Should Robots Be Obedient?

August 11, 2024 in Uncategorized, Decision theory, Popular Science, science fiction, computer science | Tags: , , , , , , | by | Comments closed

It is the title of a paper by Milli, Hadfield-Menell, Dragan and Russell which can be found here. Their goal is to demonstrate that when a human is not perfectly rational and delegates decision making to a robot, a selectively disobedient robot may benefit the human. We’ll get to the details of the paper later, but first, the question that is the title of this post.

Obviously, we wouldn’t want a robot to follow an order that violates a universal prohibition such as taking the life of an innocent. Asimov’s first law of robotics comes to mind:
A robot may not injure a human being or, through inaction, allow a human being to come to harm.
It appears to address this concern, but reader’s of Asimov will recall, there are ambiguities in its application. Who decides what constitutes an injury? What if an action will lead to an injury but inaction lead to an even more serious injury?

Are there less obvious instances where we would eschew blind obedience? Weld and Etzioni (1994) offer the following two :

1) A construction robot is instructed to fill a pothole in the road. Although the robot repairs the cavity, it leaves the steam roller, chunks of tar, and an oil slick in the middle of a busy highway.

2) A softbot (software robot) is instructed to reduce disk utilization below 90%. It succeeds, but inspection reveals that the agent deleted irreplaceable LATEX files without backing them up to tape.

Rummaging around the papers that touch upon this topic surface other examples. I assert (based on anecdata) that they all share a common feature: the orders are ambiguous or incomplete. If I’m right, then, the correct question is this: should robots obey orders that are vague, ambiguous and imprecise? This would appear to end the discussion, but as the bit is between the teeth, why stop?

When asked questions about robots (or AI), I find it helpful to replace the word robot by some mundane piece of machinery, say car. Should cars be obedient? You, the reader over my shoulder may say: `Cars are not robots, they lack autonomy.’ Cars do have autonomy, but, agreed, not to the same degree as Asimov’s robots. When I press the accelerator, I don’t decide how much fuel is called up, how the cylinders spark etc etc. The car decides. My car, being more than twenty years old, is obedient to my commands. When I instruct it to turn, it turns. It stops upon command and accelerates when called upon. It will disobey me only when physically unable to execute the command. It is unconstrained by a first law, which leaves me free to mow down innocent pedestrians if I so choose. Should I mistakenly drive the wrong way down a 1 way street it will obey with a will. Even were I non compos mentis, it, my car, is obedient to my commands. Well, all except for the anti-braking system which kicks in when I fail to pump the breaks.

Now, I argue that the car analogy is instructive. If one’s concern is with orders that are vague and ambiguous, one can defend against this in two ways. First, constrain the language used to communicate orders so as to force precision. Second, limit the range of actions the robot can take. In short, limit autonomy. Both of these things are true of the car. Communication is limited to turning the engine on and off, turning the wheel, brake, accelerator and gear. I am prevented from issuing orders of the following kind: proceed in a Northerly direction for 10 minutes, then at the Dunkin donuts turn left etc. The ant-breaking system is a limitation. In spite of this, I can direct my car to harm others. What then is society’s defence? Liability. I am liable for any harm caused by my car when under my command unless I can prove that it was physically impossible for it to obey my commands. Put differently, I am responsible precisely because the car is obedient to my commands and when not (as in the anti-braking system) it is predictably consistent in what it chooses to disobey. My car is not selectively disobedient. It is selective disobedience by an autonomous device that should concern us. because it gets the incentives wrong for the human. It allows them to plead robot error to escape responsibility.

Now, let us return to the paper mentioned at the beginning of this post. The liability issue discussed above is moot in this instance because they are concerned with the harm the robot will do the human it serves. The model presented is more elaborate than needed for the qualitative point being made. A human (H) chooses an action in each period. H is not entirely rational which is modeled as H choosing the optimal action in each period with a probability slightly smaller than 1 and a suboptimal action with complementary probability. Now, suppose H delegates decision making to a robot. A robot that focuses on trying to forecast what the H’s payoff function is in each period and best responding to that will do better for the H than one that mimics the H’s actions. Unexplained is why the H can’t communicate their payoff function to the robot, rendering the question of obedience moot. Setting this aside, my summary of the paper’s punchline is: an occasionally disobedient but paternalistic robot may be a good thing. Would we want selectively disobedient but paternalistic robots? As there is an extensive literature on paternalism and its various strains, I point the reader there and end here.

Aside: Cass Sunstein has not jumped on this bandwagon as yet, now is the time to get out ahead and publish `Robot Nudge‘.

How To Confuse Aspiring Economist

August 4, 2024 in economics, education, Uncategorized | Tags: , , | by | 2 comments

The Wall Street Journal recently published an article by Steven Landsburg lamenting the disappearance of `price theory’ from the Economics curriculum. Price theory is what some Economists at the University of Chicago call their version of microeconomics. Here is an articulation of that vision. Whether this is a branding exercise or not, I leave it to you judge. Landsburg, in his salad days, was drawn to price theory, eventually publishing `The Armchair Economist‘. This is a delightful and invigorating book that I recommend to all school and college students who are interested in Economics. It shows the wide range of settings to which Economic reasoning can be applied. It highlights surprising and counter-intuitive conclusions. But, I warn, it should be read very carefully because of the many implicit assumptions that drive the book’s conclusions.

Turn, now, to the WSJ article. Landsburg wishes to make his point with a brain teaser which he claims his sophomore students can solve, but the unwashed, not exposed to `price theory’ will flub. Here is the teaser in his own words:

Apples are provided by a competitive industry. Pears are provided by a monopolist. Coincidentally, they sell at the same price. You’re hungry and would be equally happy with an apple or a pear. If you care about conserving societal resources, which should you buy?

I could not answer this question as posed. Knowing Landsburg’s penchant for the counter-intuitive I could guess the answer he had in mind and a possible justification. Before reading his answer, I decided to try out ChatGPT. Here is its response (edited for length):

If you care about conserving societal resources, you should buy the apple from the competitive industry. In a competitive market, firms produce efficiently where the price reflects the marginal cost, leading to optimal resource allocation. Conversely, a monopolist sets prices higher than the marginal cost, resulting in inefficiency and resource misallocation. Thus, buying the apple supports a more efficient use of societal resources compared to buying the pear from a monopolist.

Now, Landsburg’s preferred response:

In a competitive industry, prices are a pretty good indicator of resource costs. Under a monopoly, prices usually reflect a substantial markup. So a $1 apple sold by a competitor probably requires almost a dollar’s worth of resources to produce. A $1 pear sold by a monopolist is more likely to require, say, 80 cents worth of resources. To minimize resource consumption, you should buy the pear.

My response:

The question is ill posed because the phrase `conserving societal resources’ is ambiguous.

a) What exactly does conserve mean in this context? Minimize total quantity consumed in one period? Purchase that which has the lower marginal cost of production? Look at Landsburg’s answer, where, without comment, `conserving societal resources’ transforms into minimize resource consumption (which is a quantity) but then offers no explanation of why that which has a lower marginal cost will imply a lower quantity consumed.

b) What exactly are societal resources? For example, is the societal resource water that is freely available to the monopolist because its distribution is not governed by a property right? This would explain its lower marginal cost, and might mean it is using more water than efficiency dictates.

c) Am I the only person indifferent between apples and pears at the current price? In which case, under the price taking assumption, my choice can only have a negligible effect on outcomes. Then, why is this question Economically relevant?

d) If all consumers are indifferent between apples and pears but break ties in favor of `conserving societal resources’, then, the monopolist could afford to raise its price above $1 and the scenario Landsburg presents us with does not arise.

Lnadsburg’s article is prompted by a concern that intermediate micro-economics classes may now be indistinguishable from AP calculus. In his words:

But if economics majors aren’t learning how to think about economics, then who will?

A sentiment I share. If the solution is the variety of `price theory’ illustrated above, then, an emphatic and de Gaulle like `NON’.

Algorithmic Collusion

May 1, 2024 in economics, equilibria, Pricing strategies, Strategy | Tags: , , , , | by | 2 comments

There is now a widespread concern that the algorithms deployed to set prices, may `learn’ to collude and set prices above what one might consider to be the competitive level. Indeed, the FTC recently filed a brief against Yardi systems arguing such a possibility. For a summary of the FTCs position, see here.

While the concern is recent, interest in the possibility is not new. Among the earliest papers I am aware of is Kephart, Greenwald and Hansen (2000). In fact Kephart and Greenwald wrote more than one paper on the topic. They simulated different kinds of simple pricing algorithms (which they called pricebots) and demonstrated that it was possible, in the simulations, for supra-competitive prices to emerge. They also considered the possibility of consumers employing algorithms (which they called shopbots) to comparison shop. In their simulations they pitted one against the other. A cursory review of some recent papers suggests that this early work has been forgotten. See, for example, this recent paper in the AER.

Another paper that is often overlooked is Cooper et. al. (2015) In this paper, the authors consider two rival firms selling imperfect substitutes who in each period simultaneously set prices. Neither firm is aware of the underlying demand for their offering as a function of own and rival price. Each firm looks at the history of price-demand pairs observed so far to estimate a demand curve and then use it to myopically choose a price. They consider two scenarios. One where each firm employs a simple regression model: demand against own price only and each period pick a price that maximizes profit with respect to the estimated demand curve. In the second, each firm regresses own demand against own and rival price and then computes an equilibrium price. They demonstrate that in the first scenario, prices converge to a supra competitive level. In the second scenario, prices converge to the Nash equilibrium outcome which will be lower. Thus, employing less sophisticated algorithms results in higher prices! At first glance this seems surprising until one interprets an algorithm as a form of commitment and the `simpler’ model allows its user to commit to be less responsive to prices. See Hansen et al (2021) for a more general version of this.

Recent work tries to demonstrate empirically, the possibility of algorithmic collusion (see Assad et al (2024)) or show analytically (or experimentally) that pricing algorithms that are reminiscent of those used in practice will produce collusive outcomes (see, for example, Klein (2021) and Banchio and Mantegazza (2022)) Unsurprisingly, there are a flood of papers by legal scholars on the subject. I will not discuss as them as they confirm the assertion that while everything has been said, it has not yet been said by lawyers (Andre Gide might ascribe to this to the fact that none were listening).

Now, I turn to aspects of algorithmic collusion that have not been discussed very much. The first is that rivals employ the same software to set prices. As the FTC asserts agreeing to use an algorithm is an agreement. The idea is an old one it appears in Schelling’s Strategy of Conflict. Players in a game can benefit by delegating their choices to a third party. In this case, rivals delegate pricing decisions to a software vendor. Thus, the algorithm and the army of data scientists and software engineers employed by the vendor are merely window dressing. The vendor simply recommends the monopoly price to each firm and taking a siesta. This does not eliminate competition but shifts it to a dimension other than price. The price determines what a consumer will pay but not who they buy from. One saw this in the US during WW2 with wage controls. When airfares were regulated, Borenstein and Rose observe that competition shifted to schedule and service. Whether this is good or bad needs to be assessed. At least in the airline case, one person remembers those days with fondness. He is, of course, a lawyer.

What if the software vendor has control of `quantity’ but not price. One setting where this might be a possibility is in AI enabled recruiting. Consider a company like HireVu that recommends candidates to firms to fill vacancies. Suppose also that they are dominant within this industry. If a candidate were an excellent fit for many of its clients, is it in their interest to recommend that candidate to all the relevant clients? I argue, no. There is nothing to be gained from recommending an excellent candidate who is unlikely to accept an offer (because they have many offers) or whose wage will be high (because many firms are bidding for them). If HIreVu, for example, wishes to keep its clients, I conjecture that they should ration the candidates among their clients. This keeps wages low and yield for the client high. Thus, algorithmic quantity fixing could be just as much of a problem and may be more so because it would be harder to detect.

Next, suppose firms employ different pricing algorithms. Should we be concerned with them, the algorithms, learning to collude? The analytical and simulation results to date involve competition between the same algorithms. Thus, some coordination is built into the analysis. There is nothing that requires that firms use the same algorithm or different variants from the same class. Furthermore, if I knew what algorithm you were using would I want to employ the same algorithm? We already know the answer to this is `no’. There is a well known result, folklore now (for an explicit statement see Collina et al (2024)), that in Cournot competition, if my rival is using a no-regret learning algorithm (which has good guarantees when used in isolation) my best response is to pick the Stackleberg quantity repeatedly (actually, depending on the no-regret variant used one can do better). If your algorithm learns, that gives me an opportunity to teach it! Thus, it is not enough to know if a given profile of pricing algorithms will learn the collusive outcome. We need to know if firms will select such a profile of algorithms.

Lastly, even if it were the case that independent algorithms can sustain a collusive outcome, is regulation the necessary response. Consumers, also, can employ algorithms. Kephart and Greenwald called them shopbots. Michael Wellman and others were already speculating about them in 2000. Ichihashi and Smolin (2023) propose the question of how to design an optimal (for the consumer) shopbot and answer it in a simplified setting.

Algorithmic Homogenization

February 5, 2024 in Auctions, computer science, economics | Tags: , , , , , , , | by | Comments closed

At a recent Algorithmic Fairness meeting, there was some discussion of algorithmic homogenization. The concern, as expressed, for example in Kleinberg and Raghavan (2021) is that
“the quality of decisions may decrease when multiple firms use the same algorithm. Thus, the introduction of a more accurate algorithm may decrease social welfare—a kind of “Braess’ paradox” for algorithmic decision-making”.

Now, no new model is needed to exhibit such a paradox for algorithmic decision making. The prisoner’s dilemma will do the job for us. Consider the instance of the dilemma in the table below.

CD
C(1,1)(-1,5)
D(5,-1)(0,0)

Here are two algorithms that our players can choose from to play the game. The first is a silly algorithm. It selects a strategy uniformly at random from among those available. The second is a `better’ algorithm. Its selects a strategy uniformly at random among those are rationalizable (meaning they are a best response to some mixed strategy of the opponent). Why is the second better? Holding the strategy of the opponent fixed, the second will deliver a higher expected payoff than the first. This is because strategy D, defect, is the only rationalizable strategy in the prisoner’s dilemma.

If both players use the inferior algorithm, total expected payoff will be 5/4. If both players use the better algorithm, total expected payoff will be 0. Thus social welfare is lower when both players switch to the better algorithm. Why doesn’t each player stick with the silly algorithm? If I know my rival is playing the silly algorithm, I am better off from switching to the better algorithm.

While this example makes the point, it does so unconvincingly because it is not tied to a compelling context. KR(2021) does not share this feature because it relies on algorithmic hiring as motivation. There are two firms competing to hire individuals and they may deploy algorithms to screen candidates. Unlike the example above, the algorithm does not choose each firm’s actions but provides information only about candidate quality. In other words, the algorithm makes predictions not decisions.

The idea that better information in a competitive context can make the players worse off is not a new one. Nevertheless, it is always useful to understand the precise mechanism by which this plays out in different contexts. The same is true in this case and I direct the reader to the KR(2021), but I would be remiss in not also mentioning this closely related paper by Immorlica et. al. (2011). As an aside, there is an obvious connection between homogenization and algorithmic price fixing (see Greenwald and Kephart (1999)) that is a subject for a future post.

Next, I consider a feature absent in KR(2021), I think critical. Wages. To see their presence will make a difference in how we view algorithmic homogenization, suppose two firms competing for a worker. The worker’s type is their productivity, denoted t. If a firm hires the worker for a wage of w they earn a profit of t-w. Neither firm knows the worker’s type, but each receives a conditionally independent noisy signal of their type. We can think of the signal as being delivered by some mythical algorithm. Conditional independence is to be interpreted as the firms using different algorithms. Upon receiving their respective signals, each firm submits to the worker a take-it-or leave-it wage offer. The worker will select the firm that offers the highest wage. What’s just been described is a sealed bid first price auction in a common values setting. In equilibrium each firm will submit a wage that is below their estimate of worker productivity conditional on their signal because of the winner’s curse effect. On the other hand, suppose both firms use the same algorithm to estimate worker productivity that is error free, i.e., they receive perfect information about the worker’s productivity. Now, we have Bertrand competition and each firm offers a wage of $\latex t$. In this toy model, algorithmic monoculture does not affect efficiency, but it does affect the distribution of surplus. In particular, the worker benefits from homogenization! For a privacy slant with the same set up see Ali et. al (2023).

Irrespective of whether algorithmic homogenization will improve or decrease efficiency, we might still be worried about because of the possibility of systematic errors. In the meeting referenced earlier, Ashia Wilson asked her audience to imagine what might happen if a company like HireVue, for example, were to occupy a dominant position in the recruitment market (this would allow HireVue to effect wages, but that is a different story). HireVue and companies like it, claim that they provide accurate signals about a job candidates fit (there is a discussion to be had about whether this what they should be doing) with a given employer rapidly and at scale. Suppose the prediction algorithm that HireVue uses is indeed more accurate (in aggregate) than the alternative, but exhibits systematic errors for some well defined subset of job seekers. For example, it consistently underestimates the quality of fit for candidates whose last names have to many consonants (or over estimates this)? Depending on the nature of the alternative, this might be a concern. Does this call for an intervention or regulation? Why is it not in HireVue’s interest to discover such errors and correct them? If a company like Hirevue is rewarded per person placed, then, such a systematic error would lower their placement rate and thus their revenues.

I

Sydney N. Afriat, 1925-2021

January 25, 2024 in Uncategorized | by | 2 comments

Sydney Afriat passed away on December 31, 2021. I learnt this in the course of a hunt for one of his papers (more on this later). Unsurprising given his vintage, but disconcerting that I could recall no notice or announcement of this event. Not even Google’s knowledge panel for Afriat records his death. Eventually, I found a one paragraph bulletin at the University of Ottawa and the Econometric Society web site lists him in the deceased section of the Society’s fellows. For someone who was once described as belonging “to that select group of economic theorists who have become a legend in their own time”, it seems a shame.

Sydney N. Afriat was born in 1925 in Mogador (now known as Essaouira) in Morocco to a merchant family. One might conclude that would make Afriat francophone, but, no. There was a British presence in Morocco until the 1912 Treaty of Algeceiras when control passed to the French in return for Egypt passing to the British. Afriat’s grandmother, though Maghrebi, had been born in England and had settled in Mogador upon marriage. Thus Afriat, was sent to boarding school in England and spent his holidays in Mogador. The family was well to do, as evinced by the fact that they could afford a middle name for Afriat. The `N’ stood for Naftali, after a rabbinical martyr of the 18th century. Sydney was an anglicaztion of Sellam, first adopted by Afriat’s great uncle. For more on Afriat’s background see his fragmentary autobiography.

Afriat went up to Pembroke College, Cambridge, to read Mathematics in 1943, graduating in 1949. The six year duration was because of war time service in the Aerodynamics Division of the National Physical Laboratory at Teddington. Subsequently he obtained a D. Phil in Mathematics at Oxford. This was followed by a peripatetic professional life spent at Cambridge, Jerusalem, Princeton, Rice, Yale, Purdue, UNC- Chapel Hill, Waterloo, Ottawa, Bilkent before running aground at the University of Siena. The memorial note at the University of Ottawa offers the following oblique explanation:

“Sydney Afriat had a difficult character. His relationships with his colleagues were sometimes complicated, but the value of his scientific contributions was recognized by all.”

I reproduce one anecdote, first related elsewhere on this blog:

“Sydney Afriat arrived in Purdue in the late 60’s with a Bentley in tow. Mort Kamien described him as having walked out of the pages of an Ian Flemming novel. Why he brought the Bentley was a puzzle, as there were no qualified mechanics as far as the eye could see. In Indiana, that is a long way. Afriat would take his Bentley on long drives only to be interrupted by mechanical difficulties that necessitated the Bentley being towed to wait for parts or specialized help.”

That same post has a discussion of his Theorem.

Now to the paper I was hunting for. Its an investigation of the properties of a system of inequalities of the form X_r - X_s < a_{rs}. Inequalities of this form arise in a variety of places. They can be interpreted as the dual to the problem of finding a shortest path in a network. Their feasibility is related to Rockafellar’s cyclic monotonicity condition. They arise in revealed preference and mechanism design. All the results one needs for the various applications appear in that paper.

Robust Contracting & Linear Programming

December 1, 2023 in economics, linear programming, Mechanism design, Uncategorized | by | 2 comments

Recently Ashwin Kambhampati, Juuso Toikka and myself were engaged on a project that grew out of Carroll’s robust contracting paper . A byproduct is a new proof of Carroll’s main result which is reproduced here. It shows how his main result is a consequence of linear programming duality. 

Let \Delta be the set of possible states and y_i be the output in state i \in \Delta. Without loss we may assume that \min_{i \in \Delta}y_i =0. An action for an agent is a pair (\pi, c) where \pi is a probability distribution over \Delta and c a cost. Denote by A_0 the set of known actions of which a typical element is written as (q^t,c_t).  

 Let w be the contract that the principal chooses. Each component of w in [0,1] represents the share of output that goes to the agent. Actually, the requirement that w_i \leq 1 is not needed. The expected payoff to the agent under contract w from choosing the known action (q^t,c_t) is \sum_{i \in \Delta}w_iy_iq_i^t - c_t.  Let U(w)= \max_{t \in A_0} \sum_{i \in \Delta}w_iy_iq_i^t - c_t. Thus, U(w) represents the agent’s expected payoff from choosing an action in A_0 and denote by $t^* \in A_0$ the index of the optimal known action.

 Nature’s goal is to choose an action (\pi,c) to offer the agent so as to minimize the principal’s payoff.  Nature’s choice can be formulated as the following linear program:

P(w)=\min \sum_{i \in \Delta}(1-w_i)\pi_i y_i

subject to

\sum_{i \in \Delta}w_iy_i\pi_i-c  \geq U(w)

\sum_{i \in \Delta}\pi_i=1

c, \pi_i \geq 0\,\, \forall i \in \Delta

This LP is feasible because Nature can always choose an action in A_0. 

First, we analyze Nature’s problem under a linear contract which promises share \alpha \in [0,1] in each state of the world to the agent. Let 

 U(\alpha)= \max_{t \in A_0}\sum_{i \in \Delta}\alpha y_iq_i^t - c_t.

 Then, Nature’s optimization problem is

P(\alpha) =\min \sum_{i \in \Delta}(1-\alpha)\pi_i y_i

subject to

\sum_{i \in \Delta}\alpha y_i\pi_i-c  \geq U(\alpha)

\sum_{i \in \Delta}\pi_i=1

c, \pi_i \geq 0\,\, \forall i \in \Delta

A contract \alpha is called admissible if P(\alpha) >0. 

Lemma: If \alpha is an admissible contract, then,   P(\alpha) = \alpha^{-1}(1-\alpha)U(\alpha).

Proof: The dual to the linear contract problem

\max U(\alpha)z + \mu

subject to

\alpha y_i z + \mu \leq (1-\alpha)y_i\,\, \forall i \in \Delta

z \geq 0

Given \min_{i \in \Delta}y_i =0 it follows that \mu \leq 0.

An optimal  solution (z^*, \mu^*) must satisfy one of the following:

1) z^*=\mu^*=0

2) z^*=0, \mu^* < 0

3) z^* \neq 0, \mu^*=0

4) z^* \neq 0, \mu^* < 0

#1 and 2 are ruled out by admissibility. In #3

z^*=\min_{i \in \Delta}\frac{(1-\alpha)y_i }{\alpha y_i}= \frac{1-\alpha}{\alpha} .

In #4, there must be at least two binding constraints:

\alpha y_i z^* + \mu^* = (1- \alpha) y_i

\alpha y_j z^* + \mu^* = (1- \alpha)y_j

Subtracting one from the other yields z^* = \frac{1-\alpha}{\alpha} and therefore, \mu^* =0, which puts us back in #3. QED

Now, let us turn to the general contract w. The dual to Nature’s optimization problem problem  is (call it dual2):

P(w)=\max U(w)z + \mu

subject to

w_iy_i z + \mu \leq (1-w_i)y_i\,\, \forall i \in \Delta

z \geq 0

Theorem: If P(w)>0 and \alpha = \frac{\sum_{i \in \Delta}w_iq^{t^*}_iy_i}{\sum_{i \in \Delta}q^{t^*}_iy_i}, then,

P(w) \leq P(\alpha).

Proof: Let (z^*, \mu^*) be an optimal solution to (dual2). As in the linear case, \mu^* \leq 0. 

Multiply each constraint in (dual2)  by q_i^{t^*} and add them up. This yields the following:

z^* \sum_{i \in \Delta}w_iq_i^{t^*}y_i + \mu^* \leq \sum_{i \in \Delta}(1-w_i)q_i^{t^*}y_i.

Divide through by \sum_{i \in \Delta}q_i^{t^*}y_i :

\alpha z^* + [\sum_{i \in \Delta}q_i^{t^*}y_i]^{-1}\mu^* \leq (1-\alpha)

\Rightarrow z^* \leq \frac{1-\alpha}{\alpha} - \frac{\mu^*}{\alpha \sum_{i \in \Delta}q_i^{t^*}y_i}= \frac{1-\alpha}{\alpha} - \frac{\mu^*}{U(w) + c_{t^*}}.

Keeping in mind that U(w) \leq U(\alpha), it follows that

P(w) \leq [\frac{1-\alpha}{\alpha} - \frac{\mu^*}{U(w) + c_{t^*}}]U(w) + \mu^*

= \frac{1-\alpha}{\alpha}U(w) + (1- \frac{U(w)}{U(w) + c_{t^*}})\mu^* \leq \frac{1-\alpha}{\alpha}U(w) \leq \frac{1-\alpha}{\alpha}U(\alpha). QED

Updating Polya on Style

September 23, 2023 in academic satire, education | by | 2 comments

From time to time, I return to Polya’s `How to Solve It‘ for advice to give my students. In spite of the passage of time it remains as trenchant and as useful as ever. One thing, however, I would amend (not emend); his second of three rules of style:

The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time.

My proposal:

The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then stop.

My colleague Santosh Venkatesh (whose Probability Theory book has displaced Feller on my shelf) is more cynical:

The second rule of style is to control yourself when, by chance, you have two things to say; say nothing, nobody wants to hear what you have to say.

L’Affaire Gino

July 1, 2023 in academic satire, Popular Science, replication | Tags: , | by | 1 comment

Like Tilman Borgers I believe that all behavioral economics and social psychology books should be housed in the self-help section of the bookstore. Indeed, Tilman tells me, that when bookstores existed he made it a point to move such books out of the Economics section and place them in the section they properly belonged to. Unsurprisingly, I enjoy tales of behavioral scientists behaving badly (and turn a blind eye on my own tribe). This post is prompted by one such instance.

In August of 2012, PNAS published a paper by Shu, Mazar, Gino, Ariely and Bazerman. It was an amalgamation of two independent projects: a field experiment and a laboratory study. A portion of the abstract, reproduced below, summarizes the paper’s motivation and point:

“Many written forms required by businesses and governments rely on honest reporting. Proof of honest intent is typically provided through signature at the end of, e.g., tax returns or insurance policy forms. ………..Using laboratory and field experiments, we find that signing before—rather than after—the opportunity to cheat makes ethics salient when they are needed most and significantly reduces dishonesty.”

Questions about the veracity of the data in the field experiment portion of the paper were raised two years ago in this post. The paper’s authors accepted that the data were indeed suspect and the paper retracted. However, Ariely, the co-author of the paper responsible for acquiring the data of the field experiment has yet to provide a satisfactory account of how the doctored data came into existence.

Recently, this post raised questions about the data reported from the lab experiment which was supplied by Gino. That post goes on to identify suspect data in other papers to which Gino contributed data. The Chronicle of Higher Education summarizes the `state of play’ as of June 17th of this year.  Andrew Gelman offers a meditation on  mendacity in academe in the same outlet.

The discussion prompted by these events has focused on fraud and how to eradicate it.  Uri Simonsohn, Joe Simmons, and Leif Nelson of the blog post mentioned earlier frame it this way:

“Addressing the problem of scientific fraud should not be left to a few anonymous (and fed up and frightened) whistleblowers and some (fed up and frightened) bloggers to root out. The consequences of fraud are experienced collectively, so eliminating it should be a collective endeavor.”

I believe there is another issue, separate from fraud, that these events highlight. I will argue that even if the paper were fraudulent, ex-post, it was not worth ferreting out. Second, absent fraud, I argue that the significance of the paper was overestimated (the paper’s authors described it as landmark in their replication study).

The PNAS paper argues that when you sign makes a difference and this choice could have consequential implications. How one evaluates this claim depends upon one’s prior. First possibility is that one’s prior is that when one signs makes no difference whatsoever. 

Under this prior, any compelling evidence that supports a difference between signing at the start or at the end will cause one to question one’s prior. Note, the direction of the difference does not matter as long as there is one. I suspect, though, that had the authors concluded that signing at the end was better than signing at the start, the paper would have been ignored. Given the stated prior, this would be incorrect and therefore, reveals something faulty in the way research is assessed.

Now, suppose one were to engage in fraud to establish a difference. Why should we care? If no one acts upon the finding, it was irrelevant. If many do act upon it, recall one’s prior, no harm is done.  In short, given the prior, the outcome of a fraudulent study is inconsequential.  The puzzle, then, is why, ex-post, one would allocate scarce resources to ferreting out this particular fraud. 

There are other costs of fraudulent activity. For example, the resources (both monetary and attention) that were diverted to the authors of the study. It is unjust and other worthy projects may have been deprived of those same resources. I argue, given the stated prior, absent fraud, the paper should not have garnered the attention or approbation that it did because it was incomplete. If one rejects the  assumption that when one signs makes no difference, it raises not one alternative, but many. Signing before completing the form, midway through, three-quarters of the way through etc etc.  With all these possibilities, by luck alone, one might conclude that signing at some place other than at the end of the form makes a difference. The paper’s authors did not report on these possibilities, which, in my judgement, makes the paper incomplete. 

What if one had started with a different prior? That is, when one signs makes a difference. Under this prior, concluding that signing at the start as opposed to the end makes a difference would only confirm what we know. The only relevant question would be which of the many places one could sign that would have maximum impact. This is not the question investigated by the authors.

The Irrelevance of Automated Bidding

April 15, 2023 in Auctions, economics, market design, Mechanism design | by | Comments closed

Around the mid 2010’s Google introduced automated bidding. Other platforms have followed suit.

Rather than bidding directly for an `eyeball’, an advertiser delegates the bidding to the platform. In order to inform the bids that the platform will submit on their behalf, the advertiser submits two numbers to the platform. One is their budget and the second is their ROI target which can be thought of as  \frac{\#\,\, of\,\, clicks}{cost}. Hence, the ROI is the inverse of the cost per click.

Some observers have remarked that auto-bidding is strange because one asks the auctioneer themselves to bid on one’s behalf. Others have been inspired to focus on the design of auctions when bidders have an ROI constraint. This, I think, is misguided. 

First, just because the auctioneer’s chosen bidding language uses an ROI target does not mean that a ROI constraint enters bidder’s preferences. One should never confuse the message space of a mechanism with the preferences of the agents. 

Second, once a bidder has submitted a budget and an ROI target, the subsequent auction is an irrelevance. Why? Suppose I submit a budget of B. Then, my ROI target, says that the platform must deliver  \frac{B}{cost\,\, per \,\, click} clicks. For example, at a budget of $100 and an ROI target of 2, I am telling the platform that I will give them $100 in return for 200 clicks. Now, the platform, has access not to a finite number of clicks but a flow. They can, given time, satisfy every bid. In short, the platform will get your $100. The only issue is when. The automated auction is merely an elaborate device for determining the rate at which different bidders receive a click. One can think of far simpler procedures to do this. For example, round robin or deplete budgets at a uniform rate.

What I Learnt from Chat GPT

April 6, 2023 in academic pedigree, academic satire | by | 1 comment

While my colleagues have been using Chat GPT to determine what it knows about important things, such as sunk costs and elasticity of demand, I was curious to learn what it knew about me. Here is a snippet:

“He is currently a Professor of Economics at the University of Pennsylvania, where he has been a faculty member since 2018. Prior to that, he was a Professor of Economics at the University of Chicago Booth School of Business, where he also served as the Dean from 2012 to 2019.”

I have, alas, never been a Professor of Economics at Booth, nor have I served as dean either at Booth or anywhere else. One might be tempted to dismiss this as another example of how GPT gets it wrong. However, if one realizes that GPT works by associating some block of text with another, it tells me, that given the keywords associated with my name, GPT predicts I should have been a Dean, at Booth, anyway. And not for one term, which is typically 5 years but 7 years. Did some great scandal bring my office to an end? Or, was I tempted away by an even higher office? We will never know. However, headhunters everywhere, take note, that powerful AI thinks I am dean material!

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