—for example there is the implicit assumption which is that labour needs will scale linearly with production demands. To address these issues, a generalisation of the input-output model [30, 37] looks as in Eq 3: (3)

This is profoundly liberating as a proposition, as we can stack production units and have different IO-coeffs values as production scales. We can also extract from individual citizens how important hitting certain targets in their profile is. Solving for x now becomes a bit harder, as F(x) could potentially be any function, but in our case, we constrain it to a specific matrix. Remember that individual columns in the IO matrix represent how much it takes to produce a single unit of output—it makes sense to define the matrix as in Eq 4 (4)

Constraining our function to this form has one important benefit; we can ask production units directly how many other goods they need in order to produce certain output units, and data scientists in these facilities can use any machine learning method to “fit” a curve and provide back a function.

When it comes to the actual solution, one can attempt to use the gradient directly. The mean squared error MSE((I − F(x))x, d) has a gradient that is ∇MSE((I − F(x))x, d) = 1/n((I − F(x))x − d)(I − F(x) − F′(x)x), which means that we can solve using any non-linear least squares algorithm—or in fact any other non-linear optimisation algorithm. Another method (that comes from [30]) is to go through the power series expansion . We can then define x_(i+1) = F(x_(i))x_(i) + d, x₍₀₎ = d—a recursive form of calculating x. This is what we are going to use in this paper, as it is based purely on linear solvers, and will find the global maximum as long as convexity is maintained. We could also attempt an end-to-end neural network solution (it is very easy to envision), but there are no (clear) advantages, unless a need arises to model exceptionally complex IO-coeffs while optimising production at the same time, something we are not doing in this paper.

3.3 Time and the transition function

When it comes to producing goods and services, a model without a time element is severely limited; real production and consumption obviously have a time dimension. In the case of production, this is expressed in various forms like gestation times, production times, business inventories and depletion of resources. Multiple input-output models that include a time element have been developed [38–40]—for an overview, see [41]. An example of such a model, from [38] is , with A matrices representing circulating capital, all B matrices representing fixed capital, z(t) is the demand at each point in time, while −s is the ticks before the time t. The problem with these models is they were (for the most part) not designed with planning (in the AI sense) in mind. What we need to introduce (as discussed before) is a transition function T(s′|s, a) and a notion of state s. This can really be anything that makes sense based on the individual components of what we have, but to simplify things we can define state as an inventory indicating how much we hold of everything we have so far, including any unwanted side effects (i.e. externalities) our methods are generating. The transition function now operates on that inventory/externalities vector, by adding things, removing things, showing when something is ready for consumption, and how much needs to be taken to gestation periods.

3.4 Plan egalitarianism and externalities

The goal of the plan is to deliver a set of products and services (termed goods in our setup) in real life, so the real rewards can only be measured when the plan has been executed. During the planning phase, however, we should have a reasonable indication of what is the level of rewards we have achieved. Let be the demand for a final good for a certain profile set to zero, with i coming from final goods C, while j coming from profile consumption P. When we removed a good from a profile, we generate a surplus. That surplus, divided by how much that profile was expected to get, we define as the egalitarianism of the plan. More formally, in Eq 5 we define egalitarianism as (5)

Every profile created puts certain requirements on the economy in terms of unwanted side effects, commonly referred to as externalities (e.g. carbon from milk and meat production). We model externalities at each point in time as ρ(e(x_t)x_t), with the total externalities for a plan being E_p—the sum of all externalities in time as in Eq 6, and ρ being a function that weights the importance of each externality for each good: (6)

The difference between the way we measure the unwanted side-effects we get versus the goals we achieve is by design. In terms of production goals, a plan is as good as its worst performance. In terms of damage, we are measuring the cumulative effect. A combination of externalities is what underlies the reward function.

3.5 Plan execution

Given that we do not have access to the real transition function (akin to training for a robot in an largely imperfect simulation), we suffer from two problems; first, that our plans are as limited in their ability to use future states as the imagination of the model creators. We will try to achieve certain goals every day for a year by following a set of actions that correspond to increasing production, without reference to future states—this is known as open loop planning—and is basically a vector x per day. The fact that we re-plan on a daily basis means that we execute the plan in a closed loop setting—so overall we do open loop planning, closed loop execution [42, 43]. This is highly reminiscent of methods like Monte Carlo Tree Search [44] that have shown tremendous success in games. The second problem is that the artificial conditions we optimise on might not correspond to reality. Again, this is a common problem in robotics and it is currently attacked by assuming fictional model hyperparameters, as to make the model robust [45].

4.1 Production units

Each production unit would have to effectively fill the columns of Matrix F by providing the function f_ij(x_i)x_i, This can be achieved trivially by some form of active learning (i.e. asking managers: “how much milk do you need to make one pound of cheese? How about two pounds? How about three?”) and interpolating accordingly. Alternatively, one can seed a classic ML model using past production data and combine it with active learning in any gaps. Now, converting these values into f_ij(x_i) simply required dividing over the number of actual products x_i for all possible values of x_i. We expect production units to innovate constantly, achieving lower externalities and better IO-coeffs, in a very organic process that amounts to optimisation coming from every part of the system.

4.2 Interactions with the market

Since the plan’s aim is to complement, rather than abolish, the market, it is worth discussing what areas of production the plan will not shape. Goods in scarcity or products whose only value is their scarcity cannot be delivered through the plan; the subjectivity of the reward function would make it exceptionally hard to calculate individual preferences (and hence profiles), and would also open up the possibility of abuses, requiring constant vigilance to stop the creation of black markets. Goods in scarcity also open questions of multi-objective optimisation [47]—that will mostly lead to a wealth of equally non-satisfactory solutions. Any invention that helps the plan should be readily adapted. New products and services could also come from market forces. This would require the market to turn into activities that look more like prospecting—anything that a plan cannot cover should generate profit. The most important point, however, when it comes to market, is not to allow it to use the plan as a way of undercutting wages; once the plan is introduced, it should be followed by a policy of increasing minimum wages and decreasing working hours, in accordance with productivity gains in order to start removing human labour from the market and reaping benefits from further automation. For example, shoe production is still a very manual process, and high wages in the sector should come from automation. This is extremely important, as current trends point to “reverse centaurs” when it comes to automation [48]. Given that it is easier to manage humans using algorithms (e.g. organise taxi drivers) vs performing the actual task (e.g. autonomous cars), there is a certain market tendency to extract profits from over-exploitation. Instead of machines aiding humans (i.e. what is called a “centaur” in chess), we run the risk of economies of very low wages where humans help machines (i.e. more akin to a very boring and intensive production line, hence “reverse centaur’)’.