\documentclass[10.5pt]{article}
\usepackage[parfill]{parskip} % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx}
\usepackage{amssymb,amsmath}
\usepackage[pdftex,colorlinks,citecolor=blue,urlcolor=blue]{hyperref} % need to make this the last package for it to work
\usepackage{titlesec}
\titleformat*{\section}{\Large\bfseries}
\titleformat*{\subsection}{\large\bfseries}
\titleformat*{\subsubsection}{\large\bfseries}
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\fancyhead[RE,LO]{Brian Tomasik}
\fancyhead[LE,RO]{\thepage}
\fancyfoot[RE,LO]{Essays on Reducing Suffering}
\fancyfoot[LE,RO]{\url{http://utilitarian-essays.com/}}
\renewcommand{\headrulewidth}{1pt}
\renewcommand{\footrulewidth}{1pt}
\begin{document}
\begin{center}
\LARGE
Utilitarian Career Choice\\
\normalsize
\vspace{.35cm}
by Brian Tomasik\\
\vspace{.2cm}
First written: 2006\\
\vspace{.6cm}
\end{center}
\thispagestyle{empty}
Conventional wisdom instructs people to ``choose a career that will make a difference." Utilitarianism instructs people to ``choose the career that will make the maximum possible difference $\Delta U(w)$."
\section{Framework for Discussion}
\subparagraph{Definition:}\begin{math} U \end{math} is the aggregated utility of the universe: the sum total of the utility of all organisms over all time.
\subparagraph{Definition:}A \textit{life's work} \begin{math} w \end{math} is a particular lifestyle that a person leads; it describes that person's job, free-time activities, and lifestyle habits. The set of all possible ways in which a given person might live is \begin{math} W \end{math}.
\subparagraph{Definition:}\begin{math} \Delta U(w_i) \end{math} signifies the lifetime change in aggregated utility that a person effectuates by choosing the \begin{math} i \end{math}th possible \begin{math} w \end{math}.
\paragraph{Definition:}The \textit{utilitarian life's work} is \begin{math} w_u \end{math}, where
\begin{equation}
\Delta U(w_u) := \max_{W}\Delta U(w_i).
\end{equation}
Now a question about causation: What does it mean for \begin{math} X \end{math} to ``make a difference" on the universe? It means that the universe with \begin{math} X \end{math} is different from the way it would have been without \begin{math} X \end{math}.
\paragraph{Definition:}Let \begin{math} _X \end{math} denote the state of the universe given \begin{math} X \end{math} and \begin{math} _{\neg X} \end{math}, the state of the universe without \begin{math} X \end{math}. The change in \begin{math} U \end{math} that results from \begin{math} X \end{math} is thus
\begin{equation}\label{impactofX}
\Delta U(X) := U_X - U_{\neg X}.
\end{equation}
Some things in the universe will not be affected at all by \begin{math} X \end{math}; that is, they will be the same whether \begin{math} X \end{math} or \begin{math} \neg X \end{math} is the case. Presumably at least everything outside of \begin{math} X \end{math}'s future light cone would fall into this category.
\paragraph{Definition:}\begin{math} N_X \end{math} represents the components of \begin{math} U_X \end{math} that are not affected by whether \begin{math} X \end{math} or \begin{math} \neg X \end{math} is the case. \begin{math} A_X \end{math} represents the components of \begin{math} U_X \end{math} that \textit{are} affected by whether \begin{math} X \end{math} or \begin{math} \neg X \end{math} is the case. Thus,
\begin{equation}
\begin{split}
U_X &:= N_X + A_X,\\
U_{\neg X} &:= N_{\neg X} + A_{\neg X}.
\end{split}
\end{equation}
Since \begin{math} N_X \equiv N_{\neg X} \end{math}, \eqref{impactofX} becomes
\begin{equation}\label{impactofX2}
\begin{split}
\Delta U(X)& \equiv (N_X + A_X) - (N_{\neg X} + A_{\neg X})\\
& \equiv A_X - A_{\neg X}.
\end{split}
\end{equation}
\begin{math} w_i \end{math} is merely a specific type of \begin{math} X \end{math}:
\begin{equation}\label{changeinU}
\Delta U(w_i) \equiv A_{w_i} - A_{\neg w_i}.
\end{equation}
But what exactly does \begin{math} \neg w_i \end{math} mean?
\paragraph{Definition:}\begin{math} \neg w_i \end{math} refers to the state in which the person who would have led \begin{math} w_i \end{math} does not exist.\footnote{As usual, this definition is arbitrary, serving only to provide a common reference point for comparisons. All that matters is the change in \begin{math} U \end{math}, so any reference point would do. This one, however, seems most natural. In addition, it makes easier the analysis of whether a person ought to continue living when he chooses lifestyle \begin{math} w_i \end{math}: his life is justified if and only if \begin{math}\Delta U(w_i) \geq 0 \end{math}.} George Bailey saw the state of his town under his own \begin{math} \neg w_i \end{math} in the climactic scene of \textit{It's a Wonderful Life}.
\paragraph{Definition:} \begin{math} A_{w_i} \end{math} and \begin{math} A_{\neg w_i} \end{math} can be divided into components:
\begin{equation}\label{identity1}
\begin{split}
A_{w_i} &:= J_{w_i} + D_{w_i} + F_{w_i} + C_{w_i} + O_{w_i} + R_{w_i},\\
A_{\neg w_i} &:= J_{\neg w_i} + D_{\neg w_i} + F_{\neg w_i} + C_{\neg w_i} + O_{\neg w_i} + R_{\neg w_i}.
\end{split}
\end{equation}
\begin{center}
\begin{tabular}{|c|c|}
\hline
This symbol & represents the component of \begin{math} A \end{math} related to\\
\hline
\begin{math} J \end{math} & direct work at a job.\\
\begin{math} D \end{math} & donation of wealth.\\
\begin{math} F \end{math} & free-time advocacy.\\
\begin{math} C \end{math} & personal consumption (of food, energy, etc.)\\
\begin{math} O \end{math} & influence on other people.\\
\begin{math} R \end{math} & everything else not mentioned above.\\
\hline
\end{tabular}
\end{center}
\begin{math} R \end{math} is a ``residual" term that makes the expressions in \eqref{identity1} identities.
Substituting \eqref{identity1} into \eqref{changeinU},
\begin{equation*}
\begin{split}
\Delta U(w_i)& \equiv (J_{w_i} + D_{w_i} + F_{w_i} + C_{w_i} + O_{w_i} + R_{w_i})\\
& - (J_{\neg w_i} + D_{\neg w_i} + F_{\neg w_i} + C_{\neg w_i} + O_{\neg w_i} + R_{\neg w_i}).
\end{split}
\end{equation*}
\begin{equation}\label{main}
\boxed{\begin{split}
\Delta U(w_i)& \equiv (J_{w_i} - J_{\neg w_i}) + (D_{w_i} - D_{\neg w_i}) + (F_{w_i} - F_{\neg w_i})\\
& + (C_{w_i} - C_{\neg w_i}) + (O_{w_i} - O_{\neg w_i}) + (R_{w_i} - R_{\neg w_i}).
\end{split}}
\end{equation}
\section{Applications}
It is often assumed that the jobs that make the biggest difference are those in which one works directly for one's goals---\textit{e.g.}, employment with a nonprofit, charity, or advocacy organization. One \textit{Wall Street Journal} article reflected this common perception in its title: ``Social Principle vs. High Salary: Reconciling Ideals with Financial Goals Can Be a Struggle for Some in Their 20s" \cite{wsj}.
However, \eqref{main} should at least make one think twice about this assumption. The impact that person Y's job makes is not just \begin{math} J_{w_i} \end{math} but \begin{math} J_{w_i} - J_{\neg w_i} \end{math}. \begin{math} J_{w_i} \end{math} represents the effect of the direct work that Y does himself: organizing citizen-lobbying groups, writing op-ed pieces, and coordinating advocacy campaigns. \begin{math} J_{\neg w_i} \end{math} represents what would have happened otherwise. Especially if Y works for an established organization, it's likely that someone else---call her person Z---would have been hired in his place using the resources that the organization had previously devoted to him. Z would have done similar advocacy work, so \begin{math} J_{\neg w_i} \end{math}---the effect of Z's efforts---would have been something close to \begin{math} J_{w_i} \end{math}. If, in general, Z would have been no less effective than Y, then \begin{math} J_{w_i} - J_{\neg w_i} \end{math} would have an expected value of 0.
Consider also second term of \eqref{main}, \begin{math} D_{w_i} - D_{\neg w_i} \end{math}. Section \ref{dollarworth}, ``How Much Is a Dollar Worth? The Case of Vegan Outreach" made it clear that a conscientious utilitarian will strive to live as frugally as possible and donate his remaining income toward cost-effective projects. \begin{math} D_{w_i} \end{math} represents the effect of person Q's donation of money. \begin{math} D_{\neg w_i} \end{math} is the effect of the donations that would only have taken place had Q not existed. Unlike \begin{math} J_{\neg w_i} \end{math}, \begin{math} D_{\neg w_i} \end{math} is probably very small (how many people are going to not donate money only because you exist and are donating money?). Meanwhile, \begin{math} D_{w_i} \end{math} might be very large.
\paragraph{Example:}Q works on Wall Street and earns \$175,000 annually. Suppose his costs of living are \$25,000 a year. If he donates his money immediately, he gives away \$150,000 per year. Q finds three people who want to spend their time on utilitarian advocacy if only they can get money to support themselves in the process. Q gives them each \$50,000 in return for their documented progress toward utilitarian objectives.\footnote{A good example of such a person would be Henry Spira, the late animal-welfare activist. Spira was himself partially funded in this way:
\begin{quote}
In addition to the \$500 a month he receives from his retirement fund and---after he turned sixty-five---his social security payments, he pays himself \$15,000 a year from Animal Rights International and reimburses himself for up to \$4,800 worth of expenses annually. Luckily, he doesn�t need to spend time raising money for his efforts because he has attracted the support of a small number of people who are prepared to make substantial donations to Animal Rights International. [\ldots One of his supporters, Helaine Lerner] finds it much more effective [contributing to Henry] than giving funding to large organizations, where the money ``can go down a deep hole and you never know what the results of it are." \cite[pp. 115-16]{spira}
\end{quote}
} Thus, in some sense, Q has tripled his effect relative to what he could have accomplished by working directly on utilitarian advocacy. Also note that---unlike Y, who worked for an established organization---all three of Q's employees engage in work that \textit{wouldn't otherwise have taken place}.
\begin{quote}
Many activists view money and wealth as evil. As a source of power, money can be used to promote either evil or good. Just think how much better the animals would be if vegans had significant amounts of money. If each vegan had enough money to buy and distribute multiple copies of educational materials, the animals would greatly benefit. Someone who works a job that isn�t directly promoting animal rights, but who can use their money to fund the resources needed by our movement, will be doing much to help the animals. \cite{norris}
\end{quote}
\begin{flushleft}
\begin{thebibliography}{widest-label}
\bibitem{norris}Norris, Jack. ``Thoughts about Nature, Progress, Careers, and Money." \textit{Vegan Outreach}. 10 June 2006 (\url{http://www.veganoutreach.org/articles/nonveganworld.html}).
\bibitem{spira}Singer, Peter. \textit{Ethics into Action: Henry Spira and the Animal Rights Movement}. Lanham: Rowman \& Littlefield, 2000.
\bibitem{wsj}Waldman, Adelle. ``Social Principle vs. High Salary: Reconciling Ideals with Financial Goals Can Be a Struggle for Some in Their 20s." \textit{Wall Street Journal} 3 May 2005. \textit{Idealist.org: Action without Borders}. 29 Dec. 2005 (\url{http://www.idealist.org/about/press/actone_ideals.pdf}).
\end{thebibliography}
\end{flushleft}
\end{document}