## Category: economics

### Personal data property rights as privacy solution. Re: Cofone, 2017

I’m working my way through Ignacio Cofone’s “The Dynamic Effect of Information Privacy Law” (2017) (link), which is an economic analysis of privacy. Without doing justice to the full scope of the article, it must be said that it is a thorough discussion of previous information economics literature and a good case for property rights over personal data. In a nutshell, one can say that markets are good for efficient and socially desirable resource allocation, but they are only good at this when there are well crafted property rights to the goods involved. Personal data, like intellectual property, is a tricky case because of the idiosyncrasies of data–its has zero-ish marginal cost, it seems to get more valuable when it’s aggregated, etc. But like intellectual property, we should expect under normal economic rationality assumptions that the more we protect the property rights of those who create personal data, the more they will be incentivized to create it.

I am very warm to this kind of argument because I feel there’s been a dearth of good information economics in my own education, though I have been looking for it! I do believe there are economic laws and that they are relevant for public policy, let alone business strategy.

I have concerns about Cofone’s argument specifically, which are these:

First, I have my doubts that seeing data as a good in any classical economic sense is going to work. Ontologically, data is just too weird for a lot of earlier modeling methods. I have been working on a different way of modeling information flow economics that tries to capture how much of what we’re concerned with are information services, not information goods.

My other concern is that Cofone’s argument gives users/data subjects credit for being rational agents, capable of addressing the risks of privacy and acting accordingly. Hoofnagle and Urban (2014) show that this is empirically not the case. In fact, if you take the average person who is not that concerned about their privacy on-line and start telling them facts about how their data is being used by third-parties, etc., they start to freak out and get a lot more worried about privacy.

This throws a wrench in the argument that stronger personal data property rights would lead to more personal data creation, therefore (I guess it’s implied) more economic growth. People seem willing to create personal data and give it away, despite actual adverse economic incentives, because cat videos are just so damn appealing. Or something. It may generally be the case that economic modeling is used by information businesses but not information policy people because average users are just so unable to act rationally; it really is a domain better suited to behavioral economics and usability research.

I’m still holding out though. Just because big data subjects are not homo economicus doesn’t mean that an economic analysis of their activity is pointless. It just means we need to have a more sophisticated economic model, on that takes into account how there are many different classes of user that are differently informed. This kind of economic modeling, and empirically fitting it to data, is within our reach. We have the technology.

References

Cofone, Ignacio N. “The Dynamic Effect of Information Privacy Law.” Minn. JL Sci. & Tech. 18 (2017): 517.

Hoofnagle, Chris Jay, and Jennifer M. Urban. “Alan Westin’s privacy homo economicus.” (2014).

### “The Microeconomics of Complex Economies”

I’m dipping into The microeconomics of complex economies: Evolutionary, institutional, neoclassical, and complexity perspectives, by Elsner, Heinrich, and Schwardt, all professors at the University of Bremen.

It is a textbook, as one would teach a class from. It is interesting because it is self-consciously written as a break from neoclassical microeconomics. According to the authors, this break had been a long time coming but the last straw was the 2008 financial crisis. This at last, they claim, showed that neoclassical faith in market equilibrium was leaving something important out.

Meanwhile, “heterodox” economics has been maturing for some time in the economics blogosphere, while complex systems people have been interested in economics since the emergence of the field. What Elsner, Heinrich, and Schwardt appear to be doing with this textbook is providing a template for an undergraduate level course on the subject, legitimizing it as a discipline. They are not alone. They cite Bowles’s Microeconomics as worthy competition.

I have not yet read the chapter of the Elsner, Heinirch, and Schwardt book that covers philosophy of science and its relationship to the validity of economics. It looks from a glance at it very well done. But I wanted to note my preliminary opinion on the matter given my recent interest in Shapiro and Varian‘s information economics and their claim to be describing ‘laws of economics’ that provide a reliable guide to business strategy.

In brief, I think Shapiro and Varian are right: they do outline laws of economics that provide a reliable guide to business strategy. This is in fact what neoclassical economics is good for.

What neoclassical economics is not always great at is predicting aggregate market behavior in a complex world. It’s not clear if any theory could ever be good at predicting aggregate market behavior in a complex world. It is likely that if there were one, it would be quickly gamed by investors in a way that would render it invalid.

Given vast information asymmetries it seems the best one could hope for is a theory of the market being able to assimilate the available information and respond wisely. This is the Hayekian view, and it’s not mainstream. It suffers the difficulty that it is hard to empirically verify that a market has performed optimally given that no one actor, including the person attempting the verify Hayekian economic claims, has all the information to begin with. Meanwhile, it seems that there is no sound a priori reason to believe this is the case. Epstein and Axtell (1996) have some computational models where they test when agents capable of trade wind up in an equilibrium with market-clearing prices and in their models this happens under only very particular an unrealistic conditions.

That said, predicting aggregate market outcomes is a vastly different problem than providing strategic advice to businesses. This is the point where academic critiques of neoclassical economics miss the mark. Since phenomena concerning supply and demand, pricing and elasticity, competition and industrial organization, and so on are part of the lived reality of somebody working in industry, formalizations of these aspects of economic life can be tested and propagated by many more kinds of people than the phenomena of total market performance. The latter is actionable only for a very rare class of policy-maker or financier.

References

Bowles, S. (2009). Microeconomics: behavior, institutions, and evolution. Princeton University Press.

Elsner, W., Heinrich, T., & Schwardt, H. (2014). The microeconomics of complex economies: Evolutionary, institutional, neoclassical, and complexity perspectives. Academic Press.

Epstein, Joshua M., and Robert Axtell. Growing artificial societies: social science from the bottom up. Brookings Institution Press, 1996.

### Market segments and clusters of privacy concerns

One result from earlier economic analysis is that in the cases where personal information is being used to judge the economic value of an agent (such as when they are going to be hired, or offered a loan), the market is divided between those that would prefer more personal information to flow (because they are highly qualified, or highly credit-worthy), and those that would rather information not flow.

I am naturally concerned about whether this microeconomic modeling has any sort of empirical validity. However, there is some corroborating evidence in the literature on privacy attitudes. Several surveys (see references) have discovered that people’s privacy attitudes cluster into several groups, those only “marginally concerned”, the “pragmatists”, and the “privacy fundamentalists”. These groups have, respectively, stronger and stronger views on the restriction of their flow of personal information.

It would be natural to suppose that some of the variation in privacy attitudes has to do with expected outcomes of information flow. I.e., if people are worried that their personal information will make them ineligible for a job, they are more likely to be concerned about this information flowing to potential employers.

I need to dig deeper into the literature to see whether factors like income have been shown to be correlated with privacy attitudes.

References

Ackerman, M. S., Cranor, L. F., & Reagle, J. (1999, November). Privacy in e-commerce: examining user scenarios and privacy preferences. In Proceedings of the 1st ACM conference on Electronic commerce (pp. 1-8). ACM.

B. Berendt et al., “Privacy in E-Commerce: Stated Preferences versus Actual Behavior,” Comm. ACM, vol. 484, pp. 101-106, 2005.

K.B. Sheehan, “Toward a Typology of Internet Users and Online Privacy Concerns,” The Information Soc., vol. 1821, pp. 21-32, 2002.

### Economic costs of context collapse

One motivation for my recent studies on information flow economics is that I’m interested in what the economic costs are when information flows across the boundaries of specific markets.

For example, there is a folk theory of why it’s important to have data protection laws in certain domains. Health care, for example. The idea is that it’s essential to have health care providers maintain the confidentiality of their patients because if they didn’t then (a) the patients could face harm due to this information getting into the wrong hands, such as those considering them for employment, and (b) this would disincentivize patients from seeking treatment, which causes them other harms.

In general, a good approximation of general expectations of data privacy is that data should not be used for purposes besides those for which the data subjects have consented. Something like this was encoded in the 1973 Fair Information Practices, for example. A more modern take on this from contextual integrity (Nissenbaum, 2004) argues that privacy is maintained when information flows appropriately with respect to the purposes of its context.

A widely acknowledged phenomenon in social media, context collapse (Marwick and boyd, 2011; Davis and Jurgenson, 2014), is when multiple social contexts in which a person is involved begin to interfere with each other because members of those contexts use the same porous information medium. Awkwardness and sometimes worse can ensue. These are some of the major ways the world has become aware of what a problem the Internet is for privacy.

I’d like to propose that an economic version of context collapse happens when different markets interfere with each other through network-enabled information flow. The bogeyman of Big Brother through Big Data, the company or government that has managed to collect data about everything about you in order to infer everything else about you, has as much to do with the ways information is being used in cross-purposed ways as it has to do with the quantity or scope of data collection.

It would be nice to get a more formal grip on the problem. Since we’ve already used it as an example, let’s try to model the case where health information is disclosed (or not) to a potential employer. We already have the building blocks for this case in our model of expertise markets and our model of labor markets.

There are now two uncertain variables of interest. First, let’s consider a variety of health treatments $J$ such that $m = \vert J \vert$. The distribution of health conditions in society is distributed such that the utility of a random person $i$ receiving a treatment $j$ is $w_{i,j}$. Utility for one treatment is not independent from utility from another. So in general $\vec{w} \sim W$, meaning a person’s utility for all treatments is sampled from an underlying distribution $W$.

There is also the uncertain variable of how effective somebody will be at a job they are interested in. We’ll say this is distributed according to $X$, and that a person’s aptitude for the job is $x_i \sim X$.

We will also say that $W$ and $X$ are not independent from each other. In this model, there are certain health conditions that are disabling with respect to a job, and this has an effect on expected performance.

I must note here that I am not taking any position on whether or not employers should take disabilities into account when hiring people. I don’t even know for sure the consequences of this model yet. You could imagine this scenario taking place in a country which does not have the Americans with Disabilities Act and other legislation that affects situations like this.

As per the models that we are drawing from, let’s suppose that normal people don’t know how much they will benefit from different medical treatments; $i$ doesn’t know $\vec{w}_i$. They may or may not know $x_i$ (I don’t yet know if this matters). What $i$ does know is their symptoms, $y_i \sim Y$.

Let’s say person $x_i$ goes to the doctor, reporting $y_i$, on the expectation that the doctor will prescribe them treatment $\hat{j}$ that maximizes their welfare:

$\hat j = arg \max_{j \in J} E[X_j \vert y]$

Now comes the tricky part. Let’s say the doctor is corrupt and willing to sell the medical records of her patients to her patient’s potential employers. By assumption $y_i$ reveals information both about $w_i$ and $x_i$. We know from our earlier study that information about $x_i$ is indeed valuable to the employer. There must be some price (at least within our neoclassical framework) that the employer is willing to pay the corrupt doctor for information about patient symptoms.

We also know that having potential employers know more about your aptitudes is good for highly qualified applicants and bad for not as qualified applicants. The more information employers know about you, the more likely they will be able to tell if you are worth hiring.

The upshot is that there may be some patients who are more than happy to have their medical records sold off to their potential employers because those particular symptoms are correlated with high job performance. These will be attracted to systems that share their information across medical and employment purposes.

But for those with symptoms correlated with lower job performance, there is now a trickier decision. If doctors are corrupt, it may be that they choose not to reveal their symptoms accurately (or at all) because this information might hurt their chances of employment.

A few more wrinkles here. Suppose it’s true the fewer people will go to corrupt doctors because they suspect or know that information will leak to their employers. If there are people who suspect or know that the information that leaks to their employers will reflect on them favorably, that creates a selection effect on who goes to the doctor. This means that the information that $i$ has gone to the doctor, or not, is a signal employers can use to discriminate between potential applicants. So to some extent the harms of the corrupt doctors fall on the less able even if they opt out of health care. They can’t opt out entirely of the secondary information effects.

We can also add the possibility that not all doctors are corrupt. Only some are. But if it’s unknown which doctors are corrupt, the possibility of corruption still affects the strategies of patients/employees in a similar way, only now in expectation. Just as in the Akerlof market for lemons, a few corrupt doctors ruins the market.

I have not made these arguments mathematically specific. I leave that to a later date. But for now I’d like to draw some tentative conclusions about what mandating the protection of health information, as in HIPAA, means for the welfare outcomes in this model.

If doctors are prohibited from selling information to employers, then the two markets do not interfere with each other. Doctors can solicit symptoms in a way that optimizes benefits to all patients. Employers can make informed choices about potential candidates through an independent process. The latter will serve to select more promising applicants from less promising applicants.

But if doctors can sell health information to employers, several things change.

• Employers will benefit from information about employee health and offer to pay doctors for the information.
• Some doctors will discretely do so.
• The possibility of corrupt doctors will scare off those patients who are afraid their symptoms will reveal a lack of job aptitude.
• These patients no longer receive treatment.
• This reduces the demand for doctors, shrinking the health care market.
• The most able will continue to see doctors. If their information is shared with employers, they will be more likely to be hired.
• Employers may take having medical records available to be bought from corrupt doctors as a signal that the patient is hiding something that would reveal poor aptitude.

In sum, without data protection laws, there are fewer people receiving beneficial treatment and fewer jobs for doctors providing beneficial treatment. Employers are able to make more advantageous decisions, and the most able employees are able to signal their aptitude through the corrupt health care system. Less able employees may wind up being identified anyway through their non-participation in the medical system. If that’s the case, they may wind up returning to doctors for treatment anyway, though they would need to have a way of paying for it besides employment.

That’s what this model says, anyway. The biggest surprise for me is the implication that data protection laws serve this interests of service providers by expanding their customer base. That is a point that is not made enough! Too often, the need for data protection laws is framed entirely in terms of the interests of the consumer. This is perhaps a politically weaker argument, because consumers are not united in their political interest (some consumers would be helped, not harmed, by weaker data protection).

References

Akerlof, G. A. (1970). The market for” lemons”: Quality uncertainty and the market mechanism. The quarterly journal of economics, 488-500.

Davis, J. L., & Jurgenson, N. (2014). Context collapse: theorizing context collusions and collisions. Information, Communication & Society, 17(4), 476-485.

Marwick, A. E., & Boyd, D. (2011). I tweet honestly, I tweet passionately: Twitter users, context collapse, and the imagined audience. New media & society, 13(1), 114-133.

Nissenbaum, H. (2004). Privacy as contextual integrity. Wash. L. Rev., 79, 119.

### Credit scores and information economics

The recent Equifax data breach brings up credit scores and their role in the information economy. Credit scoring is a controversial topic in the algorithmic accountability community. Frank Pasquale, for example, writes about it in The Black Box Society. Most of the critical writing on the subject points to how credit scoring might be done in a discriminatory or privacy-invasive way. As interesting as those critiques are from a political and ethical perspective, it’s worth reviewing what credit scores are for in the first place.

Let’s model this as we have done in other cases of information flow economics.

There’s a variable of interest, the likelihood that a potential borrower will not default on a loan, $X$. Note that any value sampled from this $x$ will vary within the interval $[0,1]$ because it is a value of probability.

There’s a decision to be made by a bank: whether or not to provide a random borrower a loan.

To keep things very simple, let’s suppose that the bank gets a payoff of $1$ if the borrower is given a loan and does not default and gets a payoff of $-1$ if the borrower gets the loan and defaults. The borrower gets a payoff of $1$ if he gets the loan and $0$ otherwise. The bank’s strategy is to avoid giving loans that lead to negative expected payoff. (This is a gross oversimplification of, but is essentially consistent with, the model of credit used by Blöchlinger and Leippold (2006).

Given a particular $x$, the expected utility of the bank is:

$x (1) + (1 - x) (-1) = 2x - 1$

Given the domain of $[0,1]$, this function ranges from -1 to 1, hitting 0 when $x = .5$.

We can now consider welfare outcomes under conditions of now information flow, total information flow, and partial information flow.

Suppose the bank has no insight into $x$ besides a prior expectation $X$. Then the expected value of the bank upon offering the loan is $E[2x+1]$. If it is above zero, the bank will offer the loan and the borrower gets a positive payoff. If it is below zero, the bank will not offer the loan and both the bank and potential borrower will get zero payoff. The outcome depends entirely on the prior probability of loan default and is either rewards borrowers or not depending on that distribution.

If the bank has total insight into $x$, then the outcomes are different. The bank can use the option to reject borrowers for whom x is less than .5, and accept those for whom x is greater than .5. If we see the game as repeated over many borrowers whose chances of paying off their loan are all sampled from $X$. Then the additional knowledge of the bank creates two classes of potential borrowers, one that gets loans and one that does not. This increases inequality among borrowers.

It also increases the utility of the bank. This is perhaps best illustrated with a simple example. Suppose the distribution $X$ is uniform over the unit interval $[0,1]$. Then the expected value of the bank’s payoff under complete information is

$\int_{.5}^{1} 2x - 1 dx = 0.25$

which is a significant improvement over the expected payoff of 0 in the uninformed case.

Putting off an analysis of the partial information case for now, suffice it to say that we expect partial information (such as a credit score) to lead to an intermediate result, improving bank profits and differentiating borrowers with respect to the bank’s choice to loan.

What is perhaps most interesting about this analysis is the similarity between it and Posner’s employment market. In both cases, the subject of the variable of interest $X$ is a person’s prospects for improving the welfare of the principle decision-maker upon their being selected, where selection also implies benefit to the subject. Uncertainty about the prospects leads to equal treatment of prospective persons and reduced benefit to the principle. More information leads to differentiated impact to the prospects and benefit to the principle.

References

Blöchlinger, A., & Leippold, M. (2006). Economic benefit of powerful credit scoring. Journal of Banking & Finance, 30(3), 851-873.

### Information flow in economics

We have formalized three different cases of information economics:

What we discovered is that each of these cases has, to some extent, a common form. That form is this:

There is a random variable of interest, $x \sim X$ (that is, a value $x$ sampled from a probability distribution $X$), that has direct effect on the welfare outcome of decisions made be agents in the economy. In our cases this was the aptitude of job applicants, consumers willingness to pay, and the utility of receiving a range of different expert recommendations, respectively.

In the extreme cases, the agent at the focus of the economic model could act with extreme ignorance of $x$, or extreme knowledge of it. Generally, the agent’s situation improves the more knowledgeable they are about $x$. The outcomes for the subjects of $X$ vary more widely.

We also considered the possibility that the agent has access to partial information about $X$ through the observation of a different variable $y \sim Y$. Upon observation of $y$, they can make their judgments based on an improved subjective expectation of the unknown variable, $P(x \vert y)$. We assumed that the agent was a Bayesian reasoner and so capable of internalizing evidence according to Bayes rule, hence they are able to compute:

$P(X \vert Y) \propto P(Y \vert X) P(X)$

However, this depends on two very important assumptions.

The first is that the agent knows the distribution $X$. This is the prior in their subjective calculation of the Bayesian update. In our models, we have been perhaps sloppy in assuming that this prior probability corresponds to the true probability distribution from which the value $x$ is drawn. We are somewhat safe in this assumption because for the purposes of determining strategy, only subjective probabilities can be taken into account and we can relax the distribution to encode something close to zero knowledge of the outcome if necessary. In more complex models, the difference between agents with different knowledge of $X$ may be more strategically significant, but we aren’t there yet.

The second important assumption is that the agent knows the likelihood function $P(Y | X)$. This is quite a strong assumption, as it implies that the agent knows truly how Y covaries with X, allowing them to “decode” the message $y$ into useful information about $x$.

It may be best to think of access and usage of the likelihood function as a rare capability. Indeed, in our model of expertise, the assumption was that the service provider (think doctor) knew more about the relationship between $X$ (appropriate treatment) and $Y$ (observable symptoms) than the consumer (patient) did. In the case of companies that use data science, the idea is that some combination of data and science gives the company an edge in knowing the true value of some uncertain property than its competitors.

What we are discovering is that it’s not just the availability of $y$ that matters, but also the ability to interpret $y$ with respect to the probability of $x$. Data does not speak for itself.

This incidentally ties in with a point which we have perhaps glossed over too quickly in the present discussion, which is what is information, really? This may seem like a distraction in a discussion about economics but it is a question that’s come up in my own idiosyncratic “disciplinary” formation. One of the best intuitive definitions of information is provided by philosopher Fred Dretske (1981; 1983). Made a presentation of Fred Dretske’s view on information and its relationship to epistemological skepticism and Shannon information theory; you can find this presentation here. But for present purposes I want to call attention to his definition of what it means for a message to carry information, which is:

[A] message carries the information that X is a dingbat, say, if and only if one could learn (come to know) that X is a dingbat from the message.

When I say that one could learn that X was a dingbat from the message, I mean, simply, that the message has whatever reliable connection with dingbats is required to enable a suitably equipped, but otherwise ignorant receiver, to learn from it that X is a dingbat.

This formulation is worth mentioning because it supplies a kind of philosophical validation for our Bayesian formulation of information flow in the economy. We are modeling situations where Y is a signal that is reliably connected with X such that instantiations of Y carry information about the value of the X. We might express this in terms of conditional entropy:

$H(X|Y) < H(X)$

While this is sufficient for Y to carry information about X, it is not sufficient for any observer of Y to consequently know X. An important part of Dretske's definition is that the receiver must be suitably equipped to make the connection.

In our models, the “suitably equipped” condition is represented as the ability to compute the Bayesian update using a realistic likelihood function $P(Y \vert X)$. This is a difficult demand. A lot of computational statistics has to do with the difficulty of tractably estimating the likelihood function, let alone computing it perfectly.

References

Dretske, F. I. (1983). The epistemology of belief. Synthese, 55(1), 3-19.

Dretske, F. (1981). Knowledge and the Flow of Information.

### Economics of expertise and information services

We have no considered two models of how information affects welfare outcomes.

In the first model, inspired by an argument from Richard Posner, the are many producers (employees, in the specific example, but it could just as well be cars, etc.) and a single consumer. When the consumer knows nothing about the quality of the producers, the consumer gets an average quality producer and the producers split the expected utility of the consumer’s purchase equally. When the consumer is informed, she benefits and so does the highest quality producer, at the detriment of the other producers.

In the second example, inspired by Shapiro and Varian’s discussion of price differentiation in the sale of information goods, there was a single producer and many consumers. When the producer knows nothing about the “quality” of the consumers–their willingness to pay–the producer charges all consumers a profit-maximizing price. This price leaves many customers out of reach of the product, and many others getting a consumer surplus because the product is cheap relative to their demand. When the producer is more informed, they make more profit by selling as personalized prices. This lets the previously unreached customers in on the product at a compellingly low price. It also allows the producer to charge higher prices to willing customers; they capture what was once consumer surplus for themselves.

In both these cases, we have assumed that there is only one kind of good in play. It can vary numerically in quality, which is measured in the same units as cost and utility.

In order to bridge from theory of information goods to theory of information services, we need to take into account a key feature of information services. Consumers buy information when they don’t know what it is they want, exactly. Producers of information services tailor what they provide to the specific needs of the consumers. This is true for information services like search engines but also other forms of expertise like physician’s services, financial advising, and education. It’s notable that these last three domains are subject to data protection laws in the United States (HIPAA, GLBA, and FERPA) respectively, and on-line information services are an area where privacy and data protection are a public concern. By studying the economics of information services and expertise, we may discover what these domains have in common.

Let’s consider just a single consumer and a single producer. The consumer has a utility function $\vec{x} \sim X$ (that is, sampled from random variable $X$, specifying the values it gets for the consumption of each of $m = \vert J \vert$ products. We’ll denote with $x_j$ the utility awarded to the consumer for the consumption of product $j \in J$.

The catch is that the consumer does not know $X$. What they do know is $y \sim Y$, which is correlated with $X$ is some way that is unknown to them. The consumer tells the producer $y$, and the producer’s job is to recommend to them $j \in J$ that will most benefit them. We’ll assume that the producer is interested in maximizing consumer welfare in good faith because, for example, they are trying to promote their professional reputation and this is roughly in proportion to customer satisfaction. (Let’s assume they pass on costs of providing the product to the consumer).

As in the other cases, let’s consider first the case where the acting party has no useful information about the particular customer. In this case, the producer has to choose their recommendation $\hat j$ based on their knowledge of the underlying probability distribution $X$, i.e.:

$\hat j = arg \max_{j \in J} E[X_j]$

where $X_j$ is the probability distribution over $x_j$ implied by $X$.

In the other extreme case, the producer has perfect information of the consumer’s utility function. They can pick the truly optimal product:

$\hat j = arg \max_{j \in J} x_j$

How much better off the consumer is in the second case, as opposed to the first, depends on the specifics of the distribution $X$. Suppose $X_j$ are all independent and identically distributed. Then an ignorant producer would be indifferent to the choice of $\hat j$, leaving the expected outcome for the consumer $E[X_j]$, whereas the higher the number of products $m$ the more $\max_{j \in J} x_j$ will approach the maximum value of $X_j$.

In the intermediate cases where the producer knows $y$ which carries partial information about $\vec{x}$, they can choose:

$\hat j = arg \max_{j \in J} E[X_j \vert y] =$

$arg \max_{j \in J} \sum x_j P(x_j = X_j \vert y) =$

$arg \max_{j \in J} \sum x_j P(y \vert x_j = X_j) P(x_j = X_j)$

The precise values of the terms here depend on the distributions $X$ and $Y$. What we can know in general is that the more informative is $y$ is about $x_j$, the more the likelihood term $P(y \vert x_j = X_j)$ dominates the prior $P(x_j = X_j)$ and the condition of the consumer improves.

Note that in this model, it is the likelihood function $P(y \vert x_j = X_j)$ that is the special information that the producer has. Knowledge of how evidence (a search query, a description of symptoms, etc.) are caused by underlying desire or need is the expertise the consumers are seeking out. This begins to tie the economics of information to theories of statistical information.

### Formalizing welfare implications of price discrimination based on personal information

In my last post I formalized Richard Posner’s 1981 argument concerning the economics of privacy. This is just one case of the economics of privacy. A more thorough analysis of the economics of privacy would consider the impact of personal information flow in more aspects of the economy. So let’s try another one.

One major theme of Shapiro and Varian’s Information Rules (1999) is the importance of price differentiation when selling information goods and how the Internet makes price differentiation easier than ever. Price differentiation likely motivates much of the data collection on the Internet, though it’s a practice that long predates the Internet. Shapiro and Varian point out that the “special offers” one gets from magazines for an extension to a subscription may well offer a personalized price based on demographic information. What’s more, this personalized price may well be an experiment, testing for the willingness of people like you to pay that price. (See Acquisti and Varian, 2005 for a detailed analysis of the economics of conditioning prices on purchase history.)

The point of this post is to analyze how a firm’s ability to differentiate its prices is a function of the knowledge it has about its customers and hence outcomes change with the flow of personal information. This makes personalized price differentiation a sub-problem of the economics of privacy.

To see this, let’s assume there are a number of customers for a job, $i \in I$, where the number of customers is $n = \left\vert{I}\right\vert$. Let’s say each has a willingness to pay for the firm’s product, $x_i$. Their willingness to pay is sampled from an underlying probability distribution $x_i \sim X$.

Note two things about how we are setting up this model. The first is that it closely mirrors our formulation of Posner’s argument about hiring job applicants. Whereas before the uncertain personal variable was aptitude for a job, in this case it is willingness to pay.

The second thing to note is that whereas it is typical to analyze price differentiation according to a model of supply and demand, here we are modeling the distribution of demand as a random variable. This is because we are interested in modeling information flow in a specific statistical sense. What we will find is that many of the more static economic tools translate well into a probabilistic domain, with some twists.

Now suppose the firm knows $X$ but does not know any specific $x_i$. Knowing nothing to differentiate the customers, the firm will choose to offer the product at the same price $z$ to everybody. Each customer will buy the product if $x_i > z$, and otherwise won’t. Each customer that buys the product contributes $z$ to the firm’s utility (we are assuming an information good with near zero marginal cost). Hence, the firm will pick $\hat z$ according to the following function:

$\hat z = arg \max_z E[\sum_i z [x_i > z]] =$

$\hat z = arg \max_z \sum_i E[z [x_i > z]] =$

$\hat z = arg \max_z \sum_i z E[[x_i > z]] =$

$\hat z = arg \max_z \sum_i z P(x_i > z) =$

$\hat z = arg \max_z \sum_i z P(X > z)$

Where $[x_i > z]$ is a function with value 1 if $x_i > z$ and 0 otherwise; this is using Iverson bracket notation.

This is almost identical to the revenue-optimizing strategy of price selection more generally, and it has a number of similar properties. One property is that for every customer for whom $x_i > z$, there is a consumer surplus of utility $late x_i – z$, that feeling of joy the customer gets for having gotten something valuable for less than they would have been happy to pay for it. There is also the deadweight loss of customers for whom $z > x_i$. These customers get 0 utility from the product and pay nothing to the producer despite their willingness to pay.

Now consider the opposite extreme, wherein the producer knows the willingness to pay of each customer $x_i$ and can pick a personalized price $z_i$ accordingly. The producer can price $z_i = x_i - \epsilon$, effectively capturing the entire demand $\sum_i x_i$ as producer surplus, while reducing all consumer surplus and deadweight loss to zero.

What are the welfare implications of the lack of consumer privacy?

Like in the case of Posner’s employer, the real winner here is the firm, who is able to capture all the value added to the market by the increased flow of information. In both cases we have assumed the firm is a monopoly, which may have something to do with this result.

As for consumers, there are two classes of impact. For those with $x_i > \hat z$, having their personal willingness to pay revealed to the firm means that they lose their consumer surplus. Their welfare is reduced.

For those consumers with $x_i < \hat z$, these discover that they now can afford the product as it is priced close to their willingness to pay.

Unlike in Posner's case, "the people" here are more equal when their personal information is revealed to the firm because now the firm is extracting every spare ounce of joy it can from each of them, whereas before some consumers were able to enjoy low prices relative to their idiosyncratically high appreciation for the good.

What if the firm has access to partial information about each consumer $y_i$ that is a clue to their true $x_i$ without giving it away completely? Well, since the firm is a Bayesian reasoner they now have the subjective belief $P(x_i \vert y_i)$ and will choose each $z_i$ in a way that maximizes their expected profit from each consumer.

$z_i = arg \max_z E[z [P(x_i > z \vert y_i)]]$

The specifics of the distributions $X$, $Y$, and $P(Y | X)$ all matter for the particular outcomes here, but intuitively one would expect the results of partial information to fall somewhere between the extremes of undifferentiated pricing and perfect price discrimination.

Perhaps the more interesting consequence of this analysis is that the firm has, for each consumer, a subjective probabilistic distribution of that consumer’s demand. Their best strategy for choosing the personalized price is similar to that of choosing a price for a large uncertain consumer demand base, only now the uncertainty is personalized. This probabilistic version of classic price differentiation theory may be more amenable to Bayesian methods, data science, etc.

References

Acquisti, A., & Varian, H. R. (2005). Conditioning prices on purchase history. Marketing Science, 24(3), 367-381.

Shapiro, C., & Varian, H. R. (1998). Information rules: a strategic guide to the network economy. Harvard Business Press.

### Formalizing Posner’s economics of privacy argument

I’d like to take a more formal look at Posner’s economics of privacy argument, in light of other principles in economics of information, such as those in Shapiro and Varian’s Information Rules.

By “formal”, what I mean is that I want to look at the mathematical form of the argument. This is intended to strip out some of the semantics of the problem, which in the case of economics of privacy can lead to a lot of distracting anxieties, often for legitimate ethical reasons. However, there are logical realities that one must face despite the ethical conundrums they cause. Indeed, if there weren’t logical constraints on what is possible, then ethics would be unnecessary. So, let’s approach the blackboard, shall we?

In our interpretation of Posner’s argument, there are a number of applicants for a job, $i \in I$, where the number of candidates is $n = \left\vert{I}\right\vert$. Let’s say each is capable of performing at a certain level based on their background and aptitude, $x_i$. Their aptitude is sampled from an underlying probability distribution $x_i \sim X$.

There is an employer who must select an applicant for the job. Let’s assume that their capacity to pay for the job is fixed, for simplicity, and that all applicants are willing to accept the wage. The employer must pick an applicant $i$ and gets utility $x_i$ for their choice. Given no information on which to base her choice, she chooses a candidate randomly, which is equivalent to sampling once from $X$. Her expected value, given no other information on which to make the choice, is $E[X]$. The expected welfare of each applicant is their utility from getting the job (let’s say it’s $1$ for simplicity) times their probability of being picked, which comes to $\frac{1}{n}$.

Now suppose the other extreme: the employer has perfect knowledge of the abilities of the applicants. Since she is able to pick the best candidate, her utility is $\max x_i$. Let $\hat i = arg\max_{i \in I} x_i$. Then the utility for applicant $\hat i$ is $1$, and it is $0$ for the other applicants.

Some things are worth noting about this outcome. There is more inequality. All expected utility from the less qualified applicants has moved to the most qualified applicant. There is also an expected surplus of $(\max x_i) - E[X]$ that accrues to the totally informed employer. One wonders if a “safety net” were to be provided those who have lost out in this change; if it could be, it would presumably be funded from this surplus. If the surplus were entirely taxed and redistributed among the applicants who did not get the job, it would provide each rejected applicant with $\frac{(\max x_i) - E[X]}{n-1}$ utility. Adding a little complexity to the model we could be more precise by computing the wage paid to the worker and identify whether redistribution could potentially recover the losses of the weaker applicants.

What about intermediary conditions? These get more analytically complex. Suppose that each applicant $i$ produces an application $y_i$ which is reflective of their abilities. When the employer makes her decision, her expectation of the performance of each applicant is

$P(x_i \vert y_i) \propto P(y_i \vert x_i)P(x_i)$

because naturally the employer is a Bayesian reasoner. She makes her decision by maximizing her expected gain, based on this evidence:

$arg\max E[P(x_i \vert y_i)] =$

$arg\max \sum_{x_i} x_i p(x_i \vert y_i) =$

$arg\max \sum_{x_i} x_i p(y_i \vert x_i) p(x_i)$

The particulars of the distributions $X$ and $Y$ and especially $P(Y \vert X)$ matter a great deal to the outcome. But from the expanded form of the equation we can see that the more revealing $y_i$ is about $x_i$< the more the likelihood term $p(y_i \vert x_i)$ will overcome the prior expectations. It would be nice to be able to capture the impact of this additional information in a general way. One would think that providing limited information about applicants to the employer would result in an intermediate outcome. Under reasonable assumptions, more qualified applicants would be more likely to be hired and the employer would accrue more value from the work.

What this goes to show is how ones evaluation of Posner's argument about the economics of privacy really has little to do with the way one feels about privacy and much more to do with how one feels about the equality and economic surplus. I've heard that a similar result has been discovered by Solon Barocas, though I'm not sure where in his large body of work to find it.

### From information goods to information services

Continuing to read through Information Rules, by Shapiro and Varian (1999), I’m struck once again by its clear presentation and precise wisdom. Many of the core principles resonate with my experience in the software business when I left it in 2011 for graduate school. I think it’s fair to say that Shapiro and Varian anticipated the following decade of  the economics of content and software distribution.

What they don’t anticipate, as far as I can tell, is what has come to dominate the decade after that, this decade. There is little in Information Rules that addresses the contemporary phenomena of cloud computing and information services, such as Software-as-a-Service, Platforms-as-a-Service, and Infrastructure-as-a-Service. Yet these are clearly the kinds of services that have come to dominate the tech market.

That’s an opening. According to a business manager in 2014, there’s no book yet on how to run an SaaS company. While sure that if I were slightly less lazy I would find several, I wonder if they are any good. By “any good”, I mean would they hold up to scientific standards in their elucidation of economic law, as opposed to being, you know, business books.

One of the challenges of working on this which has bothered me since I first became curious about these problems is that there is not very good elegant formalism available for representing competition between computing agents. The best that’s out there is probably in the AI literature. But that literature is quite messy.

Working up from something like Information Rules might be a more promising way of getting at some of these problems. For example, Shapiro and Varian start from the observation that information goods have high fixed (often, sunk) costs and low marginal costs to reproduce. This leads them to the conclusion that the market cannot look like a traditional competitive market with multiple firms selling similar goods but rather must either have a single dominant firm or a market of many similar but differentiated products.

The problem here is that most information services, even “simple” ones like a search engine, are not delivering a good. They are being responsive to some kind of query. The specific content and timing of the query, along with the state of the world at the time of the query, are unique. Consumers may make the same query with varying demand. The value-adding activity is not so much creating the good as it is selecting the right response to the query. And who can say how costly this is, marginally?

On the other hand, this framing obscures something important about information goods, which is that all information goods are, in a sense, a selection of bits from the wide range of possible bits one might send or receive. This leads to my other frustration with information economics, which is that it is insufficiently tied to the statistical definition of information and the modeling tools that have been built around it. This is all the more frustrating because I suspect that in advanced industrial settings these connections have been made and are used with confidence. However, it had been slow to make it into mainstream understanding. There’s another opportunity here.