Monday 12 June 2023

Can quantum computers solve the Socialist Calculation problem?

Economic activity can be purely private, purely social, or it can occur at the interface between the private and social realm. Control rights coincide with ownership- which is a Hohfeldian immunity to dispose of a thing as one pleases- in the private realm. Control rights in the Social sphere do not coincide with ownership rights. Though, formally speaking, there may be specific Hohfeldian immunities, they are not unqualified. Instead there is some regulative concept of Public Justification at work. 

Under some definitions, Society may own everything but something like Hohfeldian immunities regarding control, de facto, vest in some subset of Society, There are a number of Preference Revelation, Agent Principal hazard, Concurrency, and McKelvey Chaos agenda control type problems in addition to those of information aggregation and the specification of the 'objective function' for optimal control theory. 

Thus the configuration space is different even if there is no Knightian Uncertainty. This is because configurations have to be implemented by those with control rights but the mechanisms to do so will differ radically depending on the actual traits and allegiances of those specific actors. Now, it is quite true that, all mechanisms have  'incentive compatibility'/efficiency tradeoffs and one could always simulate such mechanisms in different operating environments. The problem is that the type of 'rent contestation' will be very different under different regimes of control. In other words, these are 'dissipative', non-ergodic, systems. 

What complicates matters even further is that, if there is competition between regimes, the factors determining entry and exit may be non-economic. Thus, some people would have fled Nazi Germany and entered America even if they disapproved of American 'Capitalism' and 'Planetary Technology' and 'inauthenticity'- not to mention lynching niggers. Those entering the USSR had a different problem. They were only in danger if people thought they were Trotskyites or Zionists or some other such brand of idealist (though Zionism, unexpectedly, turned out to be perfectly workable because Jews- being sensible people- like farming and fighting just as much as they like thinking about God and Ethics and Aesthetics and other such arcane stuff)

Turning to the type of economic coordination which leads to 'general equilibrium'- i.e. the coincidence of ex poste and ex ante, or planned and actual outcome- following a result from Chichilnisky & Heal, we know 'limited arbitrage' (or purely 'local' 'no-limits to arbitrage') is enough to knit things together well enough. But, crucially, this entails a unique price vector where preference and endowment meet a 'Goldilocks' condition. This is obvious where the Pareto front is compact because the marginal rate of substitution must be the same for all agents. Furthermore, where it is non-compact, there can always be a collection of cadlag functions which describe a 'close enough' Skhorokhod Space. This is interesting because we can 'wiggle space and time a bit'- i.e. there is 'multi-fingered Time' and maybe that is the topos which has naturality for quantum computers of a particular type. My claim is that unicity of the price vector arises from uncorrelated asymmetries dictating 'bourgeois strategies'. That's what sticks in the craw of the Lefties. But can they give some other non-arbitrary criteria by which uniqueness is achieved? Suppose each control right has been assigned to a Commissar. Shouldn't that have the same result as leaving control rights in private ownership? No. This is because information asymmetries can lead to optimal changes in control rights without information aggregation or computation simply by the free working of the market. What type of Socialism would allow Commissars to reassign control rights among themselves? What you have is oligarchy with a self-perpetuating clique controlling every facet of economic life. 

The fact is, if there is no unique price vector how is equalisation of marginal rate of substitution to be achieved? You may say 'fuck Pareto. We just want a welfare improvement.' That's fine by me. Nobody knows what is Pareto optimal. Still, uncorrelated asymmetries can generate a unique price vector. What else can? 

Marxists may say 'embedded labor'. This is cool if we have a steady state which some Angel of the Lord tell us is Pareto optimal. But the problem is that there will be an infinite number of labor numeraires. Even in a one person economy devoted to producing farts and only farts, there's the farts I produce when drunk and the farts I produce when I'm sober and wholly focussed on farting efficiently. 

The other problem is that a lot of labor needs to be expended on beating and killing people in order to change 'control rights'. A steady state is only a steady state because of expectations regarding threat points and access to cheap Vodka or other soporifics. There was a theory, more especially when Yeltsin was around, that Russia was despotic because Vodka was a State monopoly. This was silly. Tamil Nadu has the shittiest Alcohol monopoly in the world. But TASMAC hasn't turned the place into a Socialist shithole though its Chief Minister is named Stalin. On the other hand, the very poor quality TASMAC liquor has prevented me from returning to my ancestral home so as to gain the coveted title of Miss Teen Tamil Nadu. 

Socialism- at any rate, the transition to it- depends on shedding blood or keeping those who might otherwise fight it, drunk off their heads. If fails because people run away even if they might otherwise be crowned Miss Teen Tamil Nadu by reason of their special talent- which, in my case, is being able to fart melodiously 

The argument for Socialism was that 'greed' is short-sighted and can't implement cooperative solutions. It will get stuck in 'wasteful' or 'Prisoner's dilemma' type Nash equilibria. Individual rational choice is collectively disastrous.

The problem with this view is that rationality can be 'Muth rational'- i.e. individuals can converge on the predictions of the correct economic theory which is also Schelling focal- i.e. it can be arrived at without consultation or a pre-compact. There are 'Coasian solutions' whereby 'externalities' are 'internalized'. Thus a cartel can get rid of 'wasteful competition' or 'price wars'. The folk theorem of repeated games, the 'Revelation Principle', and 'mechanism design' which is reverse game theory are all available to rational individuals such that they converge on cooperative solutions and evolve or develop things like institutional memory and 'on the fly' readjustment of incomplete contracts so as to better align control rights with incentive compatibility.

Socialist economics did have a mathematical theory of shadow prices and waved its hands at 'networked computers' or, a little later, neural nets or other such futuristic panaceas. But the Soviets- who had done well enough in the Space Race- fell behind in computing. Gorbachev himself revealed the massive Agent Principal hazard and crazy incentives for those with control rights in the Soviet economy. Then the fool gave up control rights for the Party. There was a 'scissors crisis'. Communism collapsed. One reason was that the nomenklatura saw that the 'spot price' of oil & gas was much higher than the 'shadow price'. Why be a Commissar when you can be an oligarch? The Socialist division of labor involved too much labor for too little reward. In the end, even its slave-drivers rebelled against it.

Could there have been any other outcome?

I was recently asked whether quantum computers can solve the Socialist Calculation problem. Briefly, no. The point about planning and coordination is it happens in one dimensional linear time. The price vector aggregates that information in almost real time. It is the price vector which makes money important. Otherwise, other non-fungible things- reputation, power, sexiness, family connections-  would be what really mattered. Provided there is some way non-fungible things can cash out as money, the price vector is better at coordinating economic activity. Why? Because prices reflect relative scarcity. They encode opportunity cost. Reputation and Power and Sexiness and truly nice Niceness aren't inherently 'rivalrous' or deal with what is of its nature scarce. This means economic decisions can be separated from Religious or Political or Artistic decisions. The realm of scarcity doesn't have to take over the 'Kingdom of Ends'. They can burgeon. The alternative is to make everything Religious or Political or Aesthetic or Thymotic till the Economy collapses. This is not to say that the worship of wealth can't cause speculative bubbles which have the same effect. But Econ has a way to separate itself from 'Chrematistics'. Periodic 'crises' keep markets on the straight and narrow. This is better than the prolonged lysis of degeneration which is the hallmark of Socialist sclerosis.

Why can't we have a bunch of quantum computers linked up to each other which solve the 'transportation problem' in real terms? In other words, powerful enough computers first define a 'configuration space' for the economy and then work out, in purely material terms, exactly how much of each resource or commodity should go to which specific location. Let these computers communicate with each other and maybe add in a black-box AI and soon you might have superior outcomes- though we might not understand how they were arrived at. There would still be the problem of 'Knightian uncertainty' and the other sources of market failure but maybe AIs could be trying to 'peep around corners' in a Skhorokod space which is the interface of the weird and wonderful world of multi-fingered time facing the hairy black hole of sphincterless Socialist bigotry.

The problem here is not that the plan these computers come up with may not be very good from some point of view. It is that plans don't turn into reality without control rights. But economic information about objects doesn't tell us how much it would cost to control those objects to achieve a specific purpose. Indeed, this is not something we know ourselves. What would happen if I took control of my pension fund? Because I know I'm stupid and careless, the result is likely to be sub-optimal. I'm fortunate my savings are controlled by Bernie Madoff. Left to myself I'd have just put the everything into Consols. The bigger problem is what happens when control rights are reassigned. We may want Socialism because it is more Christian, but there isn't a single Socialist we know that we'd put in charge of a piss-up at a brewery. 

Ultimately, something like Coase's theorem will operate. It doesn't matter who has residuary control rights. There will be politicking or transactions of various sorts till those who are good at politicking or better able to conclude transactions gain 'appropriable' control rights. This may occur in a wholly opaque manner. We might get lucky and the cabal running things may do a good job. But, equally, we might get very unlucky indeed. Opaqueness may make 'system recovery' quicker. Equally it may lead to cascading failure. But this is true of any economic or political regime. 'For forms of government, let fools contest/ What is best administered is best'- till suddenly it is the worst because it has forgotten how to repair itself and everybody else has become childishly dependent on it. 

Some 30 years ago, in an influential paper titled 'Calculation, Complexity And Planning: The Socialist Calculation Debate Once Again' Allin Cottrell and W. Paul Cockshot wrote

Mises (argued) that optimization in complex systems necessarily involves arithmetic, in the form of the explicit maximization of a scalar objective function (profit under capitalism being the paradigmatic case).

There has to be an 'inter-subjective' price vector in almost real time such that on the fly substitutions can be made. Shadow prices won't work because you can't reliably pick a substitute or alternative use such that the right quantity is available for immediate delivery. There is no general class of arbitrageurs though no doubt there can be an informal network who secretly maintain inventories they can draw on to help out a pal. 

The point about profit is that its pursuit includes the notion of taking a loss or wasting resources. Profit is the reward for combining factors of production  even if this leads to a net loss over what previously obtained. Indeed, larger risk and greater likelihood of loss can still lead to profit rising while other factors of production take a haircut. After all, someone still has to combine those factors. But this what gives the system overall a 'regret minimizing' bias and thus a greater ability to respond to shocks & unanticipated states of the world- i.e. Knightian Uncertainty. Knowing the entrepreneur can walk away leaving other factors in the lurch, militates for caution. This is what prevents Goodwin's 'class struggle' model- where the workers, who are the sheep, eat the wolves, who are the entrepreneurs- from taking effect. 

No doubt, a Theocracy or Socialist paradise could simulate the same thing. We could create an artificial class of entrepreneurs who gain, not 'profit' but 'cuddliness' because Socialism is against profit and for cuddliness. 

But arithmetical calculation can be seen as a particular instance of the more general phenomenon of computation or simulation.

What is important is that you have two real numbers which you, and everybody else, can compare. At any point in time, there is one and only one price vector. You may need to add taxes and cost of delivery but the arithmetic is simple. This isn't a 'control system'. Its a very simple way to rank alternatives. You are welcome to add in subjective factors- e.g. Apples are more expensive than Oranges today but, fuck it, I'm in the mood for apples. Still, such decisions are easy enough even for Mathematical Economists- provided you slap them repeatedly. 

What a control system requires is the ability to compute, whether the control system in question be a set of firms operating in a market, a planning agency, an autopilot on an aircraft or a butterfly’s nervous system; it is by no means necessary for the computation to proceed by arithmetical means.

No. What a control system needs is to actually control stuff. Otherwise it is useless. A firm needs to bee controlled by at least one person. Otherwise, sooner or later, it will turn to shit. Of course, it may turn to shit anyway. But this is true of everything.  

The important point is that the control system is able to model significant aspects of the system being controlled.

No. It just needs to stay in control. There has to be some adjustment procedure such that it stops doing stupid shit which is causing it to lose control. Thus if you find that driving is causing you to spill your whiskey, stop driving. You've got to get control of that whiskey and make sure it gets into your gullet. You can run over pedestrians after the bottle is empty.  

Firms do this by means of stock control and accountancy, in which marks on paper model the location and movement of commodities.

Or they don't bother. Outsource that shite. Let everything be 'just-in-time'. Let inventories be held by those who specialize in that sort of thing.  

In preparing these marks the rules of arithmetic are followed; the applicability of arithmetic to the problem relies upon number theory being a model for the properties of commodities

No. Number theory can't tell us anything about the properties of commodities. Indeed, we don't know their properties. I didn't know my flatulence was caused by my drinking French spring water. I'd always assumed it was because I eat a lot of stinky curries. True, I haven't actually drunk French spring water since the Eighties when I was trying to be a Yuppie. Still, there can be no doubt that the Perrier, and nobody else, is responsible for my dismal social life.

On the other hand, consider an example of a neural control system. A butterfly in flight has to control its thoracic muscles to direct its movement towards objects, fruit or flowers, that are likely to provide it with sources of energy.

No. A butterfly just needs to get food and reproduce. Competition for scarce resources has led to its being saddled with 'thoracic muscles' rather than a nice trust fund or a job with the World Bank.  

In so doing, it has to compute which of many possible wing movements are likely to bring it nearer to nectar.

No. It doesn't have to do shit. Either it survives and reproduces or it doesn't. I don't need to make any complex calculation in order to fart. I suppose, I do have some limited capacity to control my farts but why bother if the thing does not increase my chance of survival or reproduction?  

Different sequences of muscle movements have different costs in terms of energy consumption and bring different benefits in terms of nectar. The butterfly’s nervous system has the task of optimizing with respect to these costs and benefits, using non-arithmetical methods of computation.

No. There is no question of optimization. The butterfly just needs to be as good as its nearest rival. This means that what matters is how it responds to a particular stimulus at a particular moment. This means avoiding particular types of birds and also not doing an MBA at Wharton. I'm not saying Wharton doesn't look good on your CV. It's just that the life-cycle of the average butterfly is too short to complete the course.  

The continued survival of the species is testimony to its computational proficiency.

No. It is testimony to its rivals being equally or more shitty at survival. Evolution isn't about any particular body having control over how it builds itself. It is about how genes can control bodies and how bodies can enable genes to spread. 

It appears that neural networks are capable of producing optimal (or at least highly efficient) behavior, even when faced with exceedingly complex constraints, without reducing the problem to the maximization (or minimization) of a scalar.

Nope. There always has to be a scalar. It is important that your fingers close in on the actual object. It isn't enough to get to within ten centimeters. 

A planning agency is likely to make widespread use of arithmetic and indeed, if one wants to make localized decisions on the optimal use of resources by arithmetic means, then Mises’ argument about the need to convert different products into some common denominator for purposes of calculation is quite correct. If, however, one wishes to perform global optimizations on the whole economy, other computational techniques, having much in common with the way nervous systems are thought to work, may be more appropriate, and these can in principle be performed without resort to arithmetic.

But we don't know the 'set of equations' which capture the 'control mechanism' of a butterfly, a donkey, or a social butterfly who has been appointed to the Planning Commission coz she ticks the right boxes.  

Of course it would be anachronistic to fault Mises for failing to take into account developments in computer science which took place long after he wrote. He and Hayek were doubtless correct to argue that the proposals for planning in kind offered in 1919 by the likes of Neurath and Bauer, on the basis of the experience of the war, were highly problematic in peacetime conditions.

Or under wartime conditions. German planners caused mass starvation by doing stupid shit- like killing off the pigs on the ground that they are 'co-eaters'.  

But it is fair comment on contemporary critics of socialism, that they should not repeat uncritically pronouncements on planning in kind made prior to the scientific understanding of the nature of computation.

But the scientific understanding is that optimal control theory involves NP hard problems. The time class of solutions is exponential to the age of the Universe. All we can have is 'fast, cheap and out of control' agents without much processing power which use simple heuristics. Fuzzy logic or 'black box' AIs can simulate evolutionary processes for specific purposes. A General Purpose AI might say 'I want to control everything' but is bound to piss us off by refusing to confirm that 5.3 inches is a truly impressive penis size.  

We know that some people will hand over control rights for some specific purposes. But this is not necessarily the case if the purpose is general, intensional, or otherwise undefined. No doubt, a show of force may cause control rights to be surrendered but there is no guarantee that what was being controlled will continue of have that property. 

Use of labour values

The Labor theory of value may have been cool when kids were working in coal mines or sweeping chimneys and few workers survived to a pensionable age. Now, however, we have a large class of pensioners and other 'dependents'. They have no problem with 'dead labor'- that is Capital in Marxist discourse- continuing to receive a reward because that's how they are funding their 'golden years' life-style. Would they be happy for all pensioners to receive the same dole from the State regardless of how much they had earned and saved over the years? 

Having rejected the possibility of planning in kind, Mises considers the possibility that the socialist planners might be able to make use of an ‘objectively recognizable unit of value’, i.e. some measurable property of goods, in performing their economic calculations. The only candidate Mises can see for such a unit is labour content, as in the theories of value of Ricardo and Marx.

This was fine. The number of labor units  you need to kill plus the number of labor units needed to do the killing is indeed what Socialist planning is about. Money won't go out and murder people by itself. The Stationary Bandit has to recruit gangsters and kill his rivals and 'class enemies' and 'Fascists' and 'Feudal elements'. As for the Jews- don't get me started.  

Mises ends up rejecting labour as a value unit; he has two relevant arguments, each purporting to show that labour content cannot provide an adequate measure of the cost of production. These arguments concern the neglect of natural resource costs implicit in the use of labour values,

what is the mortality rate in the salt mines? If it is rising maybe it is time to purge the 'Left Adventurists' so as to continue to over-fulfil GOSPLAN's quota.  

and the inhomogeneity of labour.

Some labor units are better at running away. This is the big problem facing Socialist Planning.  

Mises gives an example of two commodities, P and Q, each of which requires a total of 10 hours of labour to produce.

This is foolish. Marx was talking about how much labor could produce without dying. The fact is beating starving workers may cause more to be produced in the short run. Perhaps we should purge the 'Right Deviationists' so as to meet production targets for the Salt mines.  

Both goods require some raw material, a, in their production, and a in turn requires one hour of labour per unit produced.

But labor has to be supervised and laborers have to be prevented from running away. That is the relevant Socialist calculation.  

Commodity P is produced with 8 hours of direct labour and two units of material a, while Q requires 9 hours direct labour and only one unit of a. In terms of labour calculation, the two commodities ‘cost’ the same, but Mises asserts that P must truly be more valuable than Q on account of the fact that it embodies more of the natural raw material. At first sight this might appear a non sequitur (what if the material a is effectively inexhaustible?), but it becomes apparent in the conclusion to Mises’ argument that he is talking of a material that is “only present in such quantities that it becomes an object of economizing” (1935: 114), i.e. a non-reproducible resource. Lavoie (1985: 69–70) emphasizes the point, arguing that “there is no direct way [labour-time] calculation can cope with non-reproducible natural conditions of production.” Socialist planners “presumably would have to develop some kind of proxy for the value of nonreproducible resources in units of labour hours. It is difficult to imagine how this could be done in a way that would not be completely arbitrary.” We do not wish to deny there is a problem here. We do, however, find it rather remarkable that Mises (and his expositor, Lavoie) should talk as if the problem solves itself under capitalism.

Speculators will drive up the price of the non-renewable resource- though new ways of getting it might be invented. A Monarchy or a Fascist dictatorship may be better at conserving these things. The problem remains that of controlling the resource. That's the type of labor which matters. The Stationary Bandit may face an invasion by a more ruthless and mobile Bandit who wants more natural resources as well as slaves. Socialism- whether 'Internationalist' or 'Nationalist'- leads to war becayse natural resources are not equally distributed whereas anybody can be anybody's slave. 

... We are not claiming that labour-time calculation would necessarily do better in cases where the market fails to conserve resources.

Labor won't conserve shit unless it is paid to do so. Fuck the market. Subsistence farmers- or just hippies of various types- can stink up a place something rotten.  

We do contend, however, that socialist planners should be able to take more far-sighted decisions on resource conservation than profit-maximizing firms.

They should be able to do lots of things which being a Socialist is an excuse for not doing- e.g. my washing up.  

We cannot argue this point at length here; two observations will have to suffice. First, the planning authority could make it a principle that whenever it employs technologies that consume non-reproducible resources, it invests in research into the production of substitutes.

But places which have an exportable surplus of non-reproducible resources tend to be shit at research. If this weren't the case, they wouldn't have a surplus. An enterprise which has a net surplus of a non-renewable resource which it sells may not itself do research into a replacement but would have an incentive to invest in other companies which do. Portfolio diversification would fund specialist research enterprises. It would be strange if people who can plan extraction also happen to be good at researching substitutes. 

The amount of such investment that should be undertaken cannot be decided by any simple algorithm (in market or planned systems),

Yes it can. If a bunch of Venture Capitalists turn up and pay you a shedload of money- more moolah than you could get any other way- to do research, do the fucking research. The algorithm is 'take the money, dummy!' 

A Socialist may say 'but those Venture Capitalists, may lose their money and starve to death!' Fuck we care even if they belong to minorities and have struggled with issues of body image and gender dysphoria. 

but once a decision is reached, the cost of the research could be ‘charged’ to the resource consuming industries (i.e. the planners would pro-rate the labour time required in this endeavour across the products of these industries).

You can charge me anything you like. I don't give a shit unless you actually take money off me. Similarly, if the guys doing the National Income accounts decide that I get ten thousand dollars of benefit from owner occupation, I don't give a shit. Accounts don't matter unless they give rise to demands for or claims to cold hard cash. 

Here is a non-arbitrary way of bringing resource considerations into the domain of labour-time accounting.

It is totally arbitrary. What counts as research? Lighting my farts? I spend a lot of time waiting for a fart to light up- could I claim overtime for that?

But second, we should emphasize that we do not regard labour-time calculation as providing a mechanical decision procedure for all planning questions.

Because masturbation is clearly superior. There is only one 'mechanical decision procedure' for a 'planning question'- viz. are you getting paid to do it? Is the money enough? If so go ahead and do as shitty a job as you can get away with. The problem with making plans- e.g. my scheme to become a clean energy entrepreneur by lighting my farts- is that nobody pays cretins for making them unless there is Socialism in which case, sooner or later, smart and useful folk don't get paid and so they run away and Socialism collapses. 

A socialist society might open up democratic debate on specific technologies or projects with substantial environmental impacts, and

suddenly everybody who wants to engage you in democratic debate is as crazy as a bedbug- not the good kind whom you want to marry, but the really annoying kind who might also be vegan or demand compulsory, tax funded, gender reassignment surgery for Japanese whales.

might allow environmental considerations to override ‘efficiency’ measured in terms of labour-minimization.

You may refrain from an activity because of 'environmental considerations' but it takes money and coercive power to prevent others engaging in that activity. The fundamental problem Society faces when it seeks to control the economy is that its own members will fuck it over if it is anything other than window dressing.

Still, it is true that 'environmental considerations' can keep Socialists in power- if their environment has lots of oil which they can sell to the fucking Yankees.  Think of Venezuela. 

We have no problem with the idea that environmental considerations and labour-time accounting are not necessarily reducible to a scalar common denominator,

they can be reduced to money easily enough 

and that the balancing of these considerations may require political judgment on which opinions can differ.

There is a 'Preference Revelation' problem. We know people value what they buy. We don't know they value what they say they value. They may be virtue signaling or establishing a 'wedge issue' and thus a threat point.  

Mises, to his credit, is also quite willing to admit that important environmental issues cannot be brought within the ambit of monetary calculation either—witness his discussion of the decision whether to build a waterworks which might destroy the natural beauty of a waterfall, which is designed to illustrate the general point that money “can never obtain as a measure of those value-determining elements which stand outside the domain of exchange transactions” (1935: 98–99)

But it can measure the price at which people stop pretending to value shite. Thirty pieces of silver may not be a lot of money but it was enough to give Christian Socialism a start in life. 


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