## Category: Interdisciplinary

2月3日晚，我在BlockMania第47期直播间为大家做关于“激进市场与慈善”的分享。这次分享主要聊了三点：

1、商业到底是不是最大的慈善？

2、QF如何能够激进地改进当今的慈善事业？

3、传统商业与激进慈善如何结合

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QV的一个衍生是Quadratic Funding (QF)，也是我们今天重点要讨论的与慈善基金如何分配的市场设计。这个词来源自Vitalik Buterin, Zoe Hitzig和Glen Weyl的一篇较新的论文: https://pubsonline.informs.org/doi/10.1287/mnsc.2019.3337

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1.     《激进市场》对于一般读者难度偏高，很多人觉得晦涩难懂。我们需要把书中的观点结合中国实际进行进一步细化和通俗化解读，让更多人能够读懂这本书。
2. 除了《激进市场》，目前相关领域的研究进展也很迅速，我们需要有人专门去跟进这方面的研究，才能赶上这个快速发展的世界的步伐。我们需要专业的翻译、编辑、研究人员等等。
4. 以《激进市场》为链接点，我们可以链接到各行各业不同领域的人，有政府工作者、有企业家，学者和学生，还有明星和艺术家等。他们都有慈善和关注社会变革的美好发心，所以我们想花一些力气把我们的读者社群管理好、服务好，向大家提供一个思想能互相交流碰撞、各种资源互相链接的好的社会公共物品。
7. 除去日常运营费用，如果还有多余的资金，我们会建立自己的慈善基金，利用二次方匹配法去资助需要帮助的人和公益项目。

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## Job Opening at MetLife: I am looking for business partners 寻找事业合作伙伴（本广告长期有效）

I am looking for business partners (west point agency managers, WAM) to join my team at MetLife Beijing branch . Those who are interested are welcome to contact me via Boss Zhipin app, or send a CV and a cover letter to 8601010791@metlife.com.cn or hu.yuqing@hotmail.com. Please share with anyone who might be interested. Thank you!

MetLife成立150年之际，推出“150非凡企业家”全球招募计划。储备营业处经理专享福利有：

1. 新加坡流明实验室创新培训 (http://lumenlab.sg/)
2. 日韩深度学习之旅
3. 美国常春藤名校深造
4. 150万个人奖金

In its 150 years’ anniversary, MetLife launched its “150 Extraordinary Entrepreneurs” global recruitment program. The West Point Agency Manager (WAM) will have the following exclusive benefits:

1. Training in Lumen Lab in Singapore (http://lumenlab.sg/)
2. In-depth travel and study in Japan and South Korea
3. Study at ivy league schools in the United States
4. 1.5 million scholarship for each individual

1. 接受公司培训，熟悉以需求为导向的顾问行销方法和流程；了解保险、基金、股权等知识，以及合同法、保险法、继承法等法律法规；根据法律和行规调整，与时俱进
2. 为客户提供专业而全面的资产安全规划分析，并提供风险控制、养老规划、资产传承等方面的建议
3. 入职后继续接受组内培训和管理职一对一的辅导
4. 招募新人；发展自己的团队；带领团队达成业绩目标
5. 参与并组织晨会、每周例会，月度例会与其他公司活动
6. 协助和参与公司的宣传与推广工作；塑造良好的营业处氛围和企业文化

Job Description:

1. Taking MetLife’s training courses, getting familiar with the need-based sales (NBS) methods and processes; Understanding insurance, funds and equity, as well as contract law, insurance law, inheritance law, and other laws and regulations; Staying up-to-date on regulation changes and industry updates
2. Providing customers with comprehensive and professional analysis in financial security planning, and offering advice on risk control, retirement, asset inheritance, etc.
3. Constantly receiving group training and one-on-one coaching from mentors
4. Recruiting new team members; Developing his/her own team; Leading the team to achieve sales goals
5. Attending and organizing morning meetings, weekly meetings, monthly meetings and other company-level activities
6. Assisting and participating in MetLife’s promotion activities; Creating good business atmosphere and corporate culture

1. 有责任底薪，加上按业绩的提成，收入无上限
2. 公司内部设各种奖励和竞赛（比如针对新人有“新人王”和“菁英会”项目），每年有多种奖金和多次国内外免费旅游的机会
3. 有明确的晋升路线，每6个月一次晋升机会；晋升管理职后有增员奖金和管理奖金；最快两年能晋升至营业处经理
4. 每周工作日从周一到周五，每个月最低要求80%的工作日打卡，工作时间自主有弹性
5. 有机会参加百万圆桌会（MDRT）等国际寿险会议

Salary and other Benefits:

1. Basic salary plus commission, without upper limit
2. Awards from competitions within the company (e.g. “New Sales Kings” and “Elite Clubs” for new members); Bonus based on performance; Opportunities for free travel at home and abroad every year.
3. A clear promotion route, with one promotion opportunity every 6 months; Team management bonus and recruiting bonus after promotion to a managerial position; Possibility of being promoted to the agency manager (AM) in two years.
4. Working from Monday to Friday, with minimum 80% of the working days in office per month; Time is flexible
5. Opportunities to participate in international life insurance conferences such as the Million Dollar Round Table (MDRT)

1. 年龄25-48周岁
2. 有责任感、乐于学习；乐于助人，具有亲和力；自我驱动，兼具竞争和团结合作意识
3. 本科学历及以上；专业不限
4. 过往年收入15万及以上
5. 无寿险经验
6. 良好的职业道德；良好的心态

Basic Requirements:

1. age 25-48
2. Responsible and willing to learn; Willing to help others and having high level of affinities; Self-driven, competitive and cooperative
3. Bachelor’s degree and above; Any major is welcome
4. Average annual income from the past above 150,000
5. No prior life insurance sales experience
6. Good professional ethics; Stable mood

1. 重点院校毕业生（比如211、985学校）
2. 硕士及以上学历
3. 有5年以上（管理）工作经验
4. 海外留学或工作经历
5. 团队管理或项目经验
6. 人脉广，在北京居住两年及以上
7. 逻辑思维和共情能力；创新能力

Pluses:

1. Graduated from key point schools (e.g. 211 and 985 schools)
2. Master’s degree and above
3. At least 5 years’ (managerial) working experience
4. Overseas study or working experience
5. Team management or project experience
6. Having extensive contacts in Beijing, or living in Beijing for more than two years
7. Logical thinking and empathy; Creativity

## Translator’s Review of Radical Markets 一场波澜壮阔的思维实验——《激进市场》译者序

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!

## Review of Posner and Weyl’s Radical Markets 激进市场推荐序

《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。

[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/

## Research Workshop in honor of Ehud Kalai

My last week in Israel before I come back to Beijing 🙂

### Program

 Talks and coffee breaks are in Dan David 001 Dinner and lunches are in Gan Hadkalim (in front of exact sciences building).    Monday, July 10, 2017   10:10 — 10:20    Coffee 10:30 — 11:00     Adam Kalai                        Unambiguous communication without a common prior 11:00 — 11:30    Éva Tardos 11:30 — 11:50     Coffee break 11:50 — 12:20     Moshe Tennenholtz        A Game Theoretic Approach to Information Retrieval 12:20 — 12:50    Ariel Rubinstein              Multi-dimensional Reasoning in Games: Framework, Equilibrium and Applications 13:00 — 14:30    Lunch break 14:30 — 15:00    Yuval Salant                   Statistical Inference in Games 15:00 — 15:30    Georgy Egorov               Strategic Communication with Minimal Verification  15:30 — 16:00    Peter Klibanoff                Incomplete Information Games with Ambiguity Averse Players 16:00 — 16:20    Coffee break 16:20 — 16:50    Peyton Young                 Games, Norms, and Institutions 16:50 — 17:20    David Schmeidler           Desirability 17:20 — 17:50    Robert Aumann              My Ehud 18:30                 Dinner     Tuesday, July 11, 2017   10:10 — 10:20    Coffee 10:30 — 11:00    Tim Roughgarden          On a Theorem of Kalai and Samet 11:00 — 11:30    Michal Feldman              Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic Inputs 11:30 — 11:50    Coffee break 11:50 — 12:20    Abraham Neyman          Cooperative Strategic Games 12:20 — 12:50    Rann Smorodinsky         Bayesian Learning in Markets with Common Value 13:00 — 14:30    Lunch break 14:30 — 15:00    Leeat Yariv 15:00 — 15:30    Johannes Hörner 15:30 — 16:00    Jonathan Weinstein        Complementarity Revisited 16:00                 Coffee   Wednesday, July 12, 2017   10:10 — 10:20    Coffee 10:30 — 11:00    Paul Milgrom                    Economics and Computer Science of a Radio Spectrum Reallocation 11:00 — 11:30    TBA, Microsoft Research 11:30 — 11:50    Coffee break 11:50 — 12:20    Rakesh Vohra 12:20 — 12:50    Noam Nisan 13:00 — 14:30    Lunch break 14:30 — 15:00    Yair Tauman                    Coordination games with unknown outside options 15:00 — 15:30    Dov Samet 15:30 — 16:00    Chaim Fershtman           The Competitive Effects of Information Sharing 16:00 — 16:20    Coffee break 16:20 — 16:50    Ehud Lehrer 16:50 — 17:20    Ehud Kalai 17:30                 Reception

## 3rd Workshop on Marketplace Innovation

Workshop website: http://marketplaceinnovation.net/

It was such a nice stay at Stanford! Thanks for all the feedback 🙂

# 2nd LABEL – IEPR Conference

“Understanding cognition and decision making by children”

May 4 – 5, 2017

PROGRAM

Thursday, May 4, 2017

Victory AB Room
3540 South Figueroa Street
Los Angeles, California 90007

8:45 –  9:15   Continental Breakfast

9:15 –  9:30   Introductory remarks

9:30 – 10:15   “The role of agency in regret and relief in 3- to 10-year-old children”Giorgio Coricelli (USC)

10:15 – 11:00  “Young Children’s Exploration of Alternative Possibilities”.  Henrike Moll (USC)

11:00 – 11:30   Coffee break

11:30 – 12:15   “Navigating Uncertainty: Neural Correlates of Decisions from Experience in Adolescence”. Wouter van de Bos (Max Planck – Berlin)

12:15 – 1:45   Lunch

1:45 – 2:30   “The Costs and Benefits of Growing Up”. Michael Norton (Harvard U.)

2:30 – 3:15   “Using economic experiments to detect drivers of behavior at early ages: Evidence from a large field experiment in Chicago”. Ragan Petrie (Texas A&M)

3:15 – 3:45   Coffee break

3:45 – 4:30   “Does the little mermaid compete? An experiment on competitiveness with children”Marco Piovesan (U. Copenhagen)

6:30              Dinner (by invitation)

Friday May 5, 2017

Victory AB Room
3540 South Figueroa Street
Los Angeles, CA 90007

9:00 – 9:30   Continental Breakfast

9:30 – 10:15   “Altruism and strategic giving in children and adolescents”. Isabelle Brocas (USC)

10:15 – 11:00   “Theory of Mind among Disadvantaged Children”. Aldo Rustichini (U. Minnesota)

11:00 – 11:30   Coffee break

11:30 – 12:15   “The development of reciprocal sharing in relation to intertemporal choice”. Felix Warneken (Harvard U.)

12:15 – 1:45   Lunch

1:45 – 2:30   “Group and Normative Influences on Children’s Exchange Behavior”. Yarrow Dunham (Yale U.)

2:30 – 3:15   “The role of social preferences and emotions in children’s decision making -a view from developmental psychology”. Michaela Gummerum (Plymouth U.)

3:15 – 3:45   Coffee Break

3:45 – 4:30   “Socio-cognitive mechanisms of prosocial behavior”. Nadia Chernyak (Boston U.)

## GARP Consistency: Brief Literature Review in Experimental Economics

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

## Real Analysis Review: Some Clarifications of Conceptions and Relationships

Bounded: $|f(x)|\le M$ for all $x\in \mathbb E$.

Uniformly bounded: $|f_n(x)| for all $x\in\mathbb E$, $n=1, 2, 3,...$

Pointwise bounded: $|f_n(x)<\phi(x)|$ where $\phi$ is a finite valued function, and $x\in\mathbb E$, $n=1, 2, 3,...$

$K$ is compact, $f_n$ is pointwise bounded and equitcontinuous $\Rightarrow f_n$ is uniformly bounded, and $f_n$ contains a uniformly convergent subsequence.

Continuous: $f: \mathbb E\subset X\to Y, p\in\mathbb E, \forall \varepsilon>0, \exists \delta>0$ s.t. $\forall x\in\mathbb E, d_X(x, p)<\delta\Rightarrow d_Y(f(x), f(p))<\varepsilon$.

Uniformly continuous: $\forall \varepsilon>0, \exists \delta>0$ s.t. $d_X(p, q)<\delta\Rightarrow d_Y(f(p), f(q))<\varepsilon$.

Equicontinuous: $\forall \varepsilon>0, \exists \delta>0$ s.t. $d(x, y)<\delta\Rightarrow |f(x)-f(y)|<\varepsilon$.

Equicontinuous $\Rightarrow$ uniformly continuous.

Compact set, uniformly convergence $\Rightarrow$ equicontinuous.

Convergent: A sequence $\{p_n\}$ in a metric space $X, \exists p\in X$ s.t. $\forall \varepsilon>0, \exists N$ s.t. $n\ge N\Rightarrow d(p_n, p)<\varepsilon$.

Uniformly convergent (definition 1): a sequence of functions $\{f_n\}, n=1, 2, 3, ...$ converges uniformly on $\mathbb E$ to a function $f$ if $\forall \varepsilon>0, \exists N$ s.t. $n\ge N\Rightarrow |f_n(x)-f(x)|\le \varepsilon$ for all $x\in\mathbb E$.

Uniformly convergent (definition 2): $\varepsilon>0, \exists N$ s.t. $m\ge N, n\ge N, x\in\mathbb E\Rightarrow |f_n(x)-f_m(x)|\le \varepsilon$.

Pointwise convergent: $f(x)=\lim_{n\to\infty} f(x) (x\in\mathbb E)$.

If $\{f_n\}$ is uniformly convergent, then $\lim_{t\to x}\lim_{n\to\infty}f_n(t)=\lim_{n\to\infty}\lim_{t\to x}f_n(x)$.

$K$ is compact, $\{f_n\}$ is continuous and pointwise convergent, $f_n\ge f_{n+1} \Rightarrow f_n\to f$ uniformly.

$f_n\to f$ uniformly, where $f_n\in\mathcal R Rightarrow \int_a^b f d_\alpha=\lim_{n\to\infty}\int_a^b f_n d\alpha$.

$\{f_n\}$ is differentiable, $\{f_n'\}$ converge uniformly on $[a, b]\Rightarrow f_n$ converges uniformly, and $f'(x)=\lim_{n\to\infty}f_n'(x) (a\le x\le b)$.

$\{f_n\}$ is differentiable, $f'$ is uniformly bounded $\Rightarrow f_n$ is equicontinuous.

## Elucidating Partially-Adaptive Models of Value in the Brain: Mechanisms, Features and Comparisons with Fully-Adaptive and Non-Adaptive Models

by Calvin Leather, Yuqing Hu

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).

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.

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