Week 11: Fear and Loathing on the Pareto Frontier

DSAN 5450: Data Ethics and Policy
Spring 2026, Georgetown University

Class Sessions

Author

Affiliation

Jeff Jacobs

jj1088@georgetown.edu

Published

Wednesday, April 1, 2026

Open slides in new window →

Schedule

	Start	End	Topic
Lecture	3:30pm	4:00pm	A Whirlwind Tour of Prisoners’ Dilemmas
	4:00pm	4:50pm	Policy Interventions: Transforming Prisoners’ Dilemmas into Assurance/Invisible Hand Games
Break!	5:00pm	5:10pm
	5:10pm	6:00pm	“Inverse Fairness”(!): Machine-Learning What Policies Value

Where We Left Off…

Prisoners’ Dilemma feels like a silly math/econ problem at first… then you get brainwashed by pol econ PhD and suddenly see it at the “core” of 95% of global issues

Bowles & Jayadev (2014), “One Nation Under Guard”, *NYT*

**Newfoundland: cod landings in tons (1851–2014):** In the 1960s new fishing technologies allowed a dramatic increase in cod fishing, far outpacing the capacity of the fish to reproduce, and leading to total collapse by 1992 when the Canadian government banned fishing entirely. Restoration of fishing stocks to the sustainable levels of the past may occur by the 2030s.

Fishers’ Dilemma (Our “Core” Prisoners’ Dilemma)

Single, unique Nash equilibrium, and it’s Pareto inferior
(looming in background: unsustainable if total hours/day > 14)

The “Iterated Elimination” Result

		$\color{#e69f00}B$
		Fish 6h		Fish 8h
$\color{#0072b2}A$	Fish 6h	$\color{#0072b2}\cancel{1}\color{black}, \,$	$\color{#e69f00}\cancel{1}$	$\color{#0072b2}\cancel{0}\color{black},$	$\color{#e69f00}\boxed{\mathbf{1.2}}$
$\color{#0072b2}A$	Fish 8h	$\color{#0072b2}\boxed{\color{#0072b2}\mathbf{1.2}}\color{black}, \,$	$\color{#e69f00}\cancel{0}$	$\color{#0072b2}\boxed{\color{#0072b2}\mathbf{0.4}}\color{black},$	$\color{#009e73}\boxed{\color{#e69f00}\mathbf{0.4}}$

Boxes = Best Responses:

\[ \begin{aligned} {\color{#0072b2}\text{BR}_A}({\color{#e69f00}\overset{B}{6\textrm{h}}}) &= {\color{#0072b2}8\textrm{h}}, \; {\color{#0072b2}\text{BR}_A}({\color{#e69f00}\overset{B}{8\textrm{h}}}) = {\color{#0072b2}8\textrm{h}} \\ {\color{#e69f00}\text{BR}_B}( {\color{#0072b2}\underset{A}{6\textrm{h}}} ) &= {\color{#e69f00}8\textrm{h}}, \; {\color{#e69f00}\text{BR}_B}( {\color{#0072b2}\underset{A}{8\textrm{h}}} ) = {\color{#e69f00}8\textrm{h}} \end{aligned} \]

Best response is always $\text{8h}$, no matter what other player does!

\[ \begin{aligned} \implies &{\color{#0072b2}\mathbb{E}[u_A]} = {\color{#e69f00}\mathbb{E}[u_B]} = 0.4 \text{ for now}, \\ &\leadsto \; ? \text{ once fishery collapses (}\textstyle\sum\text{hrs} = 16\text{)} \end{aligned} \]

Pareto Dominance

Policy Intervention : Allow Contracts

$\leadsto$ Operationalizing Power as “second best” outside option(s)

Equally good outside options $\implies$ can contract to Pareto-optimal point $o^P$
$B$ has better outside options $\implies$ can make take it or leave it offer to $A$:
- “You ($A$) fish 6 hrs all the time. I ($B$) fish 6 hrs 41% of time, 8 hrs otherwise”

Slightly better for $A$ $\implies$ $A$ accepts:

\[ \begin{aligned} \mathbb{E}[u_A(a_A = \textsf{Reject})] &= \overset{\text{STTP}}{\boxed{0.4}} \; \text{ (prev slide) } \overset{\text{LTTP}}{\color{#e69f00}\boxed{\color{black}\leadsto -\infty}} \\ \mathbb{E}[u_A(a_A = \textsf{Accept})] &= 0.41\cdot 1 + 0.59 \cdot 0 = \boxed{0.41} \\ \mathbb{E}[u_B(a_A = \textsf{Reject})] &= \boxed{0.4} \; \text{ (prev slide) } {\color{#e69f00}\boxed{\color{black}\leadsto 0.39}} \\ \mathbb{E}[u_B(a_A = \textsf{Accept})] &= 0.41\cdot 1 + 0.59 \cdot 1.2 = \boxed{1.118} \end{aligned} \]

$B$’s offer = credible threat in both short and long term; same threat from $A$ would not be credible ($B$ knows $A$ would eventually die: $u_A \leadsto -\infty$)

HW4: observe policy outcome $o^{\text{TIOLI}}_{B \rightarrow A}$ $\Leftrightarrow$ social welfare weights $\omega_B > \omega_A$

Policy Intervention : Fines for Overfishing

$\leadsto$ Weber’s descriptive definition of “The State”: Agent with Monopoly on Legal Use of Force (Weber 1919) (remember him?)

Notice: Previous “intervention” was actually self-enforcing! However, outcome was…
- Determined entirely by asymmetric power, and
- Took no account of anyone in society besides two fishers!
- (Thought experiment: if both had “good” outside options, best for them could be fish cod to extinction then move on to “second-best” option $u = 0.4 \leadsto 0.39$)
If we identify [asymmetry of power $\leadsto$ asymmetry of outcomes] as harm bc unfair (reflective equilibrium), one “follow-up” policy intervention is make $A$’s outside options better (welfare, job retraining, etc… but who sets these up?)
If we identify [ecological damage] as harm, this forms independent “dimension” of policy analysis: if coastal waters are “public good” of Canada, may need some sort of agent representing Canada, to govern use of resource 🤔 some sort of… representative government 🤔 with power to issue fines / ban fishing 🤔

…Fines are “Easy” from Economic Perspective

An economic transaction is a solved political problem. Economics has gained the title “Queen of the Social Sciences” by choosing solved political problems as its domain. (Lerner 1972)

If we assume a “well-functioning” state—power to enforce fines, no corruption, etc.—and that this state has “agreed” to use fines to resolve the issue…
Calculation of “optimal fines” is a “solved” problem in economics (like encryption in CS): A Pigouvian tax just fines agent $B$ an amount equal to the externality(!) their defection imposes on $A$, then redistributes this collected fine back to $A$:

		$\color{#e69f00}B$
		Fish 6h		Fish 8h
$\color{#0072b2}A$	Fish 6h	$\color{#0072b2}\cancel{1}\color{black}, \,$	$\color{#e69f00}\cancel{1}$	$\underset{(+1)}{\color{#0072b2}\cancel{0}\color{black}}\underset{\; \leftarrow\vphantom{(+1)}}{,}$	$\underset{(-1)}{\color{#e69f00}\boxed{\color{#e69f00}\mathbf{1.2}}}$
$\color{#0072b2}A$	Fish 8h	$\underset{(-1)}{\color{#0072b2}\boxed{\color{#0072b2}\mathbf{1.2}}}\color{black}\underset{\rightarrow\vphantom{(+1)}}{,} \,$	$\underset{(+1)}{\color{#e69f00}\cancel{0}}$	$\color{#0072b2}\boxed{\mathbf{0.4}}\color{black},$	$\color{#e69f00}\boxed{\mathbf{0.4}}$

Figure 1: Original Fishers’ Dilemma, with Pigou fines in parentheses under “agreement-violating” outcomes

$\leadsto$
New game with tax applied

		$\color{#e69f00}B$
		Fish 6h		Fish 8h
$\color{#0072b2}A$	Fish 6h	$\color{#0072b2}\boxed{\mathbf{1}}\color{black}, \,$	$\color{#e69f00}\boxed{\mathbf{1}}$	$\color{#0072b2}\boxed{\mathbf{1}}\color{black},$	$\color{#e69f00}\cancel{0.2}$
$\color{#0072b2}A$	Fish 8h	$\color{#0072b2}\cancel{0.2}, \,$	$\color{#e69f00}\boxed{\mathbf{1}}$	$\color{#0072b2}\cancel{0.4}\color{black},$	$\color{#e69f00}\cancel{0.4}$

Figure 2: The Fishers’ Dilemma with a Pigou tax for unilaterally Fishing 8h

Policy Interventions: Fish Dilemmas $\leadsto$ Assurance Games

To “escape” prisoners’ dilemma, we had to change the rules of the game (permanently: a one-time fine would not work)
Fishers’ Dilemma:
- No institutions: $a_A, a_B \in \{6\text{ hr}, 8\text{ hr}\}$
- Institutions (courts or social norms): $\{\text{Accept}, \text{Reject}\}$
Driving “game” (two cars pull up at intersection):
- No institutions: $a_A, a_B \in \{\text{Stop}, \text{Drive}\}$
- Institutions (stoplights installed by govt or community agreement): $a_A, a_B \in \{\text{Obey Light}, \text{Run Light}\}$
If policy issue well-modeled by Assurance Game, however, may only need to “nudge” (one-time intervention) $\leadsto$ new permanent Pareto-optimal equilibrium (Nash $\implies$ self-enforcing!)

Assurance Game

Multiple equilibria; the particular outcome we observe is a function of history (path dependency)
Drive-on-left vs. drive-on-right: Assurance game where neither equilibrium Pareto-dominates other option
- Swedish Dagen H: Nudge from $o^*_{\textsf{L}} = o(\textsf{L},\textsf{L})$ to $o^*_{\textsf{R}} = o(\textsf{R},\textsf{R})$
- Either eq is self-reinforcing! (Unless you… like dying)

QWERTY vs. DVORAK / Palanpur farmers: Assurance game where observed equilibrium Pareto inferior

		$\color{#e69f00}B$
		Early	Late
$\color{#0072b2}A$	Early	$\color{#0072b2}\boxed{\mathbf{4}}\color{black}{,} \color{#e69f00}\boxed{\mathbf{4}}$	$\color{#0072b2}\cancel{0}\color{black}{,} \color{#e69f00}\cancel{3}$
$\color{#0072b2}A$	Late	$\color{#0072b2}\cancel{3}\color{black}{,} \color{#e69f00}\cancel{0}$	$\color{#0072b2}\boxed{\mathbf{2}}\color{black}{,} \color{#e69f00}\boxed{\mathbf{2}}$

Invisible Hand Game

Single, unique Nash equilibrium, and it’s Pareto efficient
$\Rightarrow$ Acting in self interest $\leadsto$ best possible outcome

It is not from the benevolence of the butcher, the brewer, or the baker that we expect our meal, but from their regard to their own interest (Smith 1776)

		$\color{#e69f00}B$
		Corn	Taro
$\color{#0072b2}A$	Corn	$\color{#0072b2}\cancel{2}\color{black}{,} \color{#e69f00}\boxed{\mathbf{4}}$	$\color{#0072b2}\boxed{\mathbf{4}}\color{black}{,} \color{#e69f00}\cancel{3}$
$\color{#0072b2}A$	Taro	$\color{#0072b2}\boxed{\mathbf{5}}\color{black}{,} \color{#e69f00}\boxed{\mathbf{5}}$	$\color{#0072b2}\cancel{3}\color{black}{,} \color{#e69f00}\cancel{2}$

Wealth of Nations SPOILER: The wealth comes from division of labor
and also dumbleydore, and semperus snake, and even poor ron the weasel, who never deserved such a fate

[…I am once again reminding you that] An economic transaction is a solved political problem. Economics gained the title “Queen of the Social Sciences” by choosing solved political problems as its domain

So We’ve Opened the Pandora’s Box of Utility…

…We need to dive a bit more! To get to
[Policy Intervention ] Property Rights
[Policy Intervention ] Yugoslav Nationalization
(called “mergers and acquisitions” when done by MBAs with $3 trillion who can’t be voted out of office)¹

Utility Function: Using the Ordering of Numbers to “Encode” the Ordering of Preferences

From Ryan Safner’s *History of Economic Thought: Welfare Economics*

Bluey obtains greater utility despite paying the same cost by moving from $E$ to $O$
$E$ denotes “Initial Endowment”, $O$ denotes “Final Outcome”

Two Can Play This Game…

Bluey obtains greater utility within the same budget by moving from $E^1$ to $O^1$
Greenie obtains greater utility within the same budget by moving from $E^2$ to $O^2$

The Edgeworth Box

Rotate Greenie’s box 180° and superimpose onto Bluey’s:

Pareto Frontier = Contract(!) Curve

From initial endowment $E$, if allowed to trade, “rational” players can reach any allocation along dashed contract curve from $G$ to $B$… (Why not $A$ or $H$?)
So, what determines which of these points they end up at? (Middle name hint)

First Fundamental Theorem of Welfare Economics

[Antecedents (Coase Conditions)] $\Rightarrow$ «markets produce Pareto-optimal outcomes»

Even Jeff finds proof (and corollaries) compelling / convincing / empirically-supported
- (It’s a full-on proof, in the mathematical sense, so doesn’t rly matter what I think; I just mean, imo, important and helpful to think through for class on policy!)
- Ex: Conditional on antecedents [(Coase) minus (perfect competition) plus (thing must be allocated via markets)], $\uparrow$ Competition $\leadsto$ More efficient allocations
Like how Gauss-Markov Assumptions $\Rightarrow$ OLS is BLUE, yet our whole field (at least, a whole class, DSAN 5300) built on what to do when GM Assumptions don’t hold
For policy development, helpful to think through
- which cases “break” FFT (more honored in the breach)
- How each violation might be “fixed” through policy
Our violation: No externalities assumption
- Possible policy “fixes”: property rights, market-socialist nationalization

Payoff from Jeff Pointing at Things Saying “Antecedents!” 500x

Consequent only true if antecedents hold! Otherwise, proper answer becomes “It depends! Let’s see if data can help us find out!” (Will minimum wage hurt/help blah blah blah… “It depends! Tell me the details!”) (Will new condos blah blah blah yimby nimby…) (Will re-allocating welfare budget from $X$ to $Y$ blah blah blah… 👀 HW4)

[Economic inequality] is a social law, something in the nature of man. (Pareto 1896)

We’ve got a [thing] made by men, isn’t that something we should be able to change? (Steinbeck 1939)

Coase Antecedents $\approx$ equalized power!

Ex 1: Perfect Competition $\Rightarrow$ ($\neg$ monopoly) $\wedge$ ($\neg$ monopsony) $\Rightarrow$ everyone’s outside option equally good $\Rightarrow$ no take-it-or-leave-it coercion possible (try to coerce, I’ll say no and go to one of the other $\infty$ people offering equally good options)
Ex 2: No Informational Asymmetries $\Rightarrow$ Can’t “trick me” into buying defective product (Akerlof (1970), “Market for Lemons”)

So… What Happens When Antecedents Don’t Hold?

$\neg$(Coase Antecedents) $\Rightarrow$ Unequal Power… Puts us in realm of Descriptive Ethics!

[What is] right, as the world goes, is only in question between equals in power; otherwise, the strong do as they please and the weak suffer what they must. [Thucydides (2013); c. 411 BC] (Think of necessary vs. sufficient conditions!)
Like how Gauss-Markov Assumptions $\Rightarrow$ OLS is BLUE, yet our whole field (at least, a whole class, DSAN5300) built on what to do when G-M Assumptions don’t hold
For policy development, helpful to think through
- which cases “break” FFT (more honored in the breach)
- How each violation might be “fixed” through policy²
Our violation: No externalities assumption
- Possible policy “fixes”: property rights, Yugoslav nationalization

Policy Intervention : Property Rights

Rawlsian Rights: Vetos on societal decisions; Constitution can make some inalienable (can’t sell self into slavery), some alienable
Property rights: alienable. You can gift or sell the rights if you want (veto is over society just, like, taking your property if someone else would be happier with it)

Case : Society decides Right to Clean Air $\prec$ Right to Smoke $\Rightarrow$ Start at $E$

$A$ can pay $B$ to alienate right (Pay $50/month, can smoke 5 ciggies) $\leadsto$ $X$
Movement along light blue curve: giving up $x$ money for $y$ smoke, equally happy. $u_A(p)$ identical for $p$ on curve
Movement to higher light blue curve () $\Rightarrow$ greater utility $u_A' > u_A$

Case Society decides Smoke $\prec$ Clean Air $\Rightarrow$ Repeat for $E' \leadsto X'$

“Edgeworth Box” for **Right to Smoke** vs. **Right to Clean Air**: $A$, $B$ are roommates; $A$ loves smokin, $B$ loves clean air; From Varian (2006)

Why Exactly Does [Commodifying Rights] Sometimes Enable [“Cancelling Out” Externalities]?

The key: Forces agent $i$ to pay a cost for inflicting disutility on agent $j$!
(Here please note: “$X$ sometimes enables $Y$” does not mean $X$ is a necessary or sufficient condition for $Y$! Think of walking into a dark room, trying different light switches until one turns on the overhead light)
Dear reader, I know what you’re thinking… But Jeff!! This is all so abstract and theoretical!! We’re sick of your ivory-tower musings, get your head out of the clouds and make it relevant to our day-to-day lives, by relating it back to Yugoslavia’s 1965 economic reforms!!
Don’t worry, I’ve listened to your concerns, and the next slide is here for you 😌

Policy Intervention : “Yugoslav Nationalization”

Last reminder: Externalities $\Leftrightarrow$ I get reward, others pay costs 🥳

Steel Mill $S$ produces amount of steel $s$ $\leadsto$ pollution $x$, total cost $c_s(s,x)$
Fishery $F$ “produces” amount of fish [$x \leadsto$] $f$, total cost $c_f(f,x)$
$S$ optimizes (price per steel $p_s$)

\[ s^*_{\text{Priv}}, x^*_{\text{Priv}} = \argmax_{s,\small\boxed{x}}\left[ p_s s - c_s(s, x) \right] \]

While $F$ optimizes (price per fish $p_f$)

\[ f^*_{\text{Priv}} = \argmax_{f}\left[ p_f f - c_f(f, x) \right] \]

If [Yugoslavia-style] nationalized, new optimization of joint steel-fish venture is

\[ s^*_{\text{Yugo}}, f^*_{\text{Yugo}}, x^*_{\text{Yugo}} = \argmax_{s, f, x}\left[ p_s s + p_f f - c_s(s, x) - c_f(f, x) \right] \]

Can prove/“prove” that $o(s^*_{\text{Yugo}}, f^*_{\text{Yugo}}, x^*_{\text{Yugo}})$ Pareto-dominates $o(s^*_{\text{Priv}}, x^*_{\text{Priv}}, f^*_{\text{Priv}})$
What determines which agents get to ignore externalities? (Dead horse/middle name)

Social Welfare Functionals

Functionals?

You probably know what a function $f(x)$ is; a functional is a function of functions: $\mathscr{G}(f)$
It’s from math, which is scary, but it’s just notation to remind us that we’re analyzing functions of functions
In our case, they “work the same way” as regular functions, e.g., $\mathscr{G}(f,g) = f^2 + g^2$, so $f(x) = x, g(x) = 2x \Rightarrow \mathscr{G}(f,g)(x) = x^2 + 4x^2 = 5x^2$

We Live In A Dang Society

Utilitarianism, Kant, Rawls can all be modeled as Social Welfare Functionals

\[ W(\mathbf{u}) = W(u_1, \ldots, u_n) \Rightarrow W(\mathbf{u})(x) = W(u_1(x), \ldots, u_n(x)) \]

$u_i(x)$: Given bundle of resources $x$, how much utility does $i$ experience? $u_i: \mathcal{X} \rightarrow \mathbb{R}$
$W(\mathbf{u})$: Aggregates $u_i(x)$ over all $i$, to produce measure of overall welfare of society. For $N$ people, $W: (\mathcal{X} \rightarrow \mathbb{R})^N \rightarrow \mathbb{R}$.
Standard assumption: $W$ additive $\Rightarrow W(\mathbf{u}) = \sum_{i=1}^n \omega_iu_i(x)$
- $\omega_i \equiv \frac{\partial W}{\partial u_i}$ is $i$’s welfare weight (❗️)
Welfare-Economic definition of Utilitarianism: Literally just $\omega_i = 1 \; \forall i$
(HW4) Decomposition to evaluate bias in policy impacts: from observed allocation $x_i$ and marginal utility $u'_i(x)$, can…
- Infer $\widehat{\omega}_i$ (how much policy does value person $i$), then
- Compare with $\omega_i^*$ (how much policy should value person $i$… conjoint survey) 🤯

Alternative SWF Specifications

Social values

\[ W(\underbrace{v_1, \ldots, v_n}_{\text{Values}})(x) \overset{\text{e.g.}}{=} \omega_1\underbrace{v_1(x)}_{\text{Privacy}} + \omega_2\underbrace{v_2(x)}_{\mathclap{\text{Public Health}}} \]

Stakeholder Analysis

\[ W(\underbrace{s_1, \ldots, s_n}_{\text{Stakeholders}})(x) = \omega_1\underbrace{u_{s_1}(x)}_{\text{Teachers}} + \omega_2\underbrace{u_{s_2}(x)}_{\text{Parents}} + \omega_3\underbrace{u_{s_3}(x)}_{\text{Students}} + \omega_4\underbrace{u_{s_4}(x)}_{\mathclap{\text{Community}}} \]

(Adapted from this great intro video!)

The Conveniently-Left-Out Detail

Recall, e.g., predictive parity:

\[ \mathbb{E}[Y \mid D = 1, A = 1] = \mathbb{E}[Y \mid D = 1, A = 0] \]

Who decides which $Y$ to pick? (Kasy and Abebe 2021)
Answer: Whoever picks the objective function!
Profit-maximizing firm: $\max\left\{ \mathbb{E}[D (Y - c)]\right\} \Rightarrow$ (Discrimination if and only if bad at profit-maximizing)
Welfare-maximizing policymaker: $\max\{ W(u_1(D), \ldots, u_n(D)) \}$
Do these align? Sometimes yes, sometimes no (See: Welfare Theorems and their antecedents, and/or Becker (1957))

Remaining (Challenging) Details

Who gets included in the SWF?
People in one household? One community? One state? One country?
People in the future?
Animals?
…OUR BEAUTIFUL ENVIRONMENT???

Back to Utilitarian SWF

Easy mode (possibly/probably your intuition?): Everyone’s welfare weight should be equal, $\omega_i = \frac{1}{n}$

\[ W(u_1, \ldots, u_n)(x) = \frac{1}{n}u_1(x) + \cdots + \frac{1}{n}u_n(x) \]

$\implies$ Utilitarian Social Welfare Functional!
The Silly Problem of Utilitarian SWF: What if everyone is made happy by $u_{\text{Jeef}} = -999999999$?

The Hard Problem of Utilitarian SWF

While the rhetoric of “all men [sic] are born equal” is typically taken to be part and parcel of egalitarianism, the effect of ignoring the interpersonal variations can, in fact, be deeply inegalitarian, in hiding the fact that equal consideration for all may demand very unequal treatment in favour of the disadvantaged (Sen 1992)

$\implies$ “Equality of What?”
What is the “thing” that egalitarianism obligates us to equalize (the equilisandum/equilisanda): Utility? Opportunity? Resources? Money? Freedom from [$X$]? Freedom to [$Y$]?

Utility $\rightarrow$ Social Welfare with Externalities

Jeef and Keef are roommates: Jeef loves listening to Tony Danza Tapdance Extravaganza, but Keef is normal and slowly dies inside with each additional song

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.5
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ lubridate 1.9.4     ✔ tibble    3.3.0
✔ purrr     1.0.4     ✔ tidyr     1.3.1
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

music_df <- tribble(
  ~Songs, ~Jeef, ~Keef,
  0, 0, 0,
  1, 13, -2,
  2, 18, -6,
  3, 24, -13,
  4, 28, -20,
  5, 30, -42
)
music_df <- music_df |>
  mutate(Total = Jeef + Keef)
music_df

Songs	Jeef	Keef	Total
0	0	0	0
1	13	-2	11
2	18	-6	12
3	24	-13	11
4	28	-20	8
5	30	-42	-12

long_df <- music_df |>
  pivot_longer(!Songs, names_to="Roommate", values_to="Utility")
util_df <- long_df |>
  filter(Roommate != "Total")
ggplot(util_df, aes(x=Songs, y=Utility, color=Roommate)) +
  geom_line(linewidth=g_linewidth) +
  geom_point(size=g_pointsize) +
  labs(
    title="Individual Utility: Jeef vs. Keef",
    x="Number of Songs Played",
    y="Utility"
  ) +
  theme_dsan("quarter")

welfare_df <- long_df |>
  filter(Roommate == "Total")
ggplot(welfare_df, aes(x=Songs, y=Utility, color=Roommate)) +
  geom_line(linewidth=g_linewidth) +
  geom_point(size=g_pointsize) +
  labs(
    title="Social Welfare: Jeef and Keef",
    x="Number of Songs Played",
    y="Social Welfare"
  ) +
  scale_color_manual(values=c(cbPalette[3]), labels=c("Total      ")) +
  theme_dsan("quarter") +
  remove_legend_title()

So What’s the Issue?

These utility values are not observed
If we try to elicit them, both Jeef and Keef have strategic incentives to lie (over-exaggerate)
Jeef maximizes own utility by reporting $u_j(s) = \infty$
- (“I will literally die if I can’t listen to Lil Wayne’s ”Peanuts 2 N Elephant” prod. Lin-Manuel Miranda all day”)
Keef maximizes own utility by reporting $u_k(s) = -\infty$
- (“I will literally die if I hear this elephant song again”)
(…Quick mechanism design demo: Second price auctions)

Now with Scarce Resources

In a given week, Jeef and Keef have 14 meals and 7 aux hours to divide amongst them

\[ \begin{align*} \max_{m_1,m_2,a_1,a_2}& W(u_1(m_1,a_1),u_2(m_2,a_2)) \\ \text{s.t. }& m_1 + m_2 \leq 14 \\ \phantom{\text{s.t. }} & ~ \, a_1 + a_2 \; \leq 7 \end{align*} \]

Let’s assume $u_i(m_i, a_i) = m_i + a_i$ for both
$\Rightarrow$ One solution: $m_1 = 14, m_2 = 0, a_1 = 7, a_2 = 0$…
$\Rightarrow$ Another: $m_1 = 0, m_2 = 14, a_1 = 0, a_2 = 7$…
Who decides? Any decision implies $\omega_1, \omega_2$ ($\omega_1 + \omega_2 = 1$)
(Last slide = last reminder…)

References

Akerlof, George A. 1970. “The Market for "Lemons": Quality Uncertainty and the Market Mechanism.” The Quarterly Journal of Economics 84 (3): 488–500. https://doi.org/10.2307/1879431.

Becker, Gary S. 1957. The Economics of Discrimination. University of Chicago Press. https://books.google.com?id=50qHcSNVVEMC.

Kasy, Maximilian, and Rediet Abebe. 2021. “Fairness, Equality, and Power in Algorithmic Decision-Making.” Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency (New York, NY, USA), FAccT ’21, March 1, 576–86. https://doi.org/10.1145/3442188.3445919.

Lerner, Abba P. 1972. “The Economics and Politics of Consumer Sovereignty.” The American Economic Review 62 (1/2): 258–66. https://www.jstor.org/stable/1821551.

Malm, Andreas. 2021. How to Blow Up a Pipeline. Verso Books. https://books.google.com?id=qUrSDwAAQBAJ.

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Footnotes

(dw, they use the profits for innovation and thought leadership and def not to buy yachts so they can party with yacht friends on privately-owned Caribbean islands)↩︎
Recall W01: [Earned Income Tax Credits, Emissions Markets, Climate Engineering, Antitrust Legistlation] $\in \text{Policy Set}$; [Black Panther Community Police Patrols, Blowing Up Oil Pipelines (Malm 2021), Bolshevik Revolution] also $\in \text{Policy Set}$↩︎

		\(\color{#e69f00}B\)
		Fish 6h		Fish 8h
\(\color{#0072b2}A\)	Fish 6h	\(\color{#0072b2}\cancel{1}\color{black}, \,\)	\(\color{#e69f00}\cancel{1}\)	\(\color{#0072b2}\cancel{0}\color{black},\)	\(\color{#e69f00}\boxed{\mathbf{1.2}}\)
\(\color{#0072b2}A\)	Fish 8h	\(\color{#0072b2}\boxed{\color{#0072b2}\mathbf{1.2}}\color{black}, \,\)	\(\color{#e69f00}\cancel{0}\)	\(\color{#0072b2}\boxed{\color{#0072b2}\mathbf{0.4}}\color{black},\)	\(\color{#009e73}\boxed{\color{#e69f00}\mathbf{0.4}}\)

		\(\color{#e69f00}B\)
		Fish 6h		Fish 8h
\(\color{#0072b2}A\)	Fish 6h	\(\color{#0072b2}\cancel{1}\color{black}, \,\)	\(\color{#e69f00}\cancel{1}\)	\(\underset{(+1)}{\color{#0072b2}\cancel{0}\color{black}}\underset{\; \leftarrow\vphantom{(+1)}}{,}\)	\(\underset{(-1)}{\color{#e69f00}\boxed{\color{#e69f00}\mathbf{1.2}}}\)
\(\color{#0072b2}A\)	Fish 8h	\(\underset{(-1)}{\color{#0072b2}\boxed{\color{#0072b2}\mathbf{1.2}}}\color{black}\underset{\rightarrow\vphantom{(+1)}}{,} \,\)	\(\underset{(+1)}{\color{#e69f00}\cancel{0}}\)	\(\color{#0072b2}\boxed{\mathbf{0.4}}\color{black},\)	\(\color{#e69f00}\boxed{\mathbf{0.4}}\)

		\(\color{#e69f00}B\)
		Fish 6h		Fish 8h
\(\color{#0072b2}A\)	Fish 6h	\(\color{#0072b2}\boxed{\mathbf{1}}\color{black}, \,\)	\(\color{#e69f00}\boxed{\mathbf{1}}\)	\(\color{#0072b2}\boxed{\mathbf{1}}\color{black},\)	\(\color{#e69f00}\cancel{0.2}\)
\(\color{#0072b2}A\)	Fish 8h	\(\color{#0072b2}\cancel{0.2}, \,\)	\(\color{#e69f00}\boxed{\mathbf{1}}\)	\(\color{#0072b2}\cancel{0.4}\color{black},\)	\(\color{#e69f00}\cancel{0.4}\)

		\(\color{#e69f00}B\)
		Early	Late
\(\color{#0072b2}A\)	Early	\(\color{#0072b2}\boxed{\mathbf{4}}\color{black}{,} \color{#e69f00}\boxed{\mathbf{4}}\)	\(\color{#0072b2}\cancel{0}\color{black}{,} \color{#e69f00}\cancel{3}\)
\(\color{#0072b2}A\)	Late	\(\color{#0072b2}\cancel{3}\color{black}{,} \color{#e69f00}\cancel{0}\)	\(\color{#0072b2}\boxed{\mathbf{2}}\color{black}{,} \color{#e69f00}\boxed{\mathbf{2}}\)

		\(\color{#e69f00}B\)
		Corn	Taro
\(\color{#0072b2}A\)	Corn	\(\color{#0072b2}\cancel{2}\color{black}{,} \color{#e69f00}\boxed{\mathbf{4}}\)	\(\color{#0072b2}\boxed{\mathbf{4}}\color{black}{,} \color{#e69f00}\cancel{3}\)
\(\color{#0072b2}A\)	Taro	\(\color{#0072b2}\boxed{\mathbf{5}}\color{black}{,} \color{#e69f00}\boxed{\mathbf{5}}\)	\(\color{#0072b2}\cancel{3}\color{black}{,} \color{#e69f00}\cancel{2}\)