[HN Gopher] The Sonnenschein-Mantel-Debreu Results After Thirty ...
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The Sonnenschein-Mantel-Debreu Results After Thirty Years
Author : gone35
Score : 27 points
Date : 2025-01-19 00:38 UTC (2 days ago)
(HTM) web link (citeseerx.ist.psu.edu)
(TXT) w3m dump (citeseerx.ist.psu.edu)
| troelsSteegin wrote:
| It's an economic theory for characterizing market dynamics. The
| paper's conclusion: "Thus many of the problematic outcomes from
| SMD theory remain entrenched."
| 1oooqooq wrote:
| like every single social science therory dressed as economic
| research truth, the slight harder look at it crumbles all
| assumptions.
|
| so tiring.
|
| best line on that paper: Much of the intuition that would seem
| to follow from the SMD results is still intact. Rationality, as
| Arrow said, does not have aggregate implica- tions, but now, we
| have to add, if only aggregate data are available.
| senkora wrote:
| I didn't know anything about this and found the article hard to
| understand at first, but thankfully the Wikipedia articles on the
| subject are pretty okay:
| https://en.wikipedia.org/wiki/Sonnenschein%E2%80%93Mantel%E2...
|
| The very abbreviated TL;DR of this post is:
|
| 1. We are taught that markets look like this:
| https://upload.wikimedia.org/wikipedia/commons/8/8c/Supply-d...
|
| 2. By applying rigorous math ("general equilibrium theory"), it
| turns out that there is no reason that markets can't look like
| this instead:
| https://upload.wikimedia.org/wikipedia/commons/a/ab/SMD_Dema...
|
| 3. OP's article summarizes how economists have reacted to this
| problem.
| hackeraccount wrote:
| For other reasons I'm reading Adam Smith's Wealth of Nations
| and this seems like nothing that Smith would object to. He'd
| say there's a natural price that that the market price
| gravitates around - very much like that second graphic.
| bckr wrote:
| The point is there are multiple "natural prices" that the
| market price may gravitate around. If Adam Smith thinks
| there's only one "natural price", then he's wrong, and you
| probably want to read with that idea in mind.
| cs702 wrote:
| The Sonnenschein-Mantel-Debreu Theorem states that the excess
| demand curve for a market economy of rational agents _can take
| the shape of any function_ , subject only to three fairly general
| conditions: the function must be continuous, must be homogeneous
| of degree zero
| (https://en.wikipedia.org/wiki/Homogeneous_function), and must
| satisfy Walras's law
| (https://en.wikipedia.org/wiki/Walras%27s_law).
|
| Inconveniently for all economic theories, the implication of this
| _mathematical proof_ is that excess demand and supply curves _can
| take any shape_ that meets those three conditions. The nicely
| sloped supply and demand curves we 've all been shown in
| Economics textbooks are basically _figments of economists '
| imaginations_.
|
| Moreover, the textbook supply-demand curves we've always been
| shown are for only one good. The curves for all goods in a market
| economy are high-dimensional.
|
| High-dimensional supply and demand curves can have multiple
| equilibrium points, and there is no guarantee that those points
| will be optimal or even good.
|
| In other words, for a long time we've had proof -- proof! -- that
| "free markets" are not guaranteed to converge toward good
| outcomes.
|
| Markets can get stuck in crappy equilibria.
| shermantanktop wrote:
| Ooh, now do the Laffer curve!
| cs702 wrote:
| I can't. There's basically no theory behind the "Laffer
| curve." IIRC, it relies on two assumptions. Assumption #1: If
| the income tax rate is 0%, the government will collect zero
| income taxes. This assumption is basically a tautology. No
| one can disagree with it. Assumption #2: If the income tax
| rate is the maximum possible, 100%, the Laffer curve assumes
| the government will collect _zero_ income taxes, because
| taxpayers will find ways to avoid paying _all_ income taxes.
| This second assumption is questionable, because taxpayers
| might successfully avoid paying only _some_ taxes. Even if
| you agree with both assumptions, there 's no agreement as to
| what tax rate would maximize government tax collections.
| shermantanktop wrote:
| In other words, nobody can draw the curve, but people
| assume it is a simple shape with a single maximum...which
| is why I made my silly request.
|
| But if it were anything other than a talking point, I'd
| expect the possibility of complex Laffer curves with
| multiple local maxima.
| bjourne wrote:
| Don't you mean homogeneous of degree one?
| cs702 wrote:
| Sorry, I wrote the equation for homogeneity of degree one by
| mistake. I edited my post to the link to the Wikipedia page
| on homogeneity instead. Thanks.
| mturmon wrote:
| Not a disagreement with your take, which was helpful to me, but
| just your parenthetical aside.
|
| Homogenous of degree 0, which is key to the conditions of the
| results in OP, means f(tx) = t^0 f(x) = f(x)
|
| [https://en.wikipedia.org/wiki/Homogeneous_function]
| cs702 wrote:
| Thank you. I inadvertently wrote the equation for degree one
| homogeneity, from memory. I replaced the equation with a link
| to the Wikipedia page.
| emmelaich wrote:
| Surely it's one thing to say that "curves can take any shape
| that meets those three conditions" and yet still hold that any
| observed or realistic actual curves will only take certain
| shapes - as long as the consumers and producers have the right
| information.
| kibwen wrote:
| _> as long as the consumers and producers have the right
| information_
|
| Honest question: what is "the right information"? Unless you
| want someone choosing what is and is not the right
| information, which feels like market distortion, then "the
| right information" becomes "all possible information". And in
| practice, we as consumers don't even have a thousandth of
| "all the information", let alone a hundredth, let alone half.
| (For example, where can I look up the details of _the entire
| supply chain_ of this phone in my hand, for every single
| material input it requires, to know what degree I 'm culpable
| in supporting slave labor, which is something that would
| influence my purchasing decision?)
|
| And then even if we gave someone all the information, or even
| some useful approximation of all the information, are humans
| even capable of using that to make decisions that are
| informed enough to allow markets to approach any sort of
| rationality? Given finite time, isn't it possible that the
| amount of time required to make a single informed decision is
| longer than a lifespan?
|
| So then the question is, if useful amounts of information are
| neither practically available nor practically actionable,
| what might that imply about our absolute faith in market
| mechanisms that require the right information to operate
| efficiently?
| emmelaich wrote:
| By "right" I mean roughly correct. To your other points I
| suspect that close to correct is often enough and is more
| correct over time. But this is where research should be
| directed I suppose.
| btilly wrote:
| I can make it worse.
|
| We make decisions based on partial information, processed
| in a probabilistic manner. The logically right way to
| reason involves the update of a Bayesian network - each
| belief ties to each other belief. But updating a Bayesian
| network - even approximately, is an NP complete problem.
|
| So we not only can't make a correct decision, we can't even
| try to approximate it in reasonable time. We can only apply
| crappy heuristics. Like, "Are you with me or against me?"
| Hence political alignment replaces our decision making.
| Even for apparently pure economic decisions.
| aaroninsf wrote:
| "Right" is alas undefined and undefinable,
|
| not least as "consumers" idon't make economic decisions wrt
| to some a priori set of N weighted dimensions within which
| a gradient of desirability is defined, or in fact by _any_
| set of such dimensions.
|
| They mostly make discretionary decisions wrt to a set of
| influences triggers habits and cues most of which are not
| about information or rational processes.
|
| A hobby horse is that an increasing number of these are
| manipulated by those in a market with the resources to
| identify exploit them.
|
| This is not uniquely the case for those making
| discretionary spending decisions... but it for those of us,
| that dissatisfaction--or dis-satiation--seems to
| perpetually "find its level." (I.e. the post-orgasmic
| clarify of the satisfaction of the craving, soon evaporates
| like the dew.)
|
| The phenomenon of perpetual unsatisfiable desire for the
| Next Thing is so ubiquitous and accepted we don't even
| attend to it any longer; and so baked in that 2500 year old
| Greek myth gives us well-known parables (c.f. the myth of
| Tantalus).
|
| Related: so, GLP-1 drugs like Ozempic have had discernible
| macroscopic impacts on "consumption" across many economic
| categories, enough so that the Economist magazine had a
| story IIRC on unease in industries most obviously based on
| addictive behavior.
|
| I am curious whether there has been a partiuclarly-
| discernible impact in "expensive hobbies" defined by
| constant pursuit of the Next Better Thing e.g. audiophiles,
| collectors, constant-tinker hobbies like mechanical
| keyboards, modular synthesizers, etc..
|
| The battle in the heavens of our psyches may be waged for
| the next period between GLP-1 agents on the one hand, and
| exploitation of ML on the other, uniquely powerful tool as
| it is for identifying and tuning efficacious triggers for
| addictive behavior.
| cratermoon wrote:
| > if useful amounts of information are neither practically
| available nor practically actionable, what might that imply
| about our absolute faith in market mechanisms that require
| the right information to operate efficiently?
|
| See e.g. Akerlof, George A. (1970). "The Market for
| 'Lemons': Quality Uncertainty and the Market Mechanism"
|
| Akerlof shared the 2001 Nobel Prize in Economic Sciences
| with A. Michael Spence and Joseph E. Stiglitz for work on
| the impact of information asymmetry on markets.
| Veserv wrote:
| It implies that you do not get absolutely 100% perfect
| allocation where everybody is maximally happy according to
| their constraints which is what "efficiently" means in that
| context. That is also a useless and impractical standard to
| hold any system to as any optimization problem is
| impossible if you have missing non-degenerate
| constraints/information.
|
| In practice, the question becomes what systems result in
| the best outcomes given normal conditions and information.
| As a example, we see that total command economies are
| dramatically worse than markets at normal amounts of
| information. Alternatively, how can conditions be changed
| in normal fashions that can be consistently enforced to
| maximize system outcomes.
|
| Things are further confused by the fact that we have a very
| poor understanding of even the implemented systems. What
| aspects are important, what are not? For instance, we can
| see that the modern Chinese economy is clearly more market-
| driven than previously, so the increased amount of market
| economics has been a dramatic improvement. Clearly, they
| were previously on the "too little market" side of that
| equation. In many ways, their markets are more
| "unrestricted" than the USA, but in others less, are they
| more market-driven than the USA or not? Are the ways in
| which they are important, are the ways in which they are
| not important? About the only thing we can really
| categorize are directional changes from a previous status
| quo and maybe we can categorize transformative impacts
| after the fact.
|
| It is these sorts of questions and observations that
| matter. Quibbling about how a system is imperfect in a
| wholly impractical limit to argue against practical matters
| is just silly especially when those same problems are held
| by literally everything.
| cs702 wrote:
| The problem is that a lot of people treat those _assumptions_
| as if they were sacred, fundamental laws of the universe.
|
| There are a lot of business people and government officials
| for whom the notion of "free, unfettered markets" is akin to
| a religious goal. Look around you.
|
| There are NO guarantees that markets will work well. They CAN
| lead to horrific equilibria, like inequality so extreme that
| large groups of people cannot afford food and shelter without
| government assistance, or financial crises that seem to come
| "out of nowhere," with too many possible culprits that could
| be blamed (greedy speculators, greedy financiers, complacent
| banks, idiotic regulators, government-sponsored entities,
| etc.), depending on who you ask.
|
| I say, let's be humble, open-minded, willing to try new
| things, and willing to change our views when the facts
| disagree with them.[a]
|
| ---
|
| [a] In the words of Lee Kuan Yew, who led the transformation
| of Singapore from one of the poorest to one of the wealthiest
| societies on earth:
|
| > My life is not guided by philosophy or theories. I get
| things done and leave others to extract the principles from
| my successful solutions. I do not work on a theory. Instead,
| I ask: what will make this work? If, after a series of
| solutions, I find that a certain approach worked, then I try
| to find out what was the principle behind the solution. So
| Plato, Aristotle, Socrates, I am not guided by them...I am
| interested in what works...Presented with the difficulty or
| major problem or an assortment of conflicting facts, I review
| what alternatives I have if my proposed solution does not
| work. I choose a solution which offers a higher probability
| of success, but if it fails, I have some other way. Never a
| dead end.
|
| > We were not ideologues. We did not believe in theories as
| such. A theory is an attractive proposition intellectually.
| What we faced was a real problem of human beings looking for
| work, to be paid, to buy their food, their clothes, their
| homes, and to bring their children up...I had read the
| theories and maybe half believed in them.
|
| > But we were sufficiently practical and pragmatic enough not
| to be cluttered up and inhibited by theories. If a thing
| works, let us work it, and that eventually evolved into the
| kind of economy that we have today. Our test was: does it
| work? Does it bring benefits to the people?...The prevailing
| theory then was that multinationals were exploiters of cheap
| labor and cheap raw materials and would suck a country
| dry...Nobody else wanted to exploit the labor. So why not, if
| they want to exploit our labor? They are welcome to it.... We
| were learning how to do a job from them, which we would never
| have learnt... We were part of the process that disproved the
| theory of the development economics school, that this was
| exploitation. We were in no position to be fussy about high-
| minded principles.
|
| Source: https://www.amazon.com/gp/product/0262019124
| emmelaich wrote:
| Sure let's be humble. I think alleging that people holding
| the notion of free markets is a religious goal is not a
| humble opinion.
| cs702 wrote:
| I did not allege that everyone holding that notion treats
| it like a religions goal.
|
| "A lot of business people and government officials" [?]
| "everyone."
|
| Please don't attack a straw-man.
| emmelaich wrote:
| They're your words. I didn't say everyone. You didn't say
| everyone. Where's the straw-man?
| Etheryte wrote:
| I think it's a pretty crude oversimplification to say it's a
| proof when the whole idea hinges on the whole rational actors
| axiom. Sure, it might be a proof with that axiom, but it
| doesn't say much anything about the real world.
| cs702 wrote:
| I'm not sure I understand what you're saying. The whole
| edifice of "markets converge toward general equilibrium"
| rests on the assumption that people are rational, i.e.,
| maximize utility -- which is economist jargon for "people are
| trying to do better for themselves." If you take away _that_
| , the whole theoretical edifice justifying markets collapses.
| cratermoon wrote:
| Another inconvenient truth for the theorem is that "a market
| economy of rational agents" is a mathematical fantasy and
| doesn't describe any real world market ever.
| Veserv wrote:
| It has been proven that global utility optimization can be
| equivalent to solving a arbitrarily complex, arbitrarily non-
| linear, arbitrarily quickly changing, function. Great. There
| exists exactly zero techniques for solving all such systems
| even if the function was not unknown.
|
| That is proof that "free markets" are not guaranteed to
| converge toward good outcomes because it proves that every
| decision/optimization process that is believed to be even
| theoretically possible is not guaranteed to converge toward
| good outcomes. Singling out "free markets" as if they are even
| somewhat uniquely susceptible is just plain ridiculous.
| Everything is thoroughly screwed in the presence of arbitrarily
| complex functions.
|
| As we have now seen and proven that everything is doomed in a
| arbitrarily malicious universe, it is only prudent to re-focus
| on problems under normal conditions and figure out the
| practical question of what systems produce good, high quality
| outcomes in a normal implementation over normal conditions.
| cs702 wrote:
| As I wrote elsewhere on this thread
| (https://news.ycombinator.com/item?id=42783130), the problem
| is that a lot of busy people treat the "practical notion"
| that markets produce good, high-quality outcomes as if it
| were a fundamental law of the universe. It's not. There are
| no guarantees. Markets can converge to horrific equilibria.
| Let's be humble, open-minded, willing to rely on markets when
| they work, willing to try other things when they don't.
| kelseyfrog wrote:
| This fundamentally changes the debate on market
| interventions. It's now possible to argue that the current
| equilibrium is only meta-stable and that interventions that
| change the supply and demand curves can potentially kick us
| out of one meta-stable equilibrium and into another more
| efficient one.
|
| I wish we had more empirical supply-demand curves so we
| could refine our priors on supply and demand curve shapes,
| but that's a topic for another day.
| cherryteastain wrote:
| Free market economics is "singled out" because, at least in
| the Anglosphere, it is the only type of economy considred to
| reach an (eventual) optimum by itself.
| vtashkov wrote:
| For even longer time we have a REAL proof (not mathematical
| wordplay) that whenever, without exception, someone takes a
| swing at free markets it leads to people dying. IT has always
| been a disaster and people always have been exiting those
| societies where that happens towards more free societies. You
| yourself have plenty of options to go somewhere with less free
| market - Cuba, Venezuela, North Korea, Russia, even China. Have
| YOU emigrated to such a country?
| lern_too_spel wrote:
| You also have the option to go somewhere with even more of a
| free market, like Somalia. Have you emigrated to such a
| country? It turns out that societies can write laws for
| mutual benefit.
| cs702 wrote:
| Oh, I'm a capitalist. I believe Churchill was right when he
| said that capitalism is the worst economic system ever
| invented, except for all the others that have been tried
| before.
|
| I never said we should do away with a market economy. All I
| said is that market economies are not guaranteed to converge
| to optimal or even good outcomes.
|
| Markets CAN lead to horrifically bad equilibria (extreme
| inequality, financial crises, recessions, depressions, etc.).
| There are no guarantees that they won't.
|
| So let's be humble, open-minded, willing to rely on markets
| when they work, willing to try other things when they don't.
|
| Please don't attack a straw-man.
| semi-extrinsic wrote:
| > whenever, without exception, someone takes a swing at free
| markets it leads to people dying
|
| Do Scandinavian socialist democracies not count as an
| exception?
|
| On the flip side, I think you will equally find that whenever
| free market solutions are applied to public services -
| healthcare, water, electricity, police, etc - people also die
| in large numbers. And although wealthy people generated by
| the free markets are philantropic, it's not in proportion to
| the harm inflicted on people. Only thing is, we ignore those
| disasters because they are inconvenient for the narrative.
|
| It seems to be obvious that certain things (like public
| utilities) should just be controlled directly by the
| government, without any free markets involved, as long as
| your objective function is to optimize the average life
| quality of your citizens.
| readthenotes1 wrote:
| Can you give some examples on actual free market solutions
| are applied to public services?
|
| The closest I can think of are the metros of Tokyo free
| government takeover, but I am not sure how free those
| actually were of government regulation.
|
| One of the struggles I have is that typically these public
| services may be carried out by private companies paid for
| by the government, but that is just begging for corruption
| twic wrote:
| It would be really helpful to see an example of one of these
| naughty excess demand curves, along with the utility function for
| each agent. For an economy with a small enough number of
| commodities and agents that it might be comprehensible, say two
| or three.
| kelseyfrog wrote:
| So the nicely sloped supply and demand curves are economic
| equivalent of spherical cows and as much as we shouldn't design a
| milk industry around spherical cows, we shouldn't design an
| economy around a nicely sloped supply and demand curves.
| cs702 wrote:
| For anyone here who doesn't get the reference to spherical
| cows, it's from an old joke:
|
| > Milk production at a dairy farm was low, so the farmer wrote
| to the local university, asking for help from academia. A
| multidisciplinary team of professors was assembled, headed by a
| theoretical physicist, and two weeks of intensive on-site
| investigation took place. The scholars then returned to the
| university, notebooks crammed with data, where the task of
| writing the report was left to the team leader. Shortly
| thereafter the physicist returned to the farm, saying to the
| farmer, "I have the solution, but it works only in the case of
| spherical cows in a vacuum."
|
| Source: https://en.wikipedia.org/wiki/Spherical_cow
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