All posts by yni957

2022 Mid-term

Nearly every pundit and journalist I heard yesterday were shocked by the no-show of the Red Tsunami they had confidently prophesized.  Today, many of them seemed to have regained confidence in their own political acumen by explaining the failure with a new theory:  obviously (with the benefit of hindsight), the omnipresence of Trump had caused GOP to underperform.  This reminds me how good humans are at inventing theories to explain things – theorizing really seems easy and natural for us.   The tragedy is that we often fool ourselves into believing the ability to explain must also give us the ability to predict. The greater tragedy is many genuinely believe in these predictions and, even worse, are committed to bringing them about.

Capital in the 21st century

“Capital in the 21st Century” explains how the distribution of income and wealth (or capital) evolves according to the laws that govern economic growth, rate of saving, and returns on capital.  Picketty argues quite convincingly the reproduction of capital tends to outpace that of the economic output (GDP).   Once set in motion, therefore, capitalism inevitably concentrates wealth, creating a self-reinforcing spiral that ends with appallingly unequal distribution of wealth.  By Picketty’s estimation, the accumulation of wealth in the developed countries has by 2010s returned to a level that the world has not seen since the eve of the World War I.  As a shocking symptom of this extreme inequality, the bottom 50% of population collectively own close to nothing everywhere, including Sweden!  If this process is to continue indefinitely, he warns, “the past will devour the future” and we will return to a society of “rentiers dominant over those who own nothing but their labor”.

It is tempting to reject out of hand Picketty’s thesis as Marxism dressed in a new costume, and his laser focus on inequality a dangerous rhetoric tacitly inciting class warfare.  Such an interpretation would be unfair, however.  His main argument against capital concentration, I think, is not a moral one.  Rather, the concern is concentrating so much capital in so few hands may be socially destabilizing. Moreover, as the stock of capital continues to grow relative to GDP, the returns on capital may eventually converge to the rate of economic growth, at which point capitalists must reinvest all income from capital in order to merely preserve “their social status relative to the average for the society”. This last point, known as the golden rule, seems to me an ultimate manifestation of involution (内卷).

How do we avoid such apocalypse then?  Picketty’s innovation is a tax directly levied on capital, including all financial assets such as (unsold) stocks and bonds.   As utopian as it might sound, the idea has gained traction in mainstream politics lately.  The Democratic Party in the US, for example, recently proposed a “billionaire tax” to pay for Biden’s ambitious social spending programs.  Conceptually, the billionaire tax is exactly a tax on capital, though it limits the taxation base literally to “billionaires”. While this proposal died quickly, I suspect similar attempts will resurface in the future, if only as a novel revenue source for desperate governments.

Picketty is an articulate and persuasive writer, and “Capital” is absolutely worth reading.  As a side note, I found his open refusal to recognize economics as a science remarkable and laudable.  My jaw almost dropped when I read “the discipline of economics has yet to get over its childish passion for mathematics”. With that kind of candidness, I am sure the book did not win Picketty many friends in his profession; but whether you agree with him or not, you must admit to “tell it as it is” in such a dramatic fashion requires conviction, courage, and integrity.

Transportation equity

Last month my group received a one-year seed grant from Northwestern University’s McCormick Catalyst  Fund to study transportation equity.   The main idea is to  incorporate various ethical theories into  public transportation system design and analyze the implications.   The project initially  originated from my interest in the theory of justice (see my review of John Rawls’ book).  More details about the project can be found here.  Stay tuned for a forthcoming paper that summarizes some initial results.

From SPQR to one-man rule

Mary Beard’s SPQR—which stands for “Senate and People of Rome”—covers the first thousand years of the Roman Empire, running from the legendary founding of the city in 753 BCE to 212 CE, when Caracalla extended citizenship to all free men living within the Empire.  Her narrative anchors at the time of Caesar and Cicero (i.e., the middle of the first century BCE), which not only saw Rome’s transition from a republic to one-man rule, but also produced a significant body of literature, including a huge volume of Cicero’s writing. Coincidentally, this period largely overlaps with the glorious thousand years of Ancient China, between the Spring and Autumn Period, officially commenced in 770 BCE, to the end of the Eastern Han Dynasty (220 CE).

You would be thoroughly disappointed if you look forward to reading the colorful stories of the famed Roman tyrants or the virtuous deeds of the five good emperors.  Beard refused to reconstruct Roman history in terms of the biographies of the rulers.
She is skeptical of the accuracy of their “standard images” passed on to us in historical records. More importantly, she does not believe “the qualities of the man on the throne” would make much difference, because all emperors, from Nero to Marcus Aurelius, ruled according to the same blueprint laid out by Augustus.  Her sentiment reminds me of an Afghan proverb I recently came across,

“Better a strong dog in the yard than a strong king in the capital”.  

Accordingly, Beard’s portrait of Rome focuses on ordinary Romans.  She depicts with vivid details the Roman way of life, from where Romans live, what they eat, to how they commemorate the dead; she describes every facet of the society, from politics, entertainment and personal finance to law enforcement and war.  Beard’s stories are always carefully backed up not only by the writings of contemporary Romans, but also by rich archeological records – many of which I’ve never known exist.    I very much appreciate her deemphasizing royal résumés and court intrigues. However, I’m not sure all emperors are as useless or harmless as she insists. It may be true that emperors had limited influences on the daily life of any ordinary peasant or aristocrat.   However, overly ambitious despots or utterly incompetent idiots could still, without great labor, throw their empires into cataclysm and destroy millions of lives in the wake. This is especially true for many Chinese dynasties, where an ever-present, sophisticated, and layered bureaucratic system could impose laws and extract resources in nearly every corner of the empire.

Beard seems to agree with Polybius—a Greek who wrote in the second century BCE a 40-volume book entitled “Histories”—that Rome’s rapid ascent to hegemony should be credited to the idea of checks-and-balances embedded in her political system.  Seeking to maintain a delicate equilibrium between consuls, the senate, and the people, the idea had influenced the United States’ constitution so much that it remains the emblem of her politics to this day.  However, I suspect Polybius had made a common mistake in social science here: extrapolating incomplete patterns into a specious theory. On the other side of Earth, the Kingdom of Qin established the first Chinese empire in 221 BCE, 75 years before Rome became the master of Mediterranean on the ruins of Carthage.  Qin was a highly centralized monarchy founded on legalism, a political philosophy antithetical to the idea of checks-and-balances. Legalists argue the more concentrated the power is into the hands of the sovereign, the better. They advised the emperor that the people are not to be entrusted with liberty or right to participatory governance; instead, they must be ruthlessly exploited for the collective national interest––whatever that means––and to save themselves from falling victim to their own vices (hence the slogan “serving the people”). Cruel as it might sound, legalism had enabled Qin to conquer a vast territory by force and remake China in its own image. To be sure, the mighty Qin dynasty lasted only 15 years.  However, the polity it pioneered had survived for millenniums – some may argue it continues to this day. Thus, checks-and-balances is probably not the secret behind Rome’s unparalleled success.  Nor had it saved Rome from the populist strong men of the first century BCE – the likes of Pompei, Caesar and Octavian.

Beard notes “Roman emperors and their advisors never solved the problem of succession”.  Rather than sticking to primogeniture, Roman rulers often resorted to— sometimes forced by biology, as in the case of Julio-Claudian dynasty—a form of ambiguous meritocracy for choosing their heir. As a result, for the period covered in the book, only three emperors, Vespasian, Marcus Aurelius and Septimius Severus, had passed the throne to their biological sons.  Those who have watched the Hollywood movie “Gladiator” may remember the scene where Marcus Aurelius was murdered by his son, Commodus, who found out the philosopher emperor was about to name an able and wise general as the heir to the throne. I have not seen much evidence supporting this dramatized version of the fateful succession that upended the era of “five-good-emperors”.  In fact, Commodus was named the co-emperor––another strange Roman invention––at the age of 15 by his father.   Nevertheless, the Hollywood story captures the Romans’ ideal succession principle, perhaps best expressed in a speech delivered to the emperor Trajan by Pliny the Younger,

“If he is to rule over all, he must be chosen from all”.

To Pliny’s contemporaries in China––the elites of the Eastern Han Dynasty––the suggestion that an emperor should be chosen from all must sound absurd, if not blasphemous.  While the legend has it that once upon a time Chinese, too, chose their ruler by merit rather than birth, that nostalgic era of Yao-Shun-Yu (尧舜禹) had long gone by the time when Pliny wrote his speech.   The point, of course, was never about which succession principle is better, but rather no principle always works under one-man rule. As Beard points out, transferring the absolute power is an inherently unstable and dangerous business, and the moment when that power was supposedly handed on was “always the moment when the empire was most vulnerable.”  To this truth millions of people can still attest even today.

 

The End of Everything

I am always attracted to “The End of XXX”. “The End of Faith”, “The End of Time”, “The End of Physics”, “The End of History”, and the list goes on.   Thus, ever since a colleague of mine named The End of Everything his favorite book about astrophysics, I knew I must read it.   I was not disappointed.

The book is a layman’s guide to cosmology, with a focus on the death of the universe. Katie Mack explains that our universe could end in five different ways and she expects humanity to survive in none of these scenarios.  Of the five endings, Heat Death seems the most humane to me.  In it, the universe will continue to expand until it reaches a thermodynamic equilibrium, at which nothing, including life in any form as we know it, can ever happen again.  The other four endings, if I understand them correctly, all involve a cataclysm that, according to Mack, you will never want to live long enough to witness.

A book entitled “The end of everything”, of course, is inherently about eschatology.  Contemplating the end of the universe was surprisingly hard and strangely personal. In fact, I found it even harder than thinking of my own death. We humans often come to terms with death using the legacies we might leave behind: passing our genes on to next generations; making the world a better place; or better yet, enshrining our ideas in eternal knowledge.  However, if humanity itself will not survive the destruction of the universe, these justifications sound unconvincing.  “At some point, in a cosmic sense, it will not have mattered that we ever lived.” Mack tells us.  This comment reminds me of the famous quote from the movie Coco, “When there is no one left in the living world who remembers you, you disappear from this world. we call it the Final Death”. The end of universe is the Final Death of Humanity.

Mack then asks the obvious question: “What does that mean for humanity and where does that leave us now?”  In the epilogue, she tried but struggled to offer a satisfactory answer.  I could not come up with an answer either.  In fact, just thinking about it makes me feel sad. Indeed, when a colleague of Mack posed that question at an academic seminar, some people in the audience cried.

Mack is a great writer and communicator.  Her infectious passion for science and sharp wit makes reading the book a joy that I look forward to everyday. For the first time, I feel that I actually understand what dark energy or cosmic background radiation is.  Of course, I still have no idea about the Higgs Field or Vacuum Decay, but that’s probably on me.

Allocation problem for the platform of platforms

Another joint work with Ruijie Li, built on our previous research of ridesharing, including A-PASS and Pricing carpool.

In this study, we consider a general problem called the Allocation Problem for the Platform of Platforms – dubbed AP3.  Such a problem might arise  in a two-sided service market, where a third-party integrator tries to allocate customers to workers separately controlled by a set of online platforms in a manner that satisfies all stakeholders.   The integrator, as a leader, influences the outcome of the game by pricing the service, whereas the platforms (followers) are given the freedom to accept or reject customers to maximize their own profit, given the prices set by the integrator (see the plot below for an illustration).  A set of nonlinear constraints are imposed on the leader’s problem to eliminate artificial scarcity, orignated from the integrator’s monopoly power.  We formulate AP3 as a Stackelberg bipartite matching problem, which is known to be NP-hard in general.  Our main result concerns the proof that AP3 can be reduced to a polynomially solvable problem by taking advantage of, somewhat paradoxically, the hard requirement of ruling out artificial scarcity.

A preprint can be downloaded here.


Abstract: We study the Allocation Problem for the Platform of Platforms (abbreviated as AP3) in a two-sided service market, where a third-party integrator tries to allocate customers to workers separately controlled by a set of online platforms in a manner that satisfies all stakeholders. AP3 is a natural Stackelberg game. The integrator, as a leader, influences the outcome of the game by pricing the service, whereas the platforms (followers) are given the freedom to accept or reject customers to maximize their own profit, given the prices set by the integrator. A set of nonlinear constraints are imposed on the leader’s problem to eliminate artificial scarcity, derived from the integrator’s monopoly power. We formulate AP3 as a Stackelberg bipartite matching problem, which is known to be NP-hard in general. Our main result concerns the proof that AP3 can be reduced to a polynomially solvable problem by taking advantage of, somewhat paradoxically, the “hard” requirement of ruling out artificial scarcity. Numerical experiments are conducted using the ride-hail service market as a case study. We find artificial scarcity negatively affects the number of customers served, although the magnitude of the effect varies with market conditions. In most cases, the integrator takes the lion’s share of the profit, but the need to eliminate artificial scarcity sometimes forces them to concede the benefits of collaboration to the platforms. The tighter the supply relative to the demand, the more the platforms benefit from removing artificial scarcity. In an over-supplied market, however, the integrator has a consistent and overwhelming advantage bestowed by its monopoly position.

Differentiable bilevel programming

A Stackelberg congestion game (SCG) is a bilevel program in which a leader aims to maximize their own gain by anticipating and manipulating the equilibrium state at which followers settle by playing a congestion game. Large-scale SCGs are well known for their intractability and complexity.   In this study,  we attempt to marry the latest developments in machine learning with traditional methodologies — notably bilevel optimization and game theory — to forge an integrative approach based on differentiable programming.  Among other advantages,  the approach enables us to treat the equilibration of a congestion game as a deep neural network (see below), so that a suite of computational tools, notably automatic differentiation, can be easily applied.  You may download a preprint here.


Abstract: A Stackelberg congestion game (SCG) is a bilevel program in which a leader aims to maximize their own gain by anticipating and manipulating the equilibrium state at which followers settle by playing a congestion game. Large-scale SCGs are well known for their intractability and complexity. This study approaches SCGs through differentiable programming, which marries the latest developments in machine learning with conventional methodologies. The core idea centers on representing the lower-level equilibrium problem using an evolution path formed by the imitative logit dynamics. It enables the use of automatic differentiation over the evolution path towards equilibrium, leading to a double-loop gradient descent algorithm. We further show the fixation on the lower-level equilibrium may be a self-imposed computational obstacle. Instead, the leader may only look ahead along the followers’ evolution path for a few steps, while updating their decisions in sync with the followers through a co-evolution process. The revelation gives rise to a single-loop algorithm that is more efficient in terms of both memory consumption and computation time. Through numerical experiments that cover a wide range of benchmark problems, we find the single-loop algorithm consistently strikes a good balance between solution quality and efficiency, outperforming not only the standard double-loop implementation but also other methods from the literature. Importantly, our results highlight both the wastefulness of “full anticipation” and the peril of “zero anticipation”. If a quick-and-dirty heuristic is needed for solving a really large SCG, the proposed single-loop algorithm with a one-step look-ahead makes an ideal candidate.

国史大纲+万古江河

钱穆的《国史大纲》和许倬云的《万古江河》都是架构宏大的中国通史,两本书覆盖范围差不多,均为上古至民国:国史大纲止于抗战时期,而万古江河以49年作结;风格也类似,都从重构历史出发,探究中华文明特质及精神,解释兴衰变迁,在当今世界中为其定位。就像钱穆说的,“治国史之第一任务,在能于国家民族之内部自身,求得其独特精神之所在。”

两位史家秉持的中华史观相差不可道里计。钱穆是传统视角,以中原地理坐标为枢轴,以中国传统文化为经纬来编制历史,尚未脱天下四方的二元理念。比如他解释中国文化演进的独特性时写道,“中国政制常偏重于中央之凝合,而不重于四围之吞并。其精神亦常偏于和平,而不重于富强;常偏于已有之完整,而略于未有之侵获;对外则曰’昭文德以来之’,对内则曰’不患寡而患不均’”。字里行间充满了对天朝文化感召力的自信,虽然没写圣人出而天下归心,四海定而万国宾服,但意思差相仿佛。 大概因为成书在抗战时期,《国史大纲》民族情结强烈,夷夏之防溢于言表,这一点从他扬明抑清的倾向中表露无疑。比如他说,“明清之际的转变,大部分是明代内部自身的政治问题,说不上民族的衰老”;又说,“中国则因有二百年来满洲部族政权之横梗作病,使之虽欲急起直追而不可得”,恨不得要把中国近代落后的总账一股脑都算在满清这个异族征服者的头上。相比之下,许倬云学贯中西,视野要开阔许多,坚持把中国放在世界地理坐标中来定位,把中国作为东亚文明圈农耕文明的翘楚,但也把北方草原文明—从秦汉的匈奴,到南北朝的五胡,再到辽金元满,乃至西夏吐蕃—放在跟它平等的地位上来描述。《万古江河》从上古中华文明圈的形成发展,到中古时代东亚文明圈内部的重整融合,再到近古时代东亚文明圈跟其他文明圈的交流冲突,最后落到全球化的愿景,鼓吹“真正天下为公的大同境界”,虽然略嫌一厢情愿 (尤其放到出版后十六年的今天,更似乎与浩浩汤汤的反全球化浪潮格格不入),但脉络清晰,逻辑自然,跟我从小读的历史教课书比,至少是一个更客观真实的角度,如果说以史为镜,那《万古江河》应该是想要反躬自省的人更需要的那面镜子。

思想上,许倬云是比较典型的进步派(progressives),他认为中华文明源远流长,胜在兼容并蓄的普世胸怀,以仁为本的儒家理念,和推己及人的人文精神。他号召全体人类自觉合作,以市场经济和“国族范围的民主政治”为基础,纳入中国儒家理念,印度众生平等思想,以及伊斯兰对自然的尊重, 完成“人类文明另一次的重大突破”。愿景虽然鼓舞人心,但未免有理想主义过头的危险。 而钱穆无疑是保守派(conservatives)。他支持中学为体、西学为用的大方向,认为中国近代落后,除了“满洲部族横梗做病”之外,更受鸦片战争以来无间断革命之害,以至于社会动荡,民不聊生,”欧洲之科学舆机械,遂终无在中国社会保养,徐徐生长成熟之机会。”,而中国社会之所以落后,“只在科学机械方面之落后。” 钱老在民族存亡之秋撰史,又处于新旧文化交战的时代,其局限性所在难免,有“咱们无非是差在科学机械”这种本末倒置的观点,无可厚非。但到了五代之下的今天如果还抱着它不放,则非因循守旧、抱残守缺八字可以解释了。

从阅读体验来说,我觉得两本书都比较枯燥,《国史大纲》因为半文半白,更兼体例关系,正文精炼扼要而辅以大量正史原文,对我这种半吊子文言文水平的人更是煎熬。《万古江河》颇多新鲜史料(尤以在商业、工业、科学、普通人生活方面),角度也新颖有趣(比如论南北宋在东亚格局中的地位,评满清对中国现代幅员做出的巨大贡献),可惜文字平实严谨有余,而风韵魅力稍逊,也算美中不足吧。

A failure of capitalism

Richard Posner is said to be the most cited legal scholar of the twentieth century.  A Failure of Capitalism, a book published toward the end of his distinguished career, is not among the most cited of his scholarly works – not even close – but probably the most read, judged by the number of ratings on Goodreads.  “The failure” of capitalism concerned herein is the financial crisis of 2008, which triggered the Great Recession, the worst recession the world had ever seen since the legendary depression of 1929.  The book attempts to explain the causes of that crisis, who should bear the blames and what lessons we may collectively draw from the event.

Posner believes the main cause of Great Recession is the confluence of lower interest rates in 2000s and the over-deregulation of financial industry that began much earlier.  On the one hand, cheap credit encouraged the expansion of homeownership, which pushed up home price because the supply in real estate market is usually slow to catch up with demand.  Rising price convinced people that houses are good investment, thereby inducing more to dive in with money borrowed beyond their means to pay back unless home price continued to rise.  On the other hand, deregulation made it harder for traditional commercial banks to raise equity capital from demand deposit accounts, owing to the competition from investment banks and hedge funds alike. To stay in the game, therefore, banks had to rely more on borrowed short-term credit, increase their leverage (the ratio of debt to equity) and make longer term (hence riskier) loans. With the huge demand for credit fueled by the low interests of 2000s, this business model was pushed to the limit, exposing the entire industry to the risk of default in the housing market should the price begin to fall.  To mitigate these risks, banks invented complex debt securitization devices, including the infamous credit-default swaps.   In hindsight, however, these tools were not so much about reducing the risks as hiding them, unconsciously or otherwise.

Given this analysis, it is hardly surprising Posner argues the leaders at Federal Reserve and other economic agencies – Alan Greenspan and, to lesser extent, Ben Bernanke, among others – are culpable for a misconceived monetary policy and the lack of foresight for the impending crisis.  He also points fingers at the US government for its deregulation of the financial industry – driven largely by market fundamentalism – and the failure to prepare a contingence plan that would have avoided the “bumbling improvisations” in the initial response.   Posner is also dismayed at the “failure of the economics profession to have grasped the dangers”.  Many, including Robert Lucas – the most distinguished macroeconomist at the time – seemed to have been completely blindsided by the disaster.    Lucas had gone so far as to downplay the imminence of a recession as late as September 19, 2008, four days after the collapse of Lehman Brothers.     However, Posner argues his fellow academics deserve lenience for missing the warning signs that they were supposedly best poised to spot.  For one thing, they were not well equipped to “empirically test rival theories of depression” and were increasingly isolated in their own silos by ever-greater specialization. More importantly, doomsaying is a tricky and unpopular craft. As Posner points out, “Cassandras rarely receive a fair hearing”, because “it is very difficult to receive praise, and indeed to avoid criticism, for preventing a bad thing from happening unless the probability of its happening is known”.

Posner pushes back forcefully against the claim that the crisis had much to do with the stupidity or greed of bank executives and hedge fund managers.  Nor does he believe they should be held responsible for not heeding the warning signs of a gigantic bubble while taking seemingly undue risks to “ride it”.     “Riding a bubble can be rational”, Posner explains, especially when money is cheap.  More importantly, nobody really knows when a bubble, unattainably large as it might seem, will burst, and until it does one could still be making much money riding it than climbing off.   Indeed, being rational could be a losing proposition when the majority is irrational, as summarized in Keynes’ famous aphorism,

“the market can stay irrational longer than you can stay solvent”.

Posner believes the duty of mitigating systematic risks resides elsewhere (i.e., government), because

“it would make no more sense for an individual businessman to worry that because of the instability of the banking industry his decisions and those of his competitors might trigger a depression than for a lion to spare a zebra out of concern that lions are eating zebras faster than the zebras can reproduce.”

Posner writes beautifully, with a combination of clarity, precision, and elegance that few authors could match.  If one wants to learn how to explain complex concepts to a layman in an accessible but still sophisticated manner, the book will make a great tutorial. I don’t know enough about macroeconomics or finance to comment on many an opinion expressed in the book.   Truth told, the book taught me a lot about those subjects – the difference between equity and security being a memorable example. However, I do question the wisdom of writing a book about an event that had not even run its course at the writing (early 2009).   If Posner had waited a few more years, perhaps he would not insist to label the crisis as a “depression”.  He might also reconsider his derision of Feds’ low-interest policy because that policy, in a much more aggressive form, had not only survived Great Recession, but also thrived for more than a decade since.