Look at it this way:
Assumptions: People have different preferences for cake relative to other things and people have some initial endowment of other things. (These are pretty reasonable assumptions.)
Definition: Efficiency is greater (meaning that people are better off) where people's endowments of cake and other things better match their preferences. The sum of the differences between final endowments and preferences for them is total social inefficiency.
Question: Under what conditions will rationing an equal portion of cake to each person better match their preferences than allowing people to exchange their initial endowments for portions of cake? In other words, when will total social efficiency under central rationing be less than under a system of trading things for portions of cake?
I believe the answer to that question, provided all trivial issues of equivalency are taken care of (such as by assuming zero costs, disinterested initial government distribution, etc.) is that rationing will be better only if, by sheer dumb luck, it turns out that each person's preference for cake relative to other things is the same. In such a case there are no possible gains from trade and people can be made better off ONLY by giving them more cake or other stuff.
(The mathematical proofs for this are provided in the first and second fundemental theorems of welfare economics, which of course include the very narrow assumptionis of perfect information, no externalities, etc. But the fact that those assumptions don't occur in the real world does not mean that markets are inferior to other allocation methods, particularly on the scale of large societies. Rather, they just provide the conditions under which it is possible to argue that non-market allocation methods might be better in specific cases.)
It can be instructive here to relax the assumption of rationing equal portions of cake. Let's say that the agent in charge of rationing is smart enough to know what each person's preferences for cake are and that there is enough cake to fill each preference. Then it is also possible that rationing will be more optimal than trading.
This leads to the question: Under what conditions can a central, distributive political authority in charge of rationing be trusted to have better knowledge about the preferences for cake and other stuff than a system that allows at least some feedback of preferences from consumers?
Looked at this way, you can certainly find cases where it is not possible to say that markets are more efficient than central rationing, but I think it would be unreasonable to use those cases to argue against my claim of the general (not specific or always) superiority (to date) of societies organized around market mechanisms for allocating things over other systems yet attempted (as opposed to merely theororized). Getting feedback is usually a necessary part of optimizing distribution, so a superior system than markets must show a better way of providing such feedback in a complex social system.
I disagree with the way you phrase the question: The fundamental theorems do not actually help in comparing any two specifically given allocation systems or algorithms. In this case, the generality they claim is misleading.
Let v be an initial allocation of goods, and let's use those theorems to obtain a maximally improved allocation which I'll write as f(v). (Improvement in any sense you like, eg total social efficiency. This leads to a comparison operation which I'll write >= ), The only thing I care about is that f(v) can be obtained through a sequence of trades starting from v, and if there are several possible f(v), we'll just pick one or if you like we can refer to all of them as f(v). Thus there is a real humanly implementable algorithm to arrive at f(v) from v, and I'm not trying to be tricky.
Now as long as you can represent the outcome of an allocation algorithm as a vector v, then you know that f(v) >= v. So naively put, one can say that optimal allocations are always achievable as the result of market mechanisms, therefore there's no need to consider non-market mechanisms at all. (I think that's what your point of view is more or less.)
BUT, this is not the real question. The real question is: If you have two algorithms, which respectively achieve the allocations v1 and v2, then what can you say about v1 compared with v2? In the rationing example, v1 = the uniform cake subdivision, and v2 = f(w), where w is the allocation where one particular individual owns the whole cake.
Now the fundamental theorems tell us that f(v) >= v for all v, which is great, but irrelevant. We actually want to know does v1 >= v2 or v2 >= v1 ? (since those are the outputs of the rationing algorithm v1 = Ration(w) and of the market algorithm v2=f(w) respectively).
Now in general, it's not possible to calculate the comparison of v1 with v2. There are very few general methods that can settle this sort of question. One is to say that there is a unique optimum. In that case f(w) >= v for all v trivially, in particular f(w) >= v1. But a system with a single global equilibrium is pretty rare. Another method is to say that there is a sequence of trades w->v1, in which case we can claim f(w) = f(v1) and so v2 >= v1. But this too is far from obviously true [this is my longwinded method above].
So I consider the question v2 >= v1 as undecidable in general, and even more so if one decides to apply market dynamics to questions which arise in other fields. One can certainly formalize some sets of preferences and impose conditions on the dynamics of some players until the market formulation coincides with the question one wishes to solve, but in so doing even the weak assumptions in the fundamental theorems are likely to be violated, and certainly one has to presume that there will be many equilibria and degenerate effects.
Note that it is not even clear that f(w) >= f(v1), where f(v1) is the output of an initial rationing step v1 = Ration(w) followed by a market trading step. We simply don't know if w and v1 both belong to the domain of attraction of the exact same equilibrium, or what the actual relationship between the two target equilibria might be otherwise. -- $E(X_t|F_s) = X_s,\quad t > s$
Another method is to say that there is a sequence of trades w->v1, which case we can claim f(w) >= f(v1) and so v2 >= v1.
It is quite true to say that I can't compare a rationing outcome and an auctioning outcome unless both outcomes are optimizing over the same criteria, which is given, a priori, by what one believes matters in life in the first place. That is why we can never say that capitalism is better than feudalism, or that either of those social systems is better than the social systems of ancient Mayans, Aztecs, or preent tribal cultures in the Amazon, for example. Different things were or are deemed important to different people.
However, different forms of capitalist social organization, as well as communist or socialist forms -- examples of what anthopologists call "modernity" -- all occur within the basic utilitarian framework of the world. That is, all "modern" means of organizing society, like both Adam Smith and Karl Marx, all agree that "better" can be reasonably defined as achieving a closer match between what people want and what they ultimately get. Outside of modernity, we can't compare rationing to markets, but inside we can by arguing around efficient and equitable solutions -- how much there is, and who gets it.
It is not at all as trivial, mathematically, as you claim, even if you accept my premise of efficiency as a definition of better, principally because there is no way to say that efficiency has more claim than equity, which means that markets, themselves, cannot achieve socially optimal outcomes, because markets have nothing to do with equity, which is a value determined as subjectively as efficiency but over different objectives. However, we can still conclude empirically that social systems that share honest information about real wants and real resources are likely to be superior within the parameters of modern society to social systems that restrict such sharing of information. I advance that markets, combined with democratic governance structures, are more likely to provide a socially desirable allocation of resources given conditions of modernity, than other allocation systems and governance structures.
Are there possible exceptions or significant problems and even contradictions with markets? Of course there are. But given the currently observable counterfactuals -- fascism, authoritarian socialism (e.g. Venezuela vs. Brazil), communism, for example (let me know what I'm missing) -- can you honestly argue that other social systems have not proven inferior to markets?
Certain kinds of markets are good at doing certain things, just as certain kinds of government structures are good at doing certain things. Broadly speaking, markets appear to be good at providing material goods that individually take up a small fraction of the median income, have a respectably high turnover within the lifetime of a single individual and are reasonably easy to transport from one place to another.
OTOH, markets are exceedingly poor at making infrastructure that actually works (education, electricity, trains, payment clearing systems, pensions). And markets are completely unable to allocate non-local costs (systemic risk, cascading failures) and long-term costs (environmental destruction, resource depletion, failures due to insufficient maintenance). Or at least markets do not seem to be able to allocate those costs in a way that does not threaten to destroy the social structures that enable markets to exist.
Goods with moderately high turnover but which are largely immobile and take up a large fraction of the median income (real estate, mainly) have decidedly mixed empirical results for markets compared to central planning.
- Jake If you only spend 20 minutes of the rest of your life on economics, go spend them here.
That there is a private real estate market beside the government pool does not detract from the fact that the government housing is centrally planned according to criteria that have to do with social policy, city planning and similar criteria.
Examples of centrally-planned, non-market housing that immediately come to mind in otherwise market-based societies are state-run prisons, some mental health institutions, military barracks, and some refugee camps. It's centrally planned if there are no choices and exchanges involved on the part of the receiving agents.
The council owns over 5,000 properties that are rented to tenants. We provide services to tenants including housing repairs and providing a local neighbourhood manager. In this section of the website you can apply to join the housing register or to move between council houses, pay your rent online, have your say in tenant participation, plus other services. We are introducing a new choice-based lettings system and also administer the council tenants' right to buy scheme. Also see the housing advice section for information on sheltered housing, emergency accommodation and other ways we support the housing needs of the district.
The council owns over 5,000 properties that are rented to tenants. We provide services to tenants including housing repairs and providing a local neighbourhood manager.
In this section of the website you can apply to join the housing register or to move between council houses, pay your rent online, have your say in tenant participation, plus other services.
We are introducing a new choice-based lettings system and also administer the council tenants' right to buy scheme.
Also see the housing advice section for information on sheltered housing, emergency accommodation and other ways we support the housing needs of the district.
In fact, if you are going by that definition of "market," any reasonably industrialised country with even a half-evolved monetary system qualifies as a "market economy." I fail to see how that is helpful to a political or economic analysis that deals with a tolerably technologically sophisticated society.
You are arguing, unless I'm missing something, that I can't define "better" as the minimization of preferences and actual outcomes.
My own argument above is purely mathematical, and applies with *your* definition of what is desirable. While I personally don't care what function is being minimized, I am happy to work within your framework exclusively. Thus: let's completely ignore the social dimension.
All my argument uses is that there may be several distinct equilibria in a market, which are implied by the preferences (fixed once and for all). If you begin with some allocation vector, then market dynamics will converge (under appropriate conditions...) to some equilibrium vector. I also grant you that. The identity of this equilibrium vector will depend upon the starting point. Two distinct starting points may end up in two distinct equilibria. If you do not agree, say so now.
Maybe I should answer your previous question at this point.
I don't have a more complete solution of this problem at this point, but neither do you(?) of the converse:
Question: If I give you two arbitrary starting points (initial endowment distributions), can you predict which starting point leads to the smaller total social inefficiency? Alternatively, if I give you a single starting point, can you describe all starting points which either 1) have a greater social inefficiency than the particular equilibrium vector reached by the first point, or 2) reach some equilibrium whose total social inefficiency is greater than the total social inefficiency of the particular equilibrium reached by the first point.
I believe you cannot, in any practically useful sense. For example, if I propose an actual carbon trading market for the world, exactly which initial endowments of carbon credits should be allocated to everyone in the market to reach the equilibrium point whose total social inefficiency is smallest of all the equilibria? Can you calculate it? -- $E(X_t|F_s) = X_s,\quad t > s$
If you begin with some allocation vector, then market dynamics will converge (under appropriate conditions...) to some equilibrium vector.
Not on any kind of time scale that's experimentally interesting.
I agree with your attacks on the validity of the underlying mathematical assumptions, and while I've used such arguments myself before, in this thread I am not. Instead, I am pointing out that the welfare theorems aren't very deep when it comes to comparing economic allocation methods, and cannot support, even under ideal mathematical conditions, the claims about the superiority of markets vs non-markets.
The only thing a market can do is improve or "polish" an allocation in some sense. This is at best a local optimum in general, not a global one. To obtain a global optimum, it is therefore necessary to study non-market mechanisms. -- $E(X_t|F_s) = X_s,\quad t > s$
I guess I'm less charitable when it comes to permitting blithe assumptions that asymptotic solutions are interesting. Once burned twice careful, I guess. (a project of mine involved a relaxation time scale to the asymptotic solution that turned out to be around 19 orders of magnitude greater than the experimental time scale - a fact that failed to become apparent until we'd already spent two weeks and a bit on it...).
