Category: Summary or Review


I just finished the final round revision of the book and submitted it to the publisher. Thank all who have helped me along the way. Really looking forward to Glen Weyl’s book tours in China and the RadicalxChange events in Beijing later this year!

今天我终于完成了《激进市场》书稿最后一轮的审校和修改工作。感谢所有老师、朋友和各位编辑们的指导和帮助!Glen Weyl今年下半年会来中国对此书和RadicalxChange(https://radicalxchange.org/)的思想做巡回演讲,大家敬请期待!

一场波澜壮阔的思维实验——《激进市场》译者序

胡雨青

 

第一次见到E·格伦·韦尔(E. Glen Weyl)是在2017年秋季美国国家经济研究局举行的《市场设计》学术研讨会上。格伦友好地冲我打招呼说:“嗨!你好,我叫格伦。”没想到一年后,这位总是穿着V领衬衫的“大男孩”竟然出版了一本极具思考深度的书,并且在西方各大媒体引起了极大反响。《激进市场:为正义社会彻底变革资本主义与民主主义》是一本雄心勃勃的著作。青年经济学家格伦和他的法学家合作者埃里克·A·波斯纳(Eric A. Posner)带领读者领略了一场空前浩大的思维实验。

本书写作的出发点是当今世界的一系列新挑战——尽管近几十年来全球经济有所增长,国与国之间的差距有所缩小,但国家内部的不平等却在加剧,而且社会与政治的分歧与分裂也日趋严重——曾经让西方世界尤其是美国引以为豪的自由主义市场经济面临前所未有的危机。变革迫在眉睫,但眼下比中央计划经济更好的替代品又还没有出现。然而,有幸的是,今天的科技进步,尤其是在大数据背景下的机器学习和人工智能技术的迅速发展,正在悄悄地重新定义社会关系与生产关系。这在一定程度上使得在几十年前可能听起来不切实际的制度设计变得可行,当下棘手的问题在新技术的助力下,可以突破制度藩篱而有了解决方案。

本书分为五章,每一章在不同的领域提出了一种“激进”的方案。对于“激进”可以有两种理解。第一种是十九世纪亨利·乔治时代产生于英国的激进主义以及它所代表的社会变革精神。作者旨在传承并继续探究这种精神并让之在今天重焕光彩,这意味着挑战传统智慧和进行大刀阔斧的改革。第二种代表“彻底”的变革,这是因为“激进”的英文radical与 “根源”(root)同源。这意味着不能再依赖治标不治本的方法,而要透彻领悟社会运作的底层逻辑,通过变革其市场机制来解决问题,只有这样才能从根本上实现社会的持续繁荣与昌盛。

第一章是全书最出彩的部分。它证明了私有财产在本质上具有垄断性,即所有者可以持有财产而不对此加以有效利用,这也阻碍了其他能将此财产加以更有效利用的人获得该财产。但极端的公有化又会造成公地悲剧。作者提出一种新形式的产权在公有和私有间取到一个最优的折中——公有制自评税(common ownership self-assessed tax,简称COST)——来打破所有者对私有财产的垄断控制,同时克服了公有制的低效率问题——利用拍卖的形式把每一种资源都交给最能利用它并投资于它的人,从而实现资源的完全配置效率。

第二章着眼于民主,是作者近五年来主要工作成果的精华。它巧妙地提出了一种二次方投票法(quadratic voting,简称QV),让选民有效地影响对他们最重要的问题,从而克服了“一人一票”下的“多数人的暴政”等问题。在QV下,一个人对一件事如果特别在意可以考虑把更多的发言权积分花在上面,但要付出更高的代价。QV能让少数民族以一种更具影响力的方式表达自己的诉求。除此之外,作者还展示了QV在其他领域中的应用前景,例如与加密货币结合来改善商业中的评级系统。

第三章提议了一种被称之为个人VIP(Visas Between Individuals Program)项目的新移民政策,提倡任何东道国的公民在任何时候都可以担保移民,并从中得到经济收益。VIP不仅使移民和他们的雇主受益,更让每个担保移民的东道国公民受益。这种互惠的关系能够让东道主与移民建立一种积极的关系,从而从政治上缓和对移民的抵触情绪。

第四章关注的是这个时代最主要的垄断形式——投资机构的崛起。投资机构因为拥有多家公司的股权而大幅降低了市场的竞争,甚至制造出一种垄断,尤其是当一家投资机构持有同行业内多家公司的股票时。但目前的反垄断法无法遣散这种垄断力量。作者提议法律可以限制投资机构在行业内部的多样化投资,但可以鼓励在行业之间的多样化。这样的做法能将市场的自由和竞争性从投资机构的控制中解放出来。

第五章提供了一个看待数据的崭新视角。科技巨头从用户的行为中收集数据用于机器学习和人工智能的训练。作者提倡将这些数据视为一种劳动成果,将数据的产生过程视为一种有尊严的工作,并给予用户相应的补偿。在此视角下,人们都将有幸成为推动数字经济运转的数据供应商,而不是被视为数字平台提供的娱乐的被动消费者。这不仅可以建立一个更公平、平等的社会,还可以刺激技术进步和经济增长。

这五章内容相对独立,但每章都背景宏大、引人入胜。读者在阅读的过程有一点需要注意的是,包括作者自己也提到,他们在这里只是提供了一场思维实验——理论模型即使再完美无缺,要把这些激进的想法真正投入实践,还需要考虑更多的因素。例如,需要考虑COST下不稳定的所有权可能导致人们不愿意对物品进行长期投资的情况;除了金钱,文化、安全、幸福感等也是移民政策获得政治支持的重要因素;宗教、文化关怀等有时比金钱更能打动和鼓励人们工作;等等。

但总而言之,这本书非常值得一读。我鼓励所有对未来感兴趣的读者都去读一读,去感受作者细腻的人文关怀和勇敢的激进精神,站在作者的角度去想象未来的画面。因为改变和改善一个社会的,不仅是物质和金钱,也不仅仅是市场制度设计,更是一个民族的胆魄、动力和精神。

最后,感谢格伦在我翻译此书时对书中一些关键背景知识的详细解释和答疑;感谢机械工业出版社的各位工作人员尤其是顾煦副主编、贾萌和王一尘文字编辑的专业而细心的工作;感谢谭国富教授对本书初稿的审校和点评;感谢徐梦玫组织的志愿者团队(唐飞虎、冯惠利、殷越、王萱仲、余舜哲、巫文强、马聪、封雨希、康丹丹、杨山青、王燕婷、汪雪、行走的翻译C、郑捷凯、陈家鸣、姚远、李玥枫、葛如钧、马跃、唐雨萱、陈寒)辛苦而仔细的审读工作;感谢普林斯顿大学出版社的乔·杰克逊(Joe Jackson)主编、萨曼塔·纳德(Samantha Nader)、丽贝卡·本戈西亚(Rebecca Bengoechea)、金伯利·威廉姆斯(Kimberley Williams)和安德鲁·德西奥 (Andrew DeSio)等各位编辑和其他工作人员的组织和协调工作,使本书得以原版引进并顺利面市。

推荐序链接

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猪年新春快乐!:) 我翻译的《激进市场》(http://radicalmarkets.com/) 将由机械工业出版社在国内年后出版,大家敬请期待!

推荐序

王健                胡雨青

在纽约市中心,你可以在鳞次栉比的王府井大街上,随着熙熙攘攘的人流,购买到物华天宝,品尝到珍馐美味。但在不远处参差不齐的布鲁克林“黑人区”,你也能见到那些用帆布糊起来的“家”,在那摇摇欲坠的屋檐之下佝偻着衣衫褴褛的身躯,并时时传来充满埋怨而又难懂的外地话。繁华与贫困共存并非纽约独有的风景——不平等是世界的普遍现象,像约热内卢、孟买、墨西哥城,等等。

不少人把贫富差距问题归咎于市场经济,主张限制市场经济的发展。表面上看,自由市场确实往往伴随着收入和财富差距的扩大,而且愈演愈烈的贫富差距升级往往以经济危机、政治分化、社会撕裂甚至军事冲突的惨烈方式收场。上世纪三十年代的全球经济大萧条以及随后的二战和大屠杀就是血淋淋的教训。而2008年全球金融危机过后,世界政治与经济再次陷入了迷局,极端民族主义也出现了令人担忧的复兴迹象:全球经济增长停滞、不平等加剧、民粹主义兴起和精英民主衰落,正一步步把全球各国从合作共赢推向敌视和对抗。例如,美国民粹主义总统川普粉墨登场。他声称为了“让美国再次强大”,必须采用“美国优先”政策;为了让美国“更加安全”,必须在美墨边境修筑一道高墙。然而,这些举措尤其是对移民的排斥和妖魔化宣传与美国自由平等的价值观背道而驰,它们既不能“让美国再次强大”,更无法保证美国的长期安全,甚至连美国的长期盟友都纷纷指责川普政府的这些行为。

除了收入不平等带来的各种冲击,当今世界日新月异的技术进步也飞速影响着传统的社会和经济关系。例如,机器学习和人工智能正在变革社会,使得数据越来越成为一种财富;共享经济正在重新定义人与人以及人与物之间的关系。在贫富差距日益扩大的严峻形势下,面对世界高速变化带来的机遇与挑战,如何化解风险,实现全球经济持续、稳定的繁荣,成为世界诸多学者和政策制定者工作的重中之重。芝加哥大学的埃里克·A·波斯纳(Eric A. Posner)[1]教授和微软首席经济学家E·格伦·韦尔(E. Glen Weyl)[2]在《激进市场》一书中大胆尝试了创新的解决方案,并提出了颠覆传统观念却能够改善社会的操作指南。

本书的两位作者在经济、法律、公共政策和金融市场领域都建树颇丰。其中波斯纳是芝加哥大学法学院教授,美国艺术与科学学院的研究员和美国法律研究所成员。其研究领域包括宪法、金融监管、人权、国际法等。除了《激进市场》,波斯纳还著有《国际人权的曙光》,《气候变化的正义性》,《国际法的限度》,《法律和社会规范》等作品。韦尔是微软的首席经济学家,研究领域包括价格理论、市场设计、产业组织、法律经济学、公共政策等。韦尔同时还是普林斯顿大学朱丽斯-拉比诺维茨公共政策和金融中心与尼奥斯国际关系学院的客座教授,以及社会组织“激进交流”(RadicalxChange)[3]的创始人和主席。

《激进市场》主要涉及五个方面:产权、民主、移民、投资、和大数据。各章分别从不同维度解读当今社会的各种不平等的根源,并提出彻底的变革方案,尝试通过全新的市场和制度设计把经济和政治资源以更有效、更民主和更公平的方式分配给人们。其核心观点认为,当今社会包括贫富差距在内的诸多问题,并不是因为经济过度市场化造成。恰恰相反,它们往往是市场化不充分或者市场被错误利用的后果——在好的市场机制下,经济不仅能实现快速增长,社会也会变得更公平。作者向读者们展示了好的机制如何能够解放市场力量,以及它们如何能够重新唤醒沉睡在十九世纪亨利·乔治时代的自由改革精神,并带来更大的平等、繁荣与合作。

全书写作思维严谨、观念新颖而且具有启发性,让人读起来爱不释手。我们强烈推荐本书给爱好经济和社会问题的广大读者!

[1] 作者主页:http://ericposner.com/。因为其父亲是著名的大法官理査德·A·波斯纳(Richard A. Posner),埃里克·A·波斯纳又被人称为“小波斯纳”。

[2] 作者主页:http://glenweyl.com/

[3] 组织主页:https://radicalxchange.org/

译者序链接

 

Yuqing Hu, Juvenn Woo

GARP, the generalized axiom of revealed preference, is a dichotomous notion. A dataset can either satisfy the theory of a rational consumer or violate it[1]. There are several challenges in testing GARP consistency in an experiment. One challenge comes from the nature of budget sets, as there are more individual-level variations in expenditure than variations in prices. This causes the overlap of two budget sets, upon which the test based could bias towards the satisfaction of GARP, with the extreme case that no violation would occur if the budget sets are nested. Another challenge stems from lack of identities of consumers such that individuals have to be treated as the same for revealed preference tests (Chambers & Echenique, 2016).

 

A few indices have been invented to measure the degree of GARP violations. One is Afriat’s efficiency index (AEI) (Afriat, 1967), which uses the degree of “deflation” of expenditure that is needed to make GARP consistent. Other variations of AEI are Varian’s efficiency index (VEI) (Varian, 1983), and the money pump index (MPI) (Echenique, Lee, & Shum, 2011).

 

There is a modest amount of literature in experimental economics that test GARP consistency, which is summarized below.

 

Battalio et al.(1973) pioneered applying GARP consistency in experimental study. They ran field experiments among psychotic patients to let them exchange tokens for different consumption goods. They induced a variety of different budget sets by changing the value of tokens, and they found that if small measurement errors were allowed, then almost all patients’ behavior was consistent with GARP.

 

Sippel (1997) ran lab experiments in which 42 students were asked to repeatedly choose a bundle of priced entertaining items under different standard budget constraints. Individuals were paid in consumption goods, and were required to actually consume the goods at the experiment. The experiment showed 63% of subjects made choices violating GARP, though the median number of violations over all subjects was only 1 of 45 choices. The number did not change even if the study perturbed demand close to actual demand. Even though the (remarkably) low number of violations for individual indicates the subjects were highly motivated when making choices, a majority of subjects could not be classified as rational in the sense of utility maximization.

 

Harbaugh, Krause and Berry (2001) examined the development of choice behavior for kids. The study conducted simple choice experiments over cohorts of second graders, sixth graders, and undergraduates. They measured and compared number of GARP violations. It found out that for the particular test, about 25% of 7-year-olds, and 60% of 11-year-olds were making choices consistent with GARP respectively, and there is no increase in consistency from 11 to 21-year old. They also found that violations of GARP are not significantly correlated with the results of a test that measures mathematical ability in children.

 

Andreoni and Miller (2002) ran dictator-game experiments to test whether the observed altruistic behavior is utility-maximizing. They found that 98% of subjects make choices that are consistent with utility maximization. Andreoni and Miller went further than most revealed-preference exercises in estimating a parametric function of a utility function accounting for subject’s choices (about half the subjects can be classified as using a linear, CES (constant elasticity of substitution), or Leontief utility).

 

Hammond and Traub (2012) designed a three-stage experiment, where participant advances to next stage of test only if he or she made GARP consistent choices at current one. It had been conducted over 41 (non-economics) undergraduates. The study found that, at the 10% significance level, only 22% of subjects (compared to 6.7% of simulated random choice-maker) passed second-stage tests, and 19.5% passed all three stage tests. The result reinforced Sippel’s study suggesting that human is generally not perfectly rational. It should be noted though conditional on passing second-stage rationality, 62.5% of subjects passed third-stage tests.

 

Choi, Kariv, Müller and Silverman (2014) conducted with CentERpanel survey a comprehensive study on rationality. Measuring GARP consistency by Afriat Critical Cost Efficiency Index (CCEI) and correlation with socio-economic factors, it found that: on average, younger subjects are more consistent than older, men more than women, high-education more than low-education, and high-income subjects more consistent than low-income.

 

Brocas, Carillo, Combs and Kodaverdian (2016) studied choice behaviors in cohorts of young and older adults, varying choice tasks from simple domain to complex domain. They showed that while both young and older adults are about equally well consistent in simple domain, older ones were observed being significantly more inconsistent in complex tasks. Beyond that, by performing working memory and fluid intelligence (IQ) test, further correlation examinations reveal that older adults’ inconsistency in complex domain can be attributed to decline in working memory and fluid intelligence.

[1] One can, however, evaluate the degree of violations.

 

Reference:

 

Afriat, S. N. (1967). The Construction of Utility Functions from Expenditure Data. International Economic Review, 8(1), 67–77.

Andreoni, J., & Miller, J. (2002). Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism. Econometrica, 70(2), 737–753.

Battalio, R. C., Kagel, J. H., Winkler, R. C., Edwin B. Fisher, J., Basmann, R. L., & Krasner, L. (1973). A Test of Consumer Demand Theory Using Observations of Individual Consumer Purchases. Western Economic Journal, XI(4), 411–428.

Brocas, I., Carillo, J. D., Combs, T. D., & Kodaverdian, N. (2016). Consistency in Simple vs. Complex Choices over the Life Cycle.

Chambers, C. P., & Echenique, F. (2016). Revealed Preference Theory. Cambridge University Press.

Choi, S., Kariv, S., Müller, W., & Silverman, D. (2014). Who Is (More) Rational? The American Economic Review, 104(6), 1518–1550.

Echenique, F., Lee, S., & Shum, M. (2011). The Money Pump as a Measure of Revealed Preference Violations. Journal of Political Economy, 119(6), 1201–1223.

Grether, D. M., & Plott, C. R. (1979). Economic Theory of Choice and the Preference Reversal Phenomenon. The American Economic Review, 69(4), 623–638.

Hammond, P., & Traub, S. (2012). A Three-Stage Experimental Test of Revealed Preference.

Harbaugh, W. T., Krause, K., & Berry, T. R. (2001). GARP for Kids: On the Development of Rational Choice Behavior. American Economic Review, 91(5), 1539–1545. http://doi.org/10.1257/aer.91.5.1539

Sippel, R. (1997). An Experiment on the Pure Theory of Consumer’s Behaviour. The Economic Journal, 107(444), 1431–1444. http://doi.org/Doi 10.1111/1468-0297.00231

Varian, H. R. (1983). Non-Parametric Tests of Consumer Behaviour. The Review of Economic Studies, 50(1), 99–110. http://doi.org/10.1007/sl0869-007-9037-x

 

 

Lemma: Let \mu be any individually rational matching with respect to strict preferences P and let M' be all men who prefer \mu to \mu_M. If M' is nonempty, there is a pair (m, w) that blocks \mu such that m is in M-M' and w is in \mu(M').

Proof. 

Case 1: \mu(M')\not=\mu_M(M'), i.e. the set of men who prefer \mu to \mu_M are matched to different sets of women under the matching rules \mu and \mu_M.

Pick any w\in\mu(M')-\mu_M(M'). Note that \mu(M')\not\subset\mu_M(M') in this case because it’s a one-to-one matching.

Denote m'=\mu(w), and m=\mu_M(w), so m'\in M', and m\not\in M'. This implies that w\succ \mu_M(m) and w\succ_m\mu(m).

Note that m\succ_w m', otherwise (m', m) will block \mu_M, contradicting to that \mu_M is stable.

Therefore, (m, w) blocks \mu such that w\in\mu(M') and $m\in M-M’$.

 

Case 2:\mu(M')=\mu_M(M'), i.e. the set of men who prefer \mu to \mu_M are matched to the same set of women under the matching rules \mu and \mu_M.

Let w be the last woman in W' to receive a proposal from an acceptable member of M' in the deferred acceptance. Denote this man by m'. So there are two possibilities: 1) w has not been proposed before, and \mu_M(m')=w; 2) w is already engaged with some other man m, and she rejects m and accepts m'.

1) is not possible: If it were true, then since w\in W', there must be some m'\in M such that \mu(m')=w\succ_{m'}\mu_M(m). That means when we run the deferred-acceptance algorithm to implement \mu_M, m' has already proposed to w and got rejected, contradicting that w has not been proposed.

2) i. m\not\in M', otherwise m will propose to another woman, contradicting that w is the last woman in W' to receive a proposal. Therefore w\succ_m\mu_M(m). And since m\not\in M', that means \mu_M(m)\succ_m\mu(m). This implies w\succ_m\mu(m).

ii. Since w is the last woman to receive the proposal, it must be that before w rejects m, she must have rejected \mu(w), i.e. her mate under \mu. That means m\succ_w\mu(m).

Combine i. and ii., we conclude that (m, w) blocks \mu.

Q.E.D.

Alternative proof: 

Case 1: The same as above.

Case 2\mu(M')=\mu_M(M').

Define the new market (M', W', P'). P'(m) is the same as P(m) restricted to W'\cup\{m\}, and P'(w) is the same as P(w) restricted to M'\cup\{w\}, \forall m\in M', w\in W'.

Note that \forall m\in M', w\in W', we must have \mu(m)\succ_m\mu_M(m) and \mu_M(m)\succ_w\mu(w), otherwise \mu_M would be blocked. We can write this as:

\mu_M\succ_{W'}\succ\mu

and

\mu\succ_{M'}\succ\mu_M.

So that means under P', w' is now ranked just below \mu(w), and m is now ranked just below \mu_M(m).

In other words, the only men in M' who are unacceptable to w are those m such that m\succeq_w \mu(w), so \mu_M(w) is acceptable to w under P' for all w\in W'.

Note that \mu_M restricted to M'\cup W' is still stable for (M', W, P'), because any pair that blocks \mu_M under P' would also block it under P.

Let \mu_M' be the M'-optimal matching for (M', W', P'), then by Pareto-optimality Theorem, it must be that

(*) \mu_M'\succ_{M'}.

Otherwise, if \mu_M=\mu_M', then it would be contradicting \mu\succ_{M'}\succ\mu_{M'}.

Furthermore, \mu_{M'}\succeq_{W'}\mu by the construction of P'.

Define \mu' on M\cup W by \mu'=\mu_{M'} on M'\cup W', and $latex\mu’=\mu_M$ on (M'-M)\cup (W'-W).

Combine it with (*), we have \mu'\succ_M\mu_M. \mu' is not stable for (M,W, P), so let \{m, w\} be a blocking pair.

i). If \{m, w\} in M'\cup W', m and w would be mutually acceptable under P', by construction of P', and so \{m, w\} would block \mu_M'. Also note that

then

w=\mu'(m)=\mu_{M'}(m)\succ_m\succ\mu_M(m)

and

\mu_{M'}(w)=\mu'(w)=m\succ_w\mu(w).

So \{m, w\} does not block \mu'.

ii). If m\in M', and m\in W-W', then

w=\mu'(m)=\mu'_M(m)\succ_m\succ\mu_M(m)

and

\mu(w)\succ_w\mu_M(w)=\mu'(w)=m.

\{m, w\} blocks \mu_M, but it does not block \mu'.

iii). If m\in M-M', w\in W-W', then

w=\mu'(m)=\mu_M(m)\succ_m\mu(m)

and

\mu(w)\succ_w\mu_M(w)=\mu'(w)=m.

So \{m, w\} does not block \mu'.

iv). If m\in M-M', w\in W', then

w=\mu'(m)=\mu_M(m)\succ_m\mu(m)

and

\mu_{M'}(w)=\mu'(w)=m\succ_w\mu(w).

So \{m, w\} does blocks \mu'. It’s the desired blocking pair.

Q.E.D.

 

 

References:

Gale, D., & Sotomayor, M. (1985). Some Remarks on the Stable Matching. Discrete Applied Mathematics, 11, 223–232.

Roth, A. E., & Sotomayor, M. (1990). Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis. Cambridge University Press.

by Calvin Leather, Yuqing Hu

In response to this article: http://www.jneurosci.org/content/36/39/10016

Recent literature in reinforcement learning has demonstrated that the context in which a decision is made influences subject reports and neural correlates of perceived reward. For example, consider visiting a restaurant where have previously had many excellent meals. Expecting another excellent meal, when you receive a merely satisfactory meal, your subjective experience is negative. Had you received this objectively decent meal elsewhere, without the positive expectations, your experience would have been better. This intuition is captured in adaptive models of value, where a stimuli’s reward (i.e. Q-value) is expressed as being relative to the expected reward in a situation, and it has been found that this accurately models activation in value regions (Palminteri et al 2015). Such a model also can be beneficial as it allows reinforcement learning models to learn to avoid punishment, as avoiding a contextually-expected negative payoff results in a positive reward. This had previously been challenging to express within the same framework as reinforcement learning models (Kim et al, 2006).

Alongside these benefits, there has been concern that adaptive models might be confused by certain choice settings. In particular, agents with an adaptive model of value would have an identical hedonic experience (i.e. Q-values in the model) when receiving a reward of +10 units, in a setting where they might receive either +10 or 0 units, and a reward of 0 units, in a setting where they might receive either -10 or 0 units (we will refer to this later as the ‘confusing situation’). With this issue in mind, Burke et. al. (2016) develop an extension to the adaptive model, where contextual information only has a partial influence on reward. So, whereas the previous, fully-adaptive model has a subjective reward (Q-value) of +5 units for receiving an objective reward of 0 in the context where the possibilities were 0 and -10, and an absolute model ignoring context would experience a reward of 0, the Burke model would experience a reward of +2.5. It takes the context into account, but only partially, and accordingly they call their model ‘partially-adaptive’. Burke et. al. compare this partially-adaptive model with a fully-adaptive model, and an absolute model (which ignores context). When subjects were given the same contexts and choices as the confusing situation outlined above, Burke et. al. found that the partially-adaptive model reflects neural data in the vmPFC and striatum better than the fully-adaptive or absolute models.

The partially-adaptive model is interesting, as it has the same advantages as the fully-adaptive model (reflecting subjective experience and neural data well, allowing for avoidance learning), while potentially avoiding the confusion outlined above. Here, we seek to investigate the implications and benefits of Burke et. al.’s partially-adaptive model more thoroughly. In particular, we will consider the confusion situation’s ecological validity and potential resolution, whether it is reasonable that partially-adaptive representations might extend beyond decision (to learning and memory), and the implications of the theory for future work. Before we do this we would like to briefly present an alternative interpretation of their findings.

The finding that the fMRI signal is best classified by a partially-adaptive model does not necessarily entail the brain utilizing a partially-adaptive encoding as the value over which decisions occur. All neurons within a voxel can influence the fMRI signal, so it is possible that the signal may reflect a combination of multiple activity patterns present within a voxel. This mixing phenomenon has been used to explain the success of decoding early visual cortex, where the overall fMRI signal in a voxel reflects the specific distribution of orientation-specific columns within a voxel (Swisher, 2010). Similarly, the partially-adaptive model’s fit might be explained by the average contribution of some cells with a full-adaptive encoding, and other cells with absolute encodings of value (within biological constraints). This concern is supported by the co-occurrence of adaptive and non-adaptive cells in macaque OFC (Kobayashi, 2010). Therefore, more work is needed to understand the local circuitry and encoding heterogeneity of regions supporting value-based decision making.

Returning to the theory presented by the authors, we would like to consider whether a fully-adaptive encoding of value is truly suboptimal. The type of confusing situation presented above was shown to be problematic for real decision makers in Pompilio and Kacelnik (2010), where starlings became indifferent between two options with different objective values, due to the contexts those options appeared in during training. However, this type of choice context might not be ecologically valid. If two stimuli are exclusively evaluated within different contexts, as in Pompilio and Kacelnik, it is not relevant whether they are confusable, as the decision maker would never need to compare them.

Separate from the confusion problem’s ecological validity is the inquiry into its solution. Burke et. al. suggest partially-adaptive encoding avoids confusion, and therefore should be preferred to a fully-adaptive encoding. However, this might only be true for the particular payoffs used in the experiment. Consider a decision maker who makes choices in two contexts. One, the loss context, has two outcomes, L0 (worth 0), and Lneg (worth less than 0), while the other, the gain context, has two outcomes, G0 (worth 0), and Gpos (worth more than 0). If L0-Lneg = Gpos– G0, as in Burke et. al., a fully-adaptive agent would be indifferent between G0 and Lneg (and between Gpos and L0). A partially-adaptive agent, however, would not be indifferent, as the value of G0 would be higher than Lneg.   Now consider what happens if we raise the value the value of Gpos. By doing this, we can raise the average value of the gain context by any amount. Now consider what this does the experienced value (Q-value) of G0. As we increase the average reward of the context, G0 becomes a poorer option in terms of its Q-value. Note that since the only reward we are changing is Gpos, the Q-values for the loss context do not change. Therefore, we can decrease the Q-value for G0 until it is equal to that of Lneg. This is exactly the confusion that we had hoped the partially-adaptive model would avoid. Furthermore, this argument will work for any partially-adaptive model: we are unable to defeat this concern by parameterizing the influence of context in the update equations, and manipulating this parameter.

As mentioned earlier, it is possible that some cells might encode partially-adaptive value, while others might have a fully- or non-adaptive encoding. We should be open to the possibility that even if partially-adaptive value occurs in decision, non-adaptive encodings might be used for storage of value information, and are transformed at the time of decision into the observed partially-adaptive signals. Why might this be reasonable? An agent who maintains partially-adaptive representations in memory faces several computational issues. One is efficiency: storage requirements for a partially-adaptive representation requires S*C quantities or distributions to be stored (one for each of the S stimuli in each of the C contexts). On the other hand, consider an agent who stores non-adaptive stimulus values and the average value of each context, and then adjusts stimulus values using the context values at the time of decision. They could utilize the same information, but only store S+C quantities. Another problem with storage of value information in an adaptive format is the transfer of learning across contexts. If I encounter a stimulus in context A, my experiences should alter my evaluation of that stimulus in context B: getting sick after eating a food should reduce my preference for that food in every context. An agent who stores value adaptively would need to update one quantity for the encountered stimulus in each context, namely C quantities. An agent who stores value non-adaptively only updates a single quantity. So, even if decision utilizes partially-adaptive encoding, non-adaptive representation is most efficient for storage. Furthermore, non-adaptive information is present in the state of the world (e.g. concentration of sucrose in a juice does not adapt to expectations), so this information is available to agents during learning. Accordingly, it must be asked why agents would discard information that might ease learning. While these differences do not necessarily affect the authors’ claims about value during decision, they should be considered when investigating the merits of different models of value.

In sum, while partial adaption is an exciting theory that may provide novel motivations for empirical work, more effort is needed to understand when and where it is optimal. If we can overcome these concerns, the new theory opens up potential investigation into the nature of contextual influence: if we allow a range of contextual influence (via a parameter) in the partially-adaptive model, do certain individuals have more contextual influence, and does this heterogeneity correlate with learning performance? Do different environments (e.g. noise in signals conveying the context) alter the parameter? Do different cells or regions respond with different amounts of contextual influence? As such, the theory opens up new experimental hypotheses that might allow us to better understand how the brain incorporates context in the learning and decision-making processes.

 

 

References

 

Burke, C. J., Baddeley, X. M., Tobler, X. P. N., & Schultz, X. W. (2016). Partial Adaptation of Obtained and Observed Value Signals Preserves Information about Gains and Losses. Journal of Neuroscience, 36(39), 10016–10025. doi:10.1523/JNEUROSCI.0487-16.2016

Kim, H., Shimojo, S., & Doherty, J. P. O. (2006). Is Avoiding an Aversive Outcome Rewarding ? Neural Substrates of Avoidance Learning in the Human Brain. PLoS Biology, 4(8), 1453–1461. doi:10.1371/journal.pbio.0040233

Kobayashi, S., Carvalho, O. P. De, & Schultz, W. (2010). Adaptation of Reward Sensitivity in Orbitofrontal Neurons. Journal of Neuroscience, 30(2), 534–544. doi:10.1523/JNEUROSCI.4009-09.2010

Palminteri, S., Khamassi, M., Joffily, M., & Coricelli, G. (2015). Contextual modulation of value signals in reward and punishment learning. Nature Communications, 6, 1–14. doi:10.1038/ncomms9096

Pompilio, L., & Kacelnik, A. (2010). Context-dependent utility overrides absolute memory as a determinant of choice. PNAS, 107(1), 508–512. doi:10.1073/pnas.0907250107

Swisher, J. D., Gatenby, J. C., Gore, J. C., Wolfe, B. A., Moon, H., Kim, S., & Tong, F. (2010). Multiscale pattern analysis of orientation-selective activity in the primary visual cortex. Journal of Neuroscience, 30(1), 325–330. doi:10.1523/JNEUROSCI.4811-09.2010.Multiscale

The original paper: download

Summary for each part:

I: The mathematical solution to constructing a rational economic order is to achieve the same marginal rates of substitution between any two goods. This is not realistic, because it relies on the assumption of complete command of knowledge in a central single mind, while in the real society the knowledge is dispersed among separate individuals. This causes misconception about the nature of economic problem, which is essentially how to efficiently allocate resources by utilizing individual knowledge, rather than utilizing it in its integrated form.

 

II: Utilizing knowledge, which involves communicating it to the planner and among different individuals, is important in designing an efficient economic system, which can be in the form of central planning, completion and monopoly. Which kind of the economic systems is more efficient depends on whether the existing knowledge can be fuller used.

 

III: Different kinds of knowledge define different positions of the economic systems. The prominent position of central planning in public imagination is due to the exaggeration of the importance of scientific knowledge. Selecting a group of experts to command such knowledge is actually only a fraction of the wider problem. The knowledge of the particular circumstances, which is not always available, is equivalently socially useful, although it is sometimes regarded as disreputable if one gains advantage by using this knowledge.

 

IV: Economic problems arise as a result of change of circumstances, making the knowledge of the particular place and time important in making economic decisions. This sort of knowledge, however, cannot be statistically calculated therefore cannot be conveyed to the central authority who make plans based on statistical information.

 

V: Decentralization is necessary in solving economic problems, because adaptions to changes in economic systems require the knowledge of the particular circumstances to be promptly used. A price system helps coordinate separate actions for individuals whose visions in their own fields sufficiently overlap through intermediaries, thus brings about the outcome that might have been achieved by central planning with complete information.

 

VI: The price system acts as a mechanism that communicates only the most essential information for individuals to take the right action, and it extends the span of resources utilization beyond the control of any single mind. Like language, this is one of the formations upon which the foundation of civilization is built.

 

VII: The dispute about the indispensability of price system is not purely a political dissent, but also intellectual and methodological differences. Schumpeter’s argument that valuation of factors of production is implied in the valuation of consumers’ goods is untrue, because it also depends on the supply of the factors. His argument disregards the essential fact of imperfection of knowledge in the real world. Thus the solution to the economic problem has to be processed by interactions of people who possess their partial knowledge.

 

In sum, the key take-away ideas are:

 

In the real world, knowledge is spread throughout the society. The knowledge of particular circumstances of place and time is not always public available, but it is useful in making economic decisions. This is an essential feature of the real world’s economic problem, which makes central planning inefficient and infeasible. That’s because central planning requires a single mind processing all the knowledge. Decentralization overcomes this problem via a price system in which individuals with their own partial knowledge coordinate with each other and utilize resources that are beyond the control of any one person.

I wrote this article to introduce the contributions of Alvin Roth, Atila Abdulkadiroglu, Parag Pathak and Tayfun Sönmez to public school choice in the U.S.

 

Here is the link: http://paper.nandu.com/nis/201501/08/314808.html

 

家长们,你们选对学校了吗?

 

胡雨青 经济学硕士  目前在世界银行任职

王健 经济学博士  美联储达拉斯联邦储备银行  高级经济学家兼政策顾问

仅代表个人观点,和任职单位无关)

 

每年一到高考季,选校和填报志愿愁煞不少家长。如何选择志愿?按照什么顺序填报志愿才最稳妥最恰当?各种志愿填报咨询会总是座无虚席;“一对一”高考志愿咨询服务虽然收费昂贵,家长对之仍然趋之若鹜。的确,一所好的学校在孩子的成长道路上起到极其重要的作用。但选校和填报志愿这一过程又复杂又繁琐,家长往往怕报高了录不上,报低了错过更好学校又不甘心。尤其是生活中“高分低就”和“低分高就”的现象并不少见,就更令很多家长和学生们担忧和困惑。

其实,不仅仅在中国,美国的家长们也面临同样的选校和填报志愿难题。每年10-12月是美国初中毕业生申请高中,填报志愿的高峰时期,子女报志愿问题也让很多美国家长​焦头烂额。可喜的是,这样的难题在纽约、波士顿等城市目前已经有了一个简单而且高效的解决途径。比如在纽约这座具有全美最多公立学校的城市,今年426所公立高中统一招生中,有超过75万的学生在申请系统里提交自己的志愿表。申请截止日仅仅过了几个小时,对学生和学校配对的电脑程序就产生了一个近乎完美的录取结果,最大程度地保障了学生被自己心仪的学校录取,避免高分低就的情况。

但在10多年前,配对情况并没有那么公平有效。很多中学生没有被任何一所想去的学校录取,而是通过补录去了一所其他的学校。这类补录的学校往往存在各种不足,比如整体教学质量不高,设备不齐全,或者生源不好等等。为了降低这种补录的风险,学生们在填报志愿时往往不敢完全按照自己的真实偏好填写。尤其是当被最心仪学校录取的概率不是那么大的时候,他们不敢把这所学校排在志愿表的第一位,因为如果没有被这所学校录取,他们也很可能同时失去了被第二、第三志愿学校录取的机会。

后来是什么样的机制克服了这种录取过程中的缺陷呢?10年前,几位博弈论经济学家包括阿尔文.罗斯 (Alvin Roth), 阿迪拉. 阿布杜卡迪罗古路 (Atila Abdulkadiroglu),帕拉戈.帕沙克 (Parag Pathak)和塔伊丰.森梅兹 (Tayfun Sönmez) 对择校机制进行了研究,并提出了改进的方法。他们的方法基于一种由大卫.盖尔 (David Gale)和劳埃德.沙普利(Lloyd Shapley)在1962年首创的延迟接受算法 (Gale-Shapley Deferred Acceptance Algorithm)。学生于是再也不需要担心自己不被第一志愿录取而丧失其他学校的录取机会,同时学校也不必担心错失优秀学生的情况。这种贡献在一定程度上帮助了罗斯和沙普利获得了2012年的诺贝尔经济学奖。

改革前:波士顿机制

虽然同样的机制长期以来在美国公立学校的录取过程中被广泛采用,由于罗斯等人最早是对波士顿地区进行研究,因此他们把这种机制命名为“波士顿机制”(Boston Mechanism)。波士顿机制的配对规则是这样的:

第​一​轮:学校只考虑第一志愿的学生,根据成绩等优先条件(priority) 给申请学生排序,然后按照排名从前往后依次录取,直到学校名额被录满;如果学校的录取名额大于第一志愿学生的总人数,

​那么​所有学生都被录取,学校再考虑第二志愿的申请人。这种录取结果将是最终结果:已被录取的学生不再进入下一轮录取,也就是说没有机会再被调到其他学校了。学生在一所学校的优先权由各种因素决定,主要因素包括学业成绩、家庭住址所在的学区和是否有兄弟姐妹在同一所学校就读。

在第一轮中没有被录取的学生进入第二轮。​

第​二​轮:进入第二轮的​学生的名单发往第二志愿的学校。如果这些​学校在第一轮已经录满,则这些学生的申请只能等到第三轮。否则这些学校会考虑这些学生并且依次录取​,录取过程跟第一轮一样;没有被录取的学生进入第三轮,他们的名单被送往第三志愿的学校。

这个过程依次类推,直到所有学校的名额都录满,或者所有学生都被录取。

波士顿机制存在一个严重的不足:如果一个学生在第一​轮没被第一志愿的学校录取,而且他申请的其他志愿的的学校在第一轮中就已经录满,那么这个学生即使成绩远超过第二和第三志愿的要求,也无法被这些学校录取了。这种风险导致很多学生不敢把他们最喜欢的学校列在申请第一位,而更保守地把他们有更大录取概率的学校列在第一位。这种志愿和真实偏好不一致的现象,在博弈论中被称为“非抗操控性”(non strategy-proof)。

波士顿机制第二个不足是学生和学校的配对结果不是稳定和有效率的。虽然有些学生因为把学校设成了第一志愿而在第一轮中就被录取,但该校可能更加偏好其他学生,只是由于这些学生没有敢把该校列为第一志愿,学校没有办法录取这些学生。与此同时,有些学生即使把该校列为了第一志愿而被录取,但他们其实更加喜欢其他的学校。这种情况对学生和学校而言,都是不公平和低效率的。

改革后:延迟接受算法

2003年,纽约率先对公立学校的录取机制进行了改革,随后波士顿、华盛顿、芝加哥等城市也进行了类似的改革。新的录取机制实现了最优的匹配结果,学生们不必担心志愿填报方法不当而不被录取,学校也不必担心无法录取到和他们层次和质量相匹配的学生了。改良后的录取步骤是这样的:

第一​轮:学校先考虑把它们列为第一志愿的学生,根据优先条件给学生们排序,选择排名靠前的学生依次进行“预录取”,直到名额被录满。这种录取被称为“预录取”是因为它并非最终结果,在随后几轮中还可能被调整。在第一轮录取中没有被录上的学生进入下一轮。

第二​轮:在第​一​轮中没有被录取的学生名单送往他们第二志愿的学校。这些学校把新收到的申请和它们已经“预录取”的学生放一起重新按照学生的优先权进行排序,而不考虑这些学生把它们列为第几志愿。按照优先权依次录取后,没有被录上的学生进入第三​轮。这种情况下,有些进入下一轮的学生可能是在第一​
轮中被预录取,但在第二​轮中被淘汰的,也有的是在前面两轮中都没有被录取的。

这种录取过程一直持续到所有学生都被录取,或者所有学校的名额都被录满,所有“预录取”的学生在最后一轮中被正式录取​,此时的录取才是最终结果​。正是因为这种正式录取被延迟到最后一轮的特点,这种算法被经济学家命名为“盖尔-沙普利-延迟接受算法” (Gale-Shapley Deferred Acceptance Algorithm)。

这种算法产生的结果是稳定和抗操控性的,因为不再存在学校错失了具有更高优先权的学生而录取了低优先权的学生的情况,同时学生也是在所有能录取他们的学校中被自己排在志愿表最前面的那个学校录取。产生这种结果的原因是在每一轮中,学校是把所有学生进行比较,而不是把他们的志愿作为首要考虑因素;​而且​
在每一轮的比较中,学生的名单发往哪所学校是按照他们的志愿先后进行的​,这就保证了学生们能先被自己喜欢的学校考虑,然后再被其次的学校考虑​。

这项改革在美国取得了显著成效。在纽约实行改革的第一年(2004年),没有被自己志愿表上的学校录取的学生从2003年的3.1万下降到了2004年的3千。

中国高考:从“顺序志愿”到“平行志愿”

中国高考近十年来很多省份在填报志愿的制度上也在进行改革,逐步由“顺序志愿”改到“平行志愿”。 从2003年由湖南省率先实施,到目前为止已经有包括江苏、上海、新疆等28个省市自治区实行了“平行志愿” 。在机制上,顺序志愿本质上是波士顿机制,平行志愿本质上是延迟接受算法,学生的成绩决定了他们录取过程中的“优先权”。平行志愿很大程度上减少了“高分低就”或“低分高就”的不公平现象。比如,今年是北京实行平行志愿的第一个年份,一批第一志愿满足率高达97%,较往年大幅提升 。

一年一度的高考牵动无数中国父母的心,家长为自己孩子学习成绩操心的同时,还要不得不为报志愿耗费精力。从上面的介绍知道,通过一些简单的制度改进,不仅可以解决家长的后顾之忧,还让整个录取过程更加高效和公平。目前仍然实行顺序志愿的省份(比如甘肃和青海),应该尽快考虑推行平行志愿的录取方式,解决“高分低就”的问题,帮助父母减少一件烦心事。

目前中国的教育体系仍然存在其他一些问题,比如各地区间录取标准不同,造成一些省份的考生比其他地区考生要高出几百分才能被同样大学录取。这些政策严重妨碍了教育资源的公平和有效配置。另外,最近提倡的自主招生和素质教育虽然在一定程度上减轻了对分数的过分重视问题,但也加剧了地区间教育机会的不平等。经济发达地区的考生拥有更好的教育资源,不仅容易在高考中取得好成绩,也更加容易通过自主招生进入重点大学,排挤了欠发达地区考生受教育的机会。

 

参考资料:

Abdulkadiroglu, A., & Sonmez, T. (2003). School Choice: A Mechanism Design Approach. American Economic Review, 93(3), 729–747. Retrieved from http://www.jstor.org/stable/10.2307/3132114

Abdulkadiroglu, A., Pathak, P. A., & Roth, A. E. (2005). The New York city high school match. American Economic Review, 95(2), 364–367. Retrieved from http://www.jstor.org/stable/10.2307/4132848

新浪教育. (2014)“北京首次平行志愿,高考呈现四大特点”. Retrieved from http://edu.sina.com.cn/gaokao/2014-09-10/1721433217.shtml

Tullis. T. (2014) How Game Theory Helped Improve New York City’s High School Application Process. Retrieved fromhttp://www.nytimes.com/2014/12/07/nyregion/how-game-theory-helped-improve-new-york-city-high-school-application-process.html?_r=0

 

In this review report, I will summarize Neal and Schanzenbach’s paper based on my presentation on April 18, and I will highlight some points that we discussed in class. My review proceeds according to the following outline:

  1. Research Question and Main Results
  2. Literature and Contribution of this Paper
  3. Theoretical Model
  4. Research Context and Data
  5. Empirical Strategy
  6. Result Summary
  7. Policy Implications

Slides: Left Behind by Design

Written Review: Written Review-Neal and Schanzenbach 2010 Left Behind by Desigh

In this review report, I will summarize Jepsen and Rivikin’s paper based on my presentation on February 7, and I will highlight some of the points based on the comments made in our discussion. My review proceeds according to the following outline:

  1. Background and motivation
  2. Research question and main results
  3. Relation with literature
  4. Empirical model
  5. Data and descriptive results
  6. Analytical results
  7. Conclusion and policy implications

Slides here;

Review on Jepsen and Rivikin;

Our group’s presentation on Wednesday for Econ 206.

Notes Click Here   Paper Click Here

Background:

Akerlof explains his motivation for writing “The Market for Lemons” by arguing that microeconomic theory models in the 1960s were characterized by their generic nature{they dealt with perfect competition and general equilibrium. Situational and speci c considerations were left out (such as information asymmetries). By the 1990s more speci c theory models be came important. Now, economic models are custom, describing important features of observed situations. Since “lemons” exempli ed this new style, it was an integral part in the transformation of how theory was presented and discussed.

Akerlof notes that investigations of the car market were driven by his interest in macroeconmic issues such as the business cycle and unemployment. He wanted to know what caused the business cycle{noting that at the time this was related to the signi cant variation in new automobile sales. He wondered why this uctuation existed for new cars, and attempted to understand why people bought new cars, rather than renting or buying used ones. Akerlof noticed that the presence of information asymmetries served as an explanation as to why people preferred to purchase new cars rather than used cars” noting “their suspicion of the motives of the sellers of used cars.”

Extensions of this paper can be made to virtually any situation in which asymmetric information exists. This can happen in any market where the true quality of goods is dicult to perceive. This paper uses the auto mobile market as an explanatory example. But the explanatory capacity of the Lemon Principle are enormous.

Ironically, this theory was rejected on multiple accounts. According to Akerlof himself: “By June of 1967 the paper was ready and I sent it to the American Economic Review for publication…Fairly shortly…I received my first rejection letter from the American Economic Review. The editor explained that the Review did not publish papers on subjects of such triviality….Michael Farrell, an editor of the Review of Economic Studies, … had urged me to submit Lemons to the Review, but he had also been quite explicit in giving no guarantees. I submitted Lemons there, which was again rejected on the grounds that the Review did not publish papers on topics of such triviality. The next rejection was more interesting. I sent Lemons to the Journal of Political Economy, which sent me two referee reports, carefully argued as to why I was incorrect. After all, eggs of di fferent grades were sorted and sold (I do not believe that this is just my memory confusing it with my original perception of the egg-grader model), as were other agricultural commodities. If this paper was correct, then no goods could be traded (an exaggeration of the claims of the paper). Besides – and this was the killer – if this paper was correct, economics would be di fferent.”