1. Introduction
Chung (Reference Chung2023) purports to derive conditions under which a Utilitarian principle of justice Pareto dominates Rawls’s difference principle – that is, conditions under which all members of society attain higher welfare under Utilitarianism than under the difference principle. Chung’s strategy is to construct a model of economic production and redistributive taxation and compare individuals’ welfare under competing assumptions: first, that the income tax rate is chosen to maximize total welfare (i.e. a Utilitarian society); second, that the tax rate is chosen to maximize the income of the least advantaged members of society (i.e. a Rawlsian society).Footnote 1 Using this model, he purports to show that when the wage premium paid to more advantaged members of society is high enough, all members of society attain higher welfare in a Utilitarian society.
The basic setup of the model is sensible enough: the government in each society sets the income tax rate to achieve its goal and, given this tax rate, individuals in society choose to allocate their time between work and leisure. Workers are divided into two groups: MAG (the most advantaged group) and LAG (the least advantaged group), with members of MAG receiving a higher wage than members of LAG for the same amount of work. The income tax is purely redistributive: only members of MAG are taxed, with members of LAG receiving the proceeds.
Early in Chung’s analysis of the model, however, we find a reason to question the plausibility of his dominance result: LAG individuals’ income is unaffected by the tax rate. How could every individual prefer the Utilitarian society to the Rawlsian society when the Rawlsian government can achieve its objective using any tax rate, including (presumably) the Utilitarian tax rate? Well, maybe not any tax rate. A Rawlsian government doesn’t seek to maximize LAG individuals’ income specifically; it seeks to maximize the lowest income. So it can’t achieve its objective using a tax rate that pushes MAG individuals’ income below LAG individuals’ (fixed) income. Plausibly, though, the rate that maximizes total welfare doesn’t do this. If that’s right, then the Rawlsian government can achieve its objective using the Utilitarian tax rate. But then the Utilitarian society can’t Pareto dominate the Rawlsian society since the latter can produce the same welfare outcomes as the former.
Let’s work through the details to confirm this thought. In the Corollary of Proposition 1, Chung establishes that, given the setup of the model, individuals in LAG have the same income regardless of the tax rate, namely,
$x_L^{\rm{*}}\left( t \right) = {1 \over 4}$
.Footnote
2
Given that the tax rate does not affect LAG individuals’ income, the Rawlsian government can maximize the lowest income using any tax rate that does not leave individuals in MAG with a lower income than individuals in LAG. Chung derives this upper bound in Proposition 3, the proof of which shows that
$$x^*_M \lt x^*_L \text{if (and only if) } t \gt {{\beta -1} \over {\beta}}.$$
(
$\beta $
is the “wage premium” received by individuals in MAG, who earn
$\beta \gt 1$
times more than individuals in LAG per unit time spent working.) Thus, the Rawlsian government can achieve its objective using any rate
$t \le {{\beta - 1} \over \beta }$
.
Chung’s Proposition 2 establishes that the Utilitarian tax rate – the rate that maximizes total social welfare – is
$t_U^{\rm{*}} = {{\beta - 1} \over {2\beta }}$
. Crucially for our purposes,
$t_U^{\rm{*}} \lt {{\beta - 1} \over \beta }$
for all
$\beta \gt 1$
. Thus, the Rawlsian government can maximize the lowest income using the Utilitarian tax rate, thereby achieving its objective while producing the same welfare outcomes as the Utilitarian government. But then the scenarios are equivalent and, so, neither Pareto dominates the other.
So how does Chung arrive at his dominance result? By assuming that the Rawlsian government uses an inefficient tax rate when it could do otherwise. To be more precise, let
$t_R^{\rm{*}}$
denote the Rawlsian government’s tax rate. Chung assumes
$t_R^{\rm{*}} = {{\beta - 1} \over \beta }$
to calculate the welfare outcomes produced by the Rawlsian society. But his proof shows that
$t_R^{\rm{*}}$
could have been any
$t \le {{\beta - 1} \over \beta }$
. Since
$t_U^{\rm{*}} \lt {{\beta - 1} \over \beta }$
, he could have assumed
$t_R^{\rm{*}} = t_U^{\rm{*}} = {{\beta - 1} \over {2\beta }}$
. More in the spirit of Rawls’s theory, he could have assumed
$t_R^{\rm{*}} = 0.5$
, the tax rate that maximizes both the income and the welfare of individuals in LAG (which is simply a function of two social goods, income and leisure).Footnote
3
This rate is less than
${{\beta - 1} \over \beta }$
for all
$\beta \gt 2$
and, thus, consistent with Chung’s constraint on
$t_R^{\rm{*}}$
. Still assuming
$\beta \gt 2$
, the scenario in which
$t_R^{\rm{*}} = 0.5$
is also preferred by all individuals to the scenario in which
$t_R^{\rm{*}} = {{\beta - 1} \over \beta }$
. If, however, we assume the Rawlsian government uses
$t_R^{\rm{*}} = 0.5$
, neither the Utilitarian nor the Rawlsian scenario dominates the other. Thus, Chung’s dominance result is an artefact of assuming that the Rawlsian government uses an inefficient tax rate when he could have assumed otherwise.
2. A Deeper Problem
Chung could weaken his result to say that Rawls’s difference principle is consistent with choosing a tax rate that leads to an outcome that is Pareto dominated by Utilitarianism. It’s not clear why we should worry about this possibility, given that the Rawlsian government can avoid it. But, in any case, Chung’s analysis faces a deeper problem: his derivation of the Utilitarian and Rawlsian tax rates violates his assumption that individuals must choose a non-negative amount of labour. Once we enforce this assumption, the dominance result falls apart: for all
$\beta \gt 1$
, MAG individuals prefer the Utilitarian society and LAG individuals prefer the Rawlsian society.
In the model setup, Chung says that individuals must choose an amount of labour
$L \in \left[ {0,T} \right]$
, which is to say: not less than zero and not more than some maximum amount
$T$
(which is assumed to be greater than
${\beta \over 4}$
). According to his Proposition 1, individuals in MAG and LAG choose their amount of labour according to the following optimal labour functions:
$$L_M^{\rm{*}}\left( t \right) = {{\beta \left( {1 - t} \right)} \over 4}\hskip4pc L_L^{\rm{*}}\left( t \right) = {{1 - {\beta ^2}t\left( {1 - t} \right)} \over 4}$$
We can see that
$L_M^{\rm{*}} \ge 0$
for any
$t \in \left[ {0,1} \right]$
. But this is not true for
$L_L^{\rm{*}}$
. Take two examples:
-
• Assume
$\beta = 3.1$
and
$t = t_U^{\rm{*}} = {{\beta - 1} \over {2\beta }}$
; then
$L_L^{\rm{*}} \approx - 0.29$
. Likewise, if
$\beta = 3.1$
and
$t = t_R^{\rm{*}} = {{\beta - 1} \over \beta }$
, then
$L_L^{\rm{*}} = - 0.275$
. -
• Assume
$\beta = 3.5$
while using the same tax rates; then
$L_L^{\rm{*}} \approx - 0.45$
under
$t_U^{\rm{*}}$
and
$L_L^{\rm{*}} = - 0.375$
under
$t_R^{\rm{*}}$
.
Notice that
$L_L^{\rm{*}}\left( {t_U^{\rm{*}}} \right) \lt L_L^{\rm{*}}\left( {t_R^{\rm{*}}} \right) \lt 0$
for both values of
$\beta $
.
What’s the significance of these examples? Recall that Chung’s proof of his dominance result assumes that
$\beta \ge 3$
. Our two examples thus fit within the scope of the proof: these are cases in which Chung says all individuals – in particular, the individuals in LAG – prefer the Utilitarian society to the Rawlsian society. But his welfare calculations for these cases assume that individuals in LAG choose negative amounts of labour, contrary to his assumption of non-negative labour. Holding income fixed, any positive amount of labour decreases an individual’s welfare (by decreasing their leisure time); by the same reasoning, any negative amount of labour increases their welfare by entering Chung’s welfare calculations as additional leisure time (see the expression in footnote 1). Since LAG individuals’ income is the same across all scenarios, differences in welfare must be due to differences in leisure time. In our examples, the Utilitarian tax rate induces individuals in LAG to choose more negative labour, thus crediting them with greater leisure and, in turn, higher welfare.
We can be more systematic about this. We start by observing that
$$\matrix{ {L_L^{\rm{*}}\left( {t_U^{\rm{*}} = {{\beta - 1} \over {2\beta }}} \right)\lt0 \Leftrightarrow \beta \gt \sqrt 5} \cr {L_L^{\rm{*}}\left( {t_R^{\rm{*}} = {{\beta - 1} \over \beta }} \right)} \lt0 \Leftrightarrow \beta \gt 2 \cr }$$
Since
$2 \lt \sqrt 5 \lt 3$
, individuals in LAG always choose a negative amount of labour in the set of scenarios for which Chung says the Utilitarian society dominates the Rawlsian society. Next, we observe that
$$\matrix{ {L_L^{\rm{*}}\left( {t_U^{\rm{*}} = {{\beta - 1} \over {2\beta }}} \right)} \hfill & \hskip-1pc { \lt L_L^{\rm{*}}\left( {t_R^{\rm{*}} = {{\beta - 1} \over \beta }} \right)} \hfill \cr \hskip3.5pc{ \Leftrightarrow \beta } \hfill & \hskip-1pc { \gt 3\; ({\rm{or\; }}\beta \lt 1,{\rm{\ which\ is\;excluded\;by\;assumption}}).} \hfill \cr }$$
So when
$\beta \gt 3$
, individuals in LAG work less under the Utilitarian tax rate than they do under Chung’s assumed Rawlsian tax rate
$( {t_R^{\rm{*}} = {{\beta - 1} \over \beta }} )$
. Combining these two observations: when
$\beta \gt 3$
, the leisure time conjured from negative labour and credited to LAG individuals is greater in Chung’s Utilitarian welfare calculation than in his Rawlsian welfare calculation. So Chung’s proof of the dominance result artificially inflates LAG individuals’ leisure time in the Utilitarian scenario by allowing them to choose “negative labour”.
Can Chung rescue the result by simply allowing negative labour? To do this, he might conceptualize “negative labour” as labour performed to one’s benefit by another person. If he takes this route, however, he would need to model the welfare consequences of such “negative labour”; in particular, he would need to explicitly model both the costs and benefits of purchasing someone else’s labour. If we are to make sense of the result, it is not enough to simply abandon his assumption that
$L_i^{\rm{*}} \ge 0$
.
Can we recover Chung’s dominance result if we enforce his non-negative labour assumption? We start by deriving the Utilitarian and Rawlsian tax rates assuming that individuals in LAG choose zero labour; once we have these tax rates, we then discharge our assumption by confirming that LAG individuals would optimally choose zero labour as a best response to these tax rates.Footnote 4 (Keep in mind that Chung compares the welfare of the two scenarios assuming that all parties choose equilibrium strategies in a game.) We then compare the welfare outcomes for these equilibria.
We can see in expression (2) (above) that
$L_M^{\rm{*}} \ge 0$
for all
$t \in \left[ {0,1} \right]$
. But we must re-specify
$L_L^{\rm{*}}\left( t \right)$
to ensure that it is non-negative. We start by observingFootnote
5
that
$L_L^{\rm{*}}\left( t \right) \le 0$
if and only if
$\beta \ge 2$
and
$t \in \left[ {\underline t}, { \overline t} \,\right]$
, with
$${\underline t}\equiv {1 \over 2}\left( {1 - \sqrt {1 - {4 \over {{\beta ^2}}}} } \right)\qquad{\overline t} \equiv {1 \over 2}\left( {1 + \sqrt {1 - {4 \over {{\beta ^2}}}} } \right)$$
We can use this observation to respecify LAG individuals’ optimal labour function:
$$L_L^{\rm{*}}\left( t \right) = \left\{ {\matrix{ 0 \hfill & {{\rm{if\;}}\beta \ge 2{\rm{\;and\;}}t \in \left[ {\underline t},{\overline t} \,\right]} \hfill \cr {{{1 - {\beta ^2}t\left( {1 - t} \right)} \over 4}} \hfill & {{\rm{otherwise}}} \hfill \cr } } \right.$$
The Rawlsian government chooses a tax rate to maximize LAG individuals’ income subject to the constraint that it is not greater than MAG individuals’ income. Given our assumption that
$L_L^{\rm{*}} = 0$
, LAG individuals’ income will simply be whatever they get from the redistributive transfer:
$$x_L^{\rm{*}}\left( t \right) = {{{\beta ^2}t\left( {1 - t} \right)} \over 4}.$$
This is at its maximum when
$t = 0.5$
. We now check whether
$t = 0.5$
pushes MAG individuals’ income below that of LAG individuals. Recalling that
$x_M^{\rm{*}}\left( t \right) = {{{\beta ^2}{{(1 - t)}^2}} \over 4}$
, we have
So, for
$t = 0.5$
, the Rawlsian government maximizes LAG individuals’ income, and this is equal to MAG individuals’ income.
Finally, we check that LAG individuals’ optimal response to
$t = 0.5$
is zero labour. Given expression (6), LAG individuals choose zero labour if
$\beta \ge 2$
and
$t \in \left[ {\underline t},{\overline t}\, \right]$
. Given expression (5), we can see that
${\underline t} = {\overline t} = 0.5$
when
$\beta = 2$
. So
$L_L^{\rm{*}}\left( {t = 0.5} \right) = 0$
when
$\beta = 2$
. What’s more,
$\underline t $
converges to zero and
${\overline t}$
converges to 1 as
$\beta $
increases; thus,
$0.5 \in \left[ {\underline t}, {\overline t} \right]$
for all
$\beta \ge 2$
, which implies that LAG individuals optimally choose zero labour given
$t = 0.5$
.
Thus, if
$\beta \ge 2$
, we have the following (unique) Rawlsian equilibrium: the government chooses
$t_R^{\rm{*}} = 0.5$
; MAG individuals choose
$L_M^{\rm{*}} = {{\beta \left( {1 - 0.5} \right)} \over 4}$
; and LAG individuals choose
$L_L^{\rm{*}} = 0$
. Given this equilibrium, we can calculate individuals’ welfare under the Rawlsian tax rate:
$$T{W_M}\left( {t = t_R^{\rm{*}}} \right) = {\beta \over 8} + T$$
$$T{W_L}\left( { t = t_R^{\rm{*}}} \right) = {\beta \over 4} + T$$
Turning now to the Utilitarian scenario, the government chooses the tax rate that maximizes total welfare. Assuming again that
$L_L^{\rm{*}} = 0$
(and
$L_M^{\rm{*}} = {{\beta \left( {1 - t} \right)} \over 4}$
), the Utilitarian solvesFootnote
6
$$\matrix{ {\mathop {{\rm{max}}}\limits_t {\rm{\;\;}}} \hfill & \hskip-1pc {TW\left( t \right) = \left[ {T{W_M}\left( t \right) + T{W_L}\left( t \right)} \right]} \hfill \cr {} \hfill & { \Rightarrow \mathop {{\rm{max}}}\limits_t \left[ {\sqrt {{{{\beta ^2}{{(1 - t)}^2}} \over 4}} + T - {{\beta \left( {1 - t} \right)} \over 4} + \sqrt {{{{\beta ^2}t\left( {1 - t} \right)} \over 4}} + T - 0} \right].} \hfill \cr } $$
Solving this gives the first-order condition
$${{\beta \left( {1 - 2t} \right)} \over {\sqrt {\left( {1 - t} \right)t} }} - \beta = 0.$$
This is equivalent to
$$\left( {1 - 2t} \right) = \sqrt {\left( {1 - t} \right)t}, \;\;\;{\rm{which}}\;{\rm{implies}}\;t = {1 \over {10}}\left( {5 - \sqrt 5 } \right).$$
So
$t_U^{\rm{*}} = {1 \over {10}}\left( {5 - \sqrt 5 } \right)$
if
$L_L^{\rm{*}} = 0$
and
$L_M^{\rm{*}} = {{\beta \left( {1 - t} \right)} \over 4}$
.
To complete the analysis, we check whether
$L_L^{\rm{*}} = 0$
if
$t_U^{\rm{*}} = {1 \over {10}}\left( {5 - \sqrt 5 } \right)$
by checking whether
$t_U^{\rm{*}} \in \left[ {\underline t}, {\overline t} \right]$
. (Recall: we know that
$L_M^{\rm{*}} = {{\beta \left( {1 - t} \right)} \over 4} \ge 0$
for any
$t$
.)
$$\matrix{ {{1 \over {10}}\left( {5 - \sqrt 5 } \right)} \hfill & \hskip-1pc { \ge \underline t = {1 \over 2}\left( {1 - \sqrt {1 - \displaystyle{4 \over {{\beta ^2}}}} } \right) \Leftrightarrow \beta \ge \sqrt 5 } \hfill \cr {{1 \over {10}}\left( {5 - \sqrt 5 } \right)} \hfill & \hskip-1pc { \le {\overline t} = {1 \over 2}\left( {1 + \sqrt {1 - \displaystyle{4 \over {{\beta ^2}}}} } \right) \Leftrightarrow \beta \ge 2} \hfill \cr }$$
In words, if
$\beta \ge \sqrt 5 $
, LAG individuals optimally choose zero labour given
$t_U^{\rm{*}} = {1 \over {10}}\left( {5 - \sqrt 5 } \right)$
.
Thus, if
$\beta \ge \sqrt 5 $
, we have the following (unique) Utilitarian equilibrium: the government chooses
$t_U^{\rm{*}} = {1 \over {10}}\left( {5 - \sqrt 5 } \right)$
;
$L_M^{\rm{*}} = {{\beta \left( {1 - t_U^{\rm{*}}} \right)} \over 4}$
;
$L_L^{\rm{*}} = 0$
. Given this equilibrium, the players’ welfare under Utilitarianism is
$$\matrix{ {T{W_M}\left( {t = t_U^{\rm{*}}} \right)} & \displaystyle \hskip-0.7pc { = {\beta \over {40}}\left( {5 + \sqrt 5 } \right) + T} \cr {T{W_L}\left( {t = t_U^{\rm{*}}} \right)} \hfill & \displaystyle\hskip-0.7pc { = {\beta \over {2\sqrt 5 }} + T.} \cr } $$
Let’s now compare individuals’ welfare in the two equilibrium scenarios.
$$\quad \; \; T{W_M}\left( {t_U^{\rm{*}}} \right) \gt T{W_M}\left( {t_R^{\rm{*}}} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\quad \;T{W_L}\left( {t_U^{\rm{*}}} \right) \lt T{W_L}\left( {t_R^{\rm{*}}} \right)\quad\quad$$
$${\beta \over 8} + {{\beta \sqrt 5 } \over {40}} + T \gt {\beta \over 8} + T\;\quad\qquad\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\beta \over {2\sqrt 5 }} + T \lt {\beta \over 4} + T\quad\qquad$$
$$\quad\;\beta \gt 0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\beta \gt 0\quad $$
Since
$\beta \gt 1$
by assumption, MAG individuals prefer the Utilitarian scenario while LAG individuals prefer the Rawlsian scenario. Thus, neither society dominates assuming
$\beta \ge \sqrt 5 $
. This is contrary to Chung’s headline result (which, recall, assumes
$\beta \ge 3 \gt \sqrt 5 $
).
We’re not finished yet. Our analysis of the Rawlsian society holds for all
$\beta \ge 2$
. However, our analysis of the Utilitarian society does not hold if
$\beta \lt \sqrt 5 $
:
$t_U^{\rm{*}}$
was derived assuming
$L_L^{\rm{*}}\left( {t_U^{\rm{*}}} \right) = 0$
; yet, given expression (6),
$L_L^{\rm{*}}\left( t \right) \gt 0$
if
$t_U^{\rm{*}} \lt \underline t $
, and the latter is true if
$\beta \lt \sqrt 5 $
. So our above welfare comparison doesn’t hold when
$2 \lt \beta \lt \sqrt 5 $
, and we need to check whether either society dominates under this assumption. (Chung’s analysis correctly implies that neither society dominates if
$1 \lt \beta \le 2$
.)
Our analysis of the Rawlsian society carries over, but we need to redo our analysis of the Utilitarian society assuming
$2 \lt \beta \lt \sqrt 5 $
.
$L_M^{\rm{*}}\left( t \right)$
remains as in expression (2).
Per expression (6), assume
$$L_L^{\rm{*}}\left( t \right) = {{1 - {\beta ^2}t\left( {1 - t} \right)} \over 4} \gt 0.$$
Following Chung’s Proposition 2,
$t_U^{\rm{*}} = {{\beta - 1} \over {2\beta }}$
. We now check that
$L_L^{\rm{*}} \ge 0$
given
$t_U^{\rm{*}} = {{\beta - 1} \over {2\beta }}$
.
$${{1 - {\beta ^2}t_U^{\rm{*}}\left( {1 - t_U^{\rm{*}}} \right)} \over 4} \le 0 \Leftrightarrow \beta \ge \sqrt 5 $$
Since we are assuming
$\beta \lt \sqrt 5 $
,
$L_L^{\rm{*}}\left( {t_U^{\rm{*}} = {{\beta - 1} \over {2\beta }}} \right) \gt 0$
. The welfare implications of Utilitarianism are thus as Chung derives in the Corollary to his Proposition 2 and, in turn, his proof of Proposition 4:
$$\matrix{ {T{W_M}\left( {t_U^{\rm{*}} = \displaystyle{{\beta - 1} \over {2\beta }}} \right)} \hfill & \hskip-0.7pc { = \sqrt {\displaystyle{{{\beta ^2}{{(1 - t_U^{\rm{*}})}^2}} \over \displaystyle 4}} + T - \displaystyle{{\beta \left( {1 - t_U^{\rm{*}}} \right)} \over 4} = {\displaystyle{\beta + 1} \over 8} + T} \hfill \cr {T{W_L}\left( {t_U^{\rm{*}} = \displaystyle{{\beta - 1} \over {2\beta }}} \right)} \hfill & \hskip-0.7pc { = \displaystyle\sqrt {{1 \over 4}} + T - {\displaystyle{1 - {\beta ^2}t_U^{\rm{*}}\left( {1 - t_U^{\rm{*}}} \right)} \over \displaystyle 4} = {{{\beta ^2} + 3} \over {16}} + T} \hfill \cr } $$
The individuals’ welfare under the difference principle are as above; reiterating for ease of reference:
$$T{W_M}(t = t_R^{\rm{*}} = 0.5) = {\beta \over 8} + T\;\;\;\;\;\;\;\;\;\;T{W_L}\left( {t = t_R^{\rm{*}} = 0.5} \right) = {\beta \over 4} + T$$
Now the comparison between the two:
$$\ \ \ \quad \quad T{W_M}\left( {t_U^{\rm{*}}} \right) \gt T{W_M}\left( {t_R^{\rm{*}}} \right)\quad\quad\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;T{W_L}\left( {t_U^{\rm{*}}} \right) \lt T{W_L}\left( {t_R^{\rm{*}}} \right)\ \quad\ $$
$${{\beta + 1} \over 8} + T \gt {\beta \over 8} + T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{{{\beta ^2} + 3} \over {16}} + T \lt {\beta \over 4} + T$$
$$\beta \in {\mathbb R}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;1 \lt \beta \lt 3$$
Thus, MAG individuals prefer the Utilitarian society for any
$\beta $
, while LAG individuals prefer the Rawlsian scenario for any
$1 \lt \beta \lt 3$
. So neither society Pareto dominates assuming
$2 \lt \beta \lt \sqrt 5 $
.
Chung’s proof for his Proposition 4 correctly shows that neither society dominates assuming
$1 \lt \beta \le 2$
. Together with our analyses above, it follows – contrary to Chung’s analysis – that neither society dominates in Chung’s model for any
$\beta \gt 1$
.
Acknowledgements
Ryuto Shibata gratefully acknowledges that this project began with a guest lecture by Professor Hun Chung on January 11, 2023, as part of Professor Akira Inoue’s graduate seminar at the University of Tokyo. He thanks Professors Chung and Inoue for their feedback on earlier drafts, as well as participants at the Online Political Theory Forum (March 2023), Inoue’s seminar (May 2023), and the Japan Forum for Young Philosophers (July 2024). He is especially grateful to Susumu Cato, Thomas Pölzler, Ko Harada, and Haruki Yamane for their insightful comments. David Wiens thanks Hun Chung for helpful discussion of his article. Both authors thank Editor Itai Sher for his guidance and the two anonymous reviewers for their persistence, patience, and generosity.
Financial support
Ryuto Shibata’s research was supported by the Japan Science and Technology Agency (JST) under the SPRING program (Grant Number JPMJSP2108), and by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for JSPS Fellows (Grant Number 24KJ0654).
Authors’ contributions
Both authors contributed to the development of the ideas and the writing of the manuscript. Shibata and Wiens independently wrote critical notes on Chung (2023) that had substantially overlapping content. Aware of this, Itai Sher suggested they come together to collaborate on a revision of Shibata’s previous submission.
Ryuto Shibata is a doctoral student at University of Tokyo. His research focus on political philosophy and economic theory, especially on formulating a theory of rights of risky action and on policy evaluation framework under uncertainty and risk. He is currently writing a dissertation on risk and rights in political philosophy.
David Wiens is Associate Professor of Political Science and Faculty Affiliate in Philosophy at the University of California, San Diego. He has published numerous articles on methodology in political theory and related topics in journals such as American Journal of Political Science, Journal of Politics, Philosophy and Phenomenological Research, Philosophy and Public Affairs and Politics, Philosophy, and Economics. He is the author of From the Best to the Rest: Idealistic Thinking in a Non-Ideal World (Oxford University Press).
