The merging process starts by shrinking a bit $B_2$ and surrounding what remains by $B_3$ so that $B_2$ is now a closed ball within what was previously $B_2$ while $B_3$ is homeomorphic to $\mathbb{S}^2 \times \mathbb{S}^1$.
On $\Sigma$, the edges that came from $D = B_1 \cap B_2$ are thus now replaced by thin bands belonging to the transformed $B_3$ with two copies of each edge as boundaries of the bands. We assume the shrinking to be small enough so that the copied edges intersect $G$ the same way the original edges do: this is always possible because the double bubble is transverse to $G$ and the vertices of $G$ have been thickened. It follows that one face of $\Gamma$ is now $B_3 \cap \Sigma$, which is $\Sigma$ with as many boundaries as there are connected components in $(B_2 \cup B_1) \cap \Sigma$ (see the unfolded torus on the right of the second row compared to the one on the right of the first row in Figure <ref>). All the other faces of $\Gamma$ are now disks whose boundaries consist of edges with $B_3$.

We now pick an arbitrary vertex $v$ of $MT(D)$ and connect $B_1$ with $B_2$ by a small solid cylinder disjoint from $\Sigma$ whose ends are glued on $B_1$ and $B_2$ in the face indicated by $v$. This new ball is denoted by $B_{1,2}$. This step can be seen on the second row of Figure <ref>.

For $e$ an edge of $MT(D)$ adjacent to $v$, we then grow this cylinder so that it entirely covers $e$. This amounts to connecting the surfaces of $\Sigma \cap B_{1,2}$ (intuitively, the bands between the copies of edges disappear, see the right column of Figure <ref>). Indeed, when the edge $e$ of $MT(D)$ is covered by the growing cylinder, the two surfaces containing the initial disks of $B_1$ and $B_2$ incident to $e$ are glued along $e$. This process is then iterated by adding more edges of $MT(D)$, thus growing a subtree of $MT(D)$, until that subtree has fully grown and is $MT(D)$. This is illustrated in the third and four rows of Figure <ref>. Eventually, the whole membrane is covered so that $B_{1,2} = B_1 \cup B_2$

We track the evolution of the ball $B_{1,2}$ during the merging process, which is parameterized by the subtree $T$ of $MT(D)$ that has been merged. This leads to the following merging function $m$:

\begin{equation*}
\begin{array}{cccl}
m : & MT(D)_{\subset} & \rightarrow & \mathcal{P}(\Sigma)\\
& T & \mapsto & B_{1,2} (T) \cap \Sigma
\end{array}
\end{equation*}

where $MT(D)_{\subset}$ is the set of subtrees of $MT(D)$ and $B_{1,2}(T)$ is the closed ball of the merging process parameterized by $T$. By definition, we have that $B_{1,2}(T)$ is contained in $B_1 \cup B_2$, transverse to $\Sigma$, and $B_{1,2}(T) \cap \Sigma = E(T)$.

It will be convenient in the following to define what kind of topology of $\Sigma$ is captured by a closed connected surface $W$ embedded on $\Sigma$. For example, an annulus can be embedded on the torus in two ways: either it contains a non-contractible curve of the torus, or it is $\pi_1$-trivial and contains irrelevant holes.
The following definition aims to “fill” these irrelevant holes. Each contractible boundary component $b$ of $W$ bounds a disk $D_b$ on $\Sigma$. We define $\obullet{W} = W \cup \oper{\bigcup}{b \in C(\partial W) \\ b \text{ contractible}}{}{D_b}$, the filled surface induced by $W$.

It directly follows from the definition that $\partial \obullet{W} \subset \partial W$. It is also worth noticing that if $W$ is $\pi_1$-trivial, then $\obullet{W} = D_b$ for one of the $b$.

We can now finally use all these objects to find a fractional packing of curves in $\Gamma$ with enough weight. Let $T$ be a minimal tree of $MT(D)_{\subset}$ such that $\obullet{m(T)}$ is not a union of disks. Note that such a tree exists, since for $T=MT(D)$, we have $B_{1,2}(T)=B_1\cup B_2$ and thus $\obullet{m(T)}=\Sigma$. Necessarily, the surface $\obullet{m(T)}$ contains exactly one component that is not a disk. Indeed, let $e$ be an edge incident to a leaf of $T$. By minimality of $T$, $\obullet{m(T \smallsetminus e)}$ is a union of disjoint disks. By definition of the merging process, $m(T)$ is $m(T \smallsetminus e)$, where two copies of an edge have been merged back. If these copies were on two different $\pi_1$-trivial surfaces, their merging would have been $\pi_1$-trivial too. Hence the two copies of an edge were on the same disk of $\obullet{m(T \smallsetminus e)}$, so that the merging of $e$ glues together two distinct segments on the boundary of that disk. This operation yields either a Möbius band, which is impossible since $\Sigma$ is orientable, or an annulus $a$.

By definition of $\obullet{m(T)}$, the boundaries of $a$ are non-contractible curves of $\Sigma$.
Lemma <ref> ensures that one of these two curves is compressible. Since they bound an annulus on $\Sigma$, they are homotopic on $\Sigma$ and thus are both compressible. Let us denote them by $b$ and $b'$.

At any stage of the merging process, some edges that were originally in $\Gamma$ are now duplicated. Therefore, while the curves $b$ and $b'$ are simple and disjoint, they might be using some of those duplicated edges of $\Gamma$, but each such edge is used at most twice. Therefore we have, denoting by $X$ the set of edges of $\Gamma$ used by $b$ and $b'$.

\begin{equation*}
\sum_{e \in X} |C(e \cap \Gamma)| \geq  \frac{1}{2} \sum_{e \in b} |C(e \cap \Gamma)| + \frac{1}{2} \sum_{e \in b'} |C(e \cap \Gamma)| \geq 2\cdot \frac{1}{2} \comprep(G,\Sigma),
\end{equation*}

where the last inequality comes from the fact that $b$ and $b'$ are compressible and the definition of $\comprep(G,\Sigma)$. This last inequality concludes the proof.

This proposition directly implies Proposition <ref>, and thus Theorem <ref>:

A compression bubble tangle immediately satisfies the bubble tangle axioms <ref> and <ref> by definition, and <ref> by Lemma <ref>. For the axiom <ref>, assume by contradiction that there exist three closed balls $B_1,B_2,B_3 \in \cT$ covering $\Sp^3$ and inducing a double bubble transverse to $\Sigma$. By Lemma <ref>, we can assume the graph $\Gamma$ induced by the intersection of the double bubble with $\Sigma$ is cellularly embedded. Then by Proposition <ref>, the total weight of $\Gamma$ is at least $\comprep(G,\Sigma)$. This is a contradiction with Lemma <ref>.

§ EXAMPLES

A torus knot $T_{p,q}$ is a knot embedded on a surface of an unknotted torus $\To$ in $\mathbb{S}^3$, for example a standard torus of revolution. It winds $p$ times around the revolution axis, and $q$ times around the core of the torus. We refer to Figure <ref> for an illustration of $T_{6,5}$. We can now combine our results to lower bound the treewidth of any diagram of a torus knot, thus proving Corollary <ref>.

Combining Proposition <ref>, Theorem <ref> and Theorem <ref>, it suffices to lower bound the compression-representativity of $T_{p,q}$ by $\min(p,q)$. The torus $\To$ has two curves which obviously bound compression disks, we prove that there are no other compressible curves. In $\mathbb{S}^3$, the torus $\To$ bounds one solid torus $\mathbb{D}^2 \times \mathbb{S}^1$ on each side, and in a solid torus $S$, exactly one of the homotopy classes of simple closed curves on the boundary is compressible, namely the one in the kernel of the inclusion map $i_*: \pi_1(\To)=\mathbb{Z}^2 \rightarrow \pi_1(S)=\mathbb{Z}$. The result follows by observing that $T_{p,q}$ intersects $p$ times the first of these homotopy classes and $q$ times the other one, and thus has compression representativity $\min(p,q)$.

More generally, the same argument can be applied to lower bound the treewidth of the $(p,q)$-cabling <cit.> of any nontrivial knot. We refer to Ozawa <cit.> for examples of spatial embeddings of any graph with high compression representativity, and thus high spherewidth.

We conclude by observing that the proof of Theorem <ref> offers more flexibility than what the theorem states and can also be applied in some settings where the compression-representativity is low. For example, a connected sum of two knots $K_1 \# K_2$ has compression-representativity two (see <cit.>), but if one these two knots, say $K_1$, has high compression-representativity separately, then we can still define a bubble-tangle of high order by considering as big sides the balls containing the surface that $K_1$ is embedded on.

We would like to thank Pierre Dehornoy and Saul Schleimer for helpful discussions, and the anonymous reviewers for their feedback which allowed us to significantly improve the paper.

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§ COVERING A TORUS WITH THREE DISKS FROM A DOUBLE BUBBLE

[scale = 0.8]
[fill = purple!90! , draw = black] (-4,-3) rectangle (4,3);
ıin 0,1,...,5

(nı) at (60*ı: 2);

[fill = green!60!purple , draw = black] (n0) – (n1) – (n2) – (n3) – (n4) – (n5) – cycle;

[fill = blue!60! , draw = black] (n0) – (4,0) – (4,-2) – (n5) – cycle;
[fill = blue!60! , draw = black] (n3) – (-4,0) – (-4,-2) .. controls +(1.5,-0.25) and (-2,-3)(-0.5,0.5) – (-0.5,-3) – (n4) – cycle;
[fill = blue!60! , draw = black] (n2) – (-2,3) – (-0.5,3) – (n1) – cycle;

Covering a torus with three disks from a double bubble.

A torus can be covered by a double bubble which induces three disks on the torus, as pictured in Figure <ref>. This double bubble is described in Figures <ref>, <ref>, <ref>, <ref> and one can prove that this is up to homeomorphism the only double bubble realizing such a cover.

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[blue] (0,0) – (0,2);

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[dotted, blue] (3,2) –(9,1);

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[red, opacity = 0.4] (3,3.5) – (9, 2.5) – (9,2.8) – (3,3.8) –cycle;
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(7.5,2) – ++(-1.25,0.208) – ++(0.5,0.333) – ++(1.25,-0.208) – cycle;
(7.5,0) – ++(0.5,0.333) – ($(7.5,0.75) +(0.5,0.333)$) – (7.5,0.75) – cycle;

The spheres $S_1$ (blue) and $S_2$ (red) up to thickening the ribbon part.

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[blue!50!red!50!, dotted] (0,0) – (3,2) – (3,4);
[dotted, blue!50!red!50!] (3,2) –(9,1);

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[fill opacity = 0.2, blue] (6,-1) – (9,1) – (9,3) – (6,1);
[fill opacity = 0.2, blue] (0,0) – (6,-1) – (9,1) – (3,2) –cycle;
[fill opacity = 0.2, blue] (0,0) – (3,2) – (3,4) – (0,2) –cycle;
[fill opacity = 0.2, blue] (3,2) – (9,1) – (9,3) – (3,4) –cycle;
[fill opacity = 0.2, blue] (0,2) – (6,1) – (9,3) – (3,4) –cycle;
[blue, dotted] (0,0) – (3,2) – (3,4);
[dotted, blue] (3,2) –(9,1);

[fill = white, opacity = 0.05] (7.5, 0.75) – ++(0.5, 0.333) – ++(0, 0.75) – ++(-0.5, -0.333) – cycle;
[blue, opacity = 0.2] (7.5,0.75) – ++(-1, 0.166) – ++(0,0.75) – ++(1,-0.166) – cycle;
[blue!50!red!50!, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) ++(0,0.75) – ++(0.5,0.333) – ++(1,-0.166) – ++(-0.5,-0.333) – cycle;
[blue!50!red!50!, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) – ++(0.5,0.333) – ++(0,0.75) – ++(-0.5,-0.333) – cycle;
[blue!50!red!50!, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) – ++(1,-0.166) – ++(0.5,0.333) – ++(-1,0.166) – cycle;
[blue, opacity = 0.2] (7.5,0.75) ++(0.5, 0.333) – ++(-1, 0.166) – ++(0,0.75) – ++(1,-0.166) – cycle;

[blue] (7.5, 0.75) – ++(0.5, 0.333) – ++(0, 0.75) – ++(-0.5, -0.333) – cycle;
[blue, dotted, thick] (7.5,0.75) – ++(-1, 0.166) – ++(0,0.75) – ++(1,-0.166);
[blue, dotted, thick] (7.5,0.75) ++(-1, 0.166) ++(0,0.75) – ++(0.5,0.333) – ++(1,-0.166);
[blue, dotted, thick] (7.5,0.75) ++(-1, 0.166) – ++(0.5,0.333) – ++(1,-0.166);
[blue, dotted, thick] (7.5,0.75) ++(-1, 0.166) ++(0.5,0.333) – ++(0,0.75);

[red, opacity = 0.2]
(7.5,0.75) ++(-1, 0.166) ++(0,0.75) – ++(0.5,0.333) – ++(1,-0.166) – ++(-0.5,-0.333) – cycle;
(7.5,0.75) ++(-1, 0.166) – ++(0.5,0.333) – ++(0,0.75) – ++(-0.5,-0.333) – cycle;
(7.5,0.75) ++(-1, 0.166) – ++(1,-0.166) – ++(0.5,0.333) – ++(-1,0.166) – cycle;
(7.5, 0.75) ++(0.5, 0.333) ++(0, 0.75) – ($(6,1) +(2,1.333)$) – ++(-0.5, -0.333) – ++(0,-0.2) – (6,0.8) – (6,0.5) –cycle;
(7.5, 0.75) ++(0,0.75) – ++(0,0.3) – (6,0.8) – (6,0.5) –cycle;
[red, opacity = 0.4] (6,0.5) – (6,0.8) – (0,1.8) – (0,1.5) –cycle;
[red, opacity = 0.4] (0,1.5) – (3,3.5) – (3,3.8) – (0,1.8) –cycle;
[red, opacity = 0.4] (3,3.5) – (9, 2.5) – (9,2.8) – (3,3.8) –cycle;
[red, opacity = 0.4] (9, 2.5) – (8,1.3) – ++(0,0.3) – (9,2.8) –cycle;
(7.5,1.5) – ++(-1,0.166) – ++(0,-0.75) – (7.5,0.75) – (7.5,0) – ++(-1.25,0.208) – ($(7.5,2)+(-1.25,0.208)$) –(7.5,2) –cycle;
[xshift = 0.5cm, yshift = 0.333 cm] (7.5,1.5) – ++(-1,0.166) – ++(0,-0.75) – (7.5,0.75) – (7.5,0) – ++(-1.25,0.208) – ($(7.5,2)+(-1.25,0.208)$) –(7.5,2) –cycle;
(7.5,0) – ++(0.5,0.333) – ++(-1.25,0.208) – ++(0,2) – ++(-0.5,-0.333) – ++(0,-2) – ++(1.25,-0.208) – cycle;
(7.5,2) – ++(-1.25,0.208) – ++(0.5,0.333) – ++(1.25,-0.208) – cycle;
(7.5,0) – ++(0.5,0.333) – ($(7.5,0.75) +(0.5,0.333)$) – (7.5,0.75) – cycle;

The ball $B_1 \cup B_2$ in purple, $B_3$ is the complementary.

[scale = 0.75]
[fill opacity = 0.2, blue] (0,0) – (6,-1) – (6,1) – (0,2) –cycle;
[fill opacity = 0.2, blue] (6,-1) – (9,1) – (9,3) – (6,1);
[fill opacity = 0.2, blue] (0,0) – (6,-1) – (9,1) – (3,2) –cycle;
[fill opacity = 0.2, blue] (0,0) – (3,2) – (3,4) – (0,2) –cycle;
[fill opacity = 0.2, blue] (3,2) – (9,1) – (9,3) – (3,4) –cycle;
[fill opacity = 0.2, blue] (0,2) – (6,1) – (9,3) – (3,4) –cycle;
[blue, dotted] (0,0) – (3,2) – (3,4);
[dotted, blue] (3,2) –(9,1);

[fill = white, opacity = 0.05] (7.5, 0.75) – ++(0.5, 0.333) – ++(0, 0.75) – ++(-0.5, -0.333) – cycle;
[blue, opacity = 0.2] (7.5,0.75) – ++(-1, 0.166) – ++(0,0.75) – ++(1,-0.166) – cycle;
[blue!50!red!50!, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) ++(0,0.75) – ++(0.5,0.333) – ++(1,-0.166) – ++(-0.5,-0.333) – cycle;
[blue!50!red!50!, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) – ++(0.5,0.333) – ++(0,0.75) – ++(-0.5,-0.333) – cycle;
[blue!50!red!50!, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) – ++(1,-0.166) – ++(0.5,0.333) – ++(-1,0.166) – cycle;
[blue, opacity = 0.2] (7.5,0.75) ++(0.5, 0.333) – ++(-1, 0.166) – ++(0,0.75) – ++(1,-0.166) – cycle;

[blue] (7.5, 0.75) – ++(0.5, 0.333) – ++(0, 0.75) – ++(-0.5, -0.333) – cycle;
[blue, dotted, thick] (7.5,0.75) – ++(-1, 0.166) – ++(0,0.75) – ++(1,-0.166);
[blue, dotted, thick] (7.5,0.75) ++(-1, 0.166) ++(0,0.75) – ++(0.5,0.333) – ++(1,-0.166);
[blue, dotted, thick] (7.5,0.75) ++(-1, 0.166) – ++(0.5,0.333) – ++(1,-0.166);
[blue, dotted, thick] (7.5,0.75) ++(-1, 0.166) ++(0.5,0.333) – ++(0,0.75);

[thick, yshift = 0cm]
($(0,0) +(\eps,\eps)$) – ($(6,-1) +(-\eps, \eps)$) – ($(6,1) +(-\eps, -\eps)$) – ($(0,2) +(\eps,-\eps)$) –cycle;
($(6,-1) +(-\eps, \eps)$) – ($(9,1) +(-\eps, \eps)$) – ($(9,3) +(-\eps, -\eps)$) – ($(6,1) +(-\eps, -\eps)$);
($(0,2) +(\eps, -\eps)$) – ($(3,4) +(\eps, -\eps)$) –  ($(9,3) +(-\eps, -\eps)$);
($(0,0) +(\eps, \eps)$) – ($(3,2) +(\eps, \eps)$) – ($(3,4) +(\eps, -\eps)$);
($(3,2) +(\eps, \eps)$) – ($(9,1) +(-\eps, \eps)$);

[thick, yshift = 0cm]
($(1,-0.166) +(\eps,\eps) +(0.5,0.333)$) – ($(5,-0.833) +(-\eps, \eps) +(0.5,0.333)$) – ($(5,1.166) +(-\eps, -\eps) +(0.5,0.333)$) – ($(1,1.833) +(\eps,-\eps) +(0.5,0.333)$) –cycle;
($(5,-0.833) +(-\eps, \eps) +(0.5,0.333)$) – ($(8,1.166) +(-\eps, \eps) +(-0.5,-0.333)$) – ($(8,3.166) +(-\eps, -\eps) +(-0.5,-0.333)$) – ($(5,1.166) +(0.5,0.333) +(-\eps, -\eps)$);
($(1,1.833) +(\eps, -\eps) +(0.5,0.333)$) – ($(4,3.833) +(\eps, -\eps) +(-0.5,-0.333)$) –  ($(8,3.166) +(-\eps, -\eps) +(-0.5,-0.333)$);
($(1,-0.166) +(0.5,0.333) +(\eps, \eps)$) – ($(4,1.833) +(-0.5,-0.333) +(\eps, \eps)$) – ($(4,3.833) +(-0.5,-0.333) +(\eps, -\eps)$);
($(4,1.833) +(-0.5,-0.333) +(\eps, \eps)$) – ($(8,1.166) +(-0.5,-0.333) +(-\eps, \eps)$);

[thick, xshift=9.5cm]
($(0,0) +(\eps,\eps)$) – ($(6,-1) +(-\eps, \eps)$) – ($(6,1) +(-\eps, -\eps)$) – ($(0,2) +(\eps,-\eps)$) –cycle;
($(6,-1) +(-\eps, \eps)$) – ($(9,1) +(-\eps, \eps)$) – ($(9,3) +(-\eps, -\eps)$) – ($(6,1) +(-\eps, -\eps)$);
($(0,2) +(\eps, -\eps)$) – ($(3,4) +(\eps, -\eps)$) –  ($(9,3) +(-\eps, -\eps)$);
($(0,0) +(\eps, \eps)$) – ($(3,2) +(\eps, \eps)$) – ($(3,4) +(\eps, -\eps)$);
($(3,2) +(\eps, \eps)$) – ($(9,1) +(-\eps, \eps)$);

($(1,-0.166) +(\eps,\eps) +(0.5,0.333)$) – ($(5,-0.833) +(-\eps, \eps) +(0.5,0.333)$) – ($(5,1.166) +(-\eps, -\eps) +(0.5,0.333)$) – ($(1,1.833) +(\eps,-\eps) +(0.5,0.333)$) –cycle;
($(5,-0.833) +(-\eps, \eps) +(0.5,0.333)$) – ($(8,1.166) +(-\eps, \eps) +(-0.5,-0.333)$) – ($(8,3.166) +(-\eps, -\eps) +(-0.5,-0.333)$) – ($(5,1.166) +(0.5,0.333) +(-\eps, -\eps)$);
($(1,1.833) +(\eps, -\eps) +(0.5,0.333)$) – ($(4,3.833) +(\eps, -\eps) +(-0.5,-0.333)$) –  ($(8,3.166) +(-\eps, -\eps) +(-0.5,-0.333)$);
($(1,-0.166) +(0.5,0.333) +(\eps, \eps)$) – ($(4,1.833) +(-0.5,-0.333) +(\eps, \eps)$) – ($(4,3.833) +(-0.5,-0.333) +(\eps, -\eps)$);
($(4,1.833) +(-0.5,-0.333) +(\eps, \eps)$) – ($(8,1.166) +(-0.5,-0.333) +(-\eps, \eps)$);

[red, opacity = 0.2]
(7.5,0.75) ++(-1, 0.166) ++(0,0.75) – ++(0.5,0.333) – ++(1,-0.166) – ++(-0.5,-0.333) – cycle;
(7.5,0.75) ++(-1, 0.166) – ++(0.5,0.333) – ++(0,0.75) – ++(-0.5,-0.333) – cycle;
(7.5,0.75) ++(-1, 0.166) – ++(1,-0.166) – ++(0.5,0.333) – ++(-1,0.166) – cycle;
(7.5, 0.75) ++(0.5, 0.333) ++(0, 0.75) – ($(6,1) +(2,1.333)$) – ++(-0.5, -0.333) – ++(0,-0.2) – (6,0.8) – (6,0.5) –cycle;
(7.5, 0.75) ++(0,0.75) – ++(0,0.3) – (6,0.8) – (6,0.5) –cycle;
[red, opacity = 0.4] (6,0.5) – (6,0.8) – (0,1.8) – (0,1.5) –cycle;
[red, opacity = 0.4] (0,1.5) – (3,3.5) – (3,3.8) – (0,1.8) –cycle;
[red, opacity = 0.4] (3,3.5) – (9, 2.5) – (9,2.8) – (3,3.8) –cycle;
[red, opacity = 0.4] (9, 2.5) – (8,1.3) – ++(0,0.3) – (9,2.8) –cycle;
(7.5,1.5) – ++(-1,0.166) – ++(0,-0.75) – (7.5,0.75) – (7.5,0) – ++(-1.25,0.208) – ($(7.5,2)+(-1.25,0.208)$) –(7.5,2) –cycle;
[xshift = 0.5cm, yshift = 0.333 cm] (7.5,1.5) – ++(-1,0.166) – ++(0,-0.75) – (7.5,0.75) – (7.5,0) – ++(-1.25,0.208) – ($(7.5,2)+(-1.25,0.208)$) –(7.5,2) –cycle;
(7.5,0) – ++(0.5,0.333) – ++(-1.25,0.208) – ++(0,2) – ++(-0.5,-0.333) – ++(0,-2) – ++(1.25,-0.208) – cycle;
(7.5,2) – ++(-1.25,0.208) – ++(0.5,0.333) – ++(1.25,-0.208) – cycle;
(7.5,0) – ++(0.5,0.333) – ($(7.5,0.75) +(0.5,0.333)$) – (7.5,0.75) – cycle;

[xshift = 5.5cm, yshift = -5.5cm]
[purple!75!] (0,0) rectangle (6,4);
[blue!60] (0,3) rectangle (4.5,4);
[blue!60] (0,0) rectangle (4.5,2.5);
[blue!60] (5,0) – (5,1.5) – (5.5,2.5) –(6,2.5) – (6,0) – cycle;
[blue!60] (5,2) – (5,4) – (6,4) –(6,3) – (5.5,3) – cycle;
(0,0) rectangle (6,4);
(4.5,2.5) rectangle (5,1);
(0,2.5) – (4.5,2.5) – (4.5,0);
(0,3) –  (4.5,3) – (4.5,4);
(5,0) – (5,1.5) – (5.5,2.5) –(6,2.5);
(6,3) – (5.5,3)–(5,2) – (5,4);

The double bubble and a torus inside, covered by three disks (up to thickening the ribbon part of $S_2$ by pushing it into $S_1$).

[scale = 0.75]
[red, opacity = 0.2] (7.5, 0.75) ++(0,0.75) – ++(0,0.3) – (6,0.8) – (6,0.5) –cycle;
[red, opacity = 0.2] (6,0.5) – (6,0.8) – (0,1.8) – (0,1.5) –cycle;
[red, opacity = 0.2] (0,1.5) – (3,3.5) – (3,3.8) – (0,1.8) –cycle;
[red, opacity = 0.2] (3,3.5) – (9, 2.5) – (9,2.8) – (3,3.8) –cycle;
[red, opacity = 0.2] (9, 2.5) – (8,1.3) – ++(0,0.3) – (9,2.8) –cycle;
[red, opacity = 0.2] (7.5,1.5) – ++(-1,0.166) – ++(0,-0.75) – (7.5,0.75) – (7.5,0) – ++(-1.25,0.208) – ($(7.5,2)+(-1.25,0.208)$) –(7.5,2) –cycle;
[xshift = 0.5cm, yshift = 0.333 cm, red, opacity = 0.2] (7.5,1.5) – ++(-1,0.166) – ++(0,-0.75) – (7.5,0.75) – (7.5,0) – ++(-1.25,0.208) – ($(7.5,2)+(-1.25,0.208)$) –(7.5,2) –cycle;
[red, opacity = 0.2] ($(7.5,0)+(0.5,0.333)+(-1.25,0.208)$) – ++(0,2) – ++(-0.5,-0.333) – ++(0,-2) – cycle;
[purple, thick] (7.5,2) – ++(-1.25,0.208) – ++(0.5,0.33) – ++(1.25,-0.208) – ++ (0,-0.5) – ++(-1,0.166) – ++ (0,-0.75) – ++(1,-0.166) – ++(0,-0.75) –++(-1.25,0.208) – ++(-0.5,-0.33) – ++(1.25,-0.208) – ++(0,0.75) – ++(-1,0.166) – ++(0,0.75) – ++(1,-0.166) – (6,0.5) – (0,1.5) – (3,3.5) – (9,2.5) – (8,1.3) – (8,1.6) – (9,2.8) – (3,3.8) – (0,1.8) – (6,0.8) – (7.5,1.8) – cycle;

[xshift = 9.5cm]
[red, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) ++(0,0.75) – ++(0.5,0.333) – ++(1,-0.166) – ++(-0.5,-0.333) – cycle;
[red, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) – ++(0.5,0.333) – ++(0,0.75) – ++(-0.5,-0.333) – cycle;
[red, opacity = 0.2] (7.5,0.75) ++(-1, 0.166) – ++(1,-0.166) – ++(0.5,0.333) – ++(-1,0.166) – cycle;
[red, opacity = 0.2] (7.5, 0.75) ++(0.5, 0.333) ++(0, 0.75) – ($(6,1) +(2,1.333)$) – ++(-0.5, -0.333) – ++(0,-0.2) – (6,0.8) – (6,0.5) –cycle;

[red, opacity = 0.2] (6,0.5) – (6,0.8) – (0,1.8) – (0,1.5) –cycle;
[red, opacity = 0.2] (0,1.5) – (3,3.5) – (3,3.8) – (0,1.8) –cycle;
[red, opacity = 0.2] (3,3.5) – (9, 2.5) – (9,2.8) – (3,3.8) –cycle;
[red, opacity = 0.2] (9, 2.5) – (8,1.3) – ++(0,0.3) – (9,2.8) –cycle;
[red, opacity = 0.2] (7.5,0) – ++(0.5,0.333) – ++(-1.25,0.208) – ++(-0.5,-0.333) – cycle;
[red, opacity = 0.2] (7.5,0) – ++(0,0.75) – ++(0.5,0.33) – ++(0,-0.75) – cycle;
[red, opacity = 0.2] (7.5,2) – ++(0.5,0.333) – ++(-1.25,0.208) – ++(-0.5,-0.333) – cycle;
[purple, thick] (7.5,2) – ++(-1.25,0.208) – ++(0.5,0.33) – ++(1.25,-0.208) – ++ (0,-0.5) – ++(-1,0.166) – ++ (0,-0.75) – ++(1,-0.166) – ++(0,-0.75) –++(-1.25,0.208) – ++(-0.5,-0.33) – ++(1.25,-0.208) – ++(0,0.75) – ++(-1,0.166) – ++(0,0.75) – ++(1,-0.166) – (6,0.5) – (0,1.5) – (3,3.5) – (9,2.5) – (8,1.3) – (8,1.6) – (9,2.8) – (3,3.8) – (0,1.8) – (6,0.8) – (7.5,1.8) – cycle;

The disks $S_1 \cap S_2$ and $S_3 \cap S_2$.


# Development and Validation of the Japanese Moral Foundations Dictionary

Akiko Matsuo  Department of Psychology, Graduate School of Environmental
Studies, Nagoya University, Nagoya, Japan  Kazutoshi Sasahara Correspondence
should be addressed to<EMAIL_ADDRESS>Department of Complex Systems
Science, Graduate School of Informatics, Nagoya University, Nagoya, Japan
JST, PRESTO, Kawaguchi, Japan  Yasuhiro Taguchi  Department of Humanities and
Social Sciences, School of Letters, Aichi University, Toyohashi, Japan  Minoru
Karasawa  Department of Cognitive and Psychological Sciences, Graduate School
of Informatics, Nagoya University, Nagoya, Japan

###### Abstract

The Moral Foundations Dictionary (MFD) is a useful tool for applying the
conceptual framework developed in Moral Foundations Theory and quantifying the
moral meanings implicated in the linguistic information people convey.
However, the applicability of the MFD is limited because it is available only
in English. Translated versions of the MFD are therefore needed to study
morality across various cultures, including non-Western cultures. The
contribution of this paper is two-fold. We developed the first Japanese
version of the MFD (referred to as the J-MFD) using a semi-automated
method—this serves as a reference when translating the MFD into other
languages. We next tested the validity of the J-MFD by analyzing open-ended
written texts about the situations that Japanese participants thought followed
and violated the five moral foundations. We found that the J-MFD correctly
categorized the Japanese participants’ descriptions into the corresponding
moral foundations, and that the Moral Foundations Questionnaire (MFQ) scores
correlated with the frequency of situations, of total words, and of J-MFD
words in the participants’ descriptions for the Harm and Fairness foundations.
The J-MFD can be used to study morality unique to the Japanese and also
multicultural comparisons in moral behavior.

## Introduction

Currently, one of the most active research areas in social and behavioral
sciences pertains to how and on what grounds ordinary people form moral
judgments. A central message from this flourishing body of research is that
people quickly decide whether a particular act is morally right or wrong;
however, it takes them a relatively long time to provide a “why” explanation
for their judgment [11]. This intuitionist model of moral judgment has
produced voluminous empirical research as well as a comprehensive theoretical
framework—this is now formulated as the Moral Foundations Theory (MFT).

The central principle of the MFT is that people inherit a limited number of
conceptual templates used for their intuitive classification of observed acts
that are potentially relevant to morality. Specifically, it is assumed that
there are five major moral foundations including: (1) “Care,” which focuses on
not harming others and protecting the vulnerable; (2) “Fairness,” which
assumes equivalent exchange without cheating to be good; (3) “Ingroup,” which
concerns a collective entity instead of individuals, such as family, nation,
team, and military; (4) “Authority,” which postulates respect for authority,
resulting in maintaining the hierarchy; and (5) “Purity,” which involves a
feeling of disgust caused by the impure.

The MFT emphasizes that moral foundations meet not only individuals’ adaptive
need to fit into their community in the “correct” ways but also a collective
need for the community to increase its unity and win against other groups.
This is how and why moral foundations are typically shared with a high level
of consensus among the community members, according to the MFT. The consensual
nature of moral foundations should manifest most visibly in linguistic
communication—this can mobilize the community toward solidarity and sanctity.
In this group process, moral foundations are assumed to show their political
aspects and provide a base for mobilizing members toward their collective
goals. To test this hypothesis concerning “political” consensuality, Haidt and
colleagues analyzed morality-relevant discourse in daily contexts [8]. A tool
developed for this purpose was the Moral Foundations Dictionary (MFD), which
quantifies virtues and vices associated with each moral foundation expressed
in written texts [8].

The MFD contains a list of words related to one or several moral foundations
such as “killing”, “justice”, and “loyal,” which correspond respectively to
the Care, Fairness, and Ingroup foundations. The usefulness of the MFD has
been demonstrated in empirical studies and combined with the use of the LIWC
software (Linguistic Inquiry and Word Count program [24]). For instance, in
the research above, Graham et al. analyzed church sermons available online and
found that liberal preachers were more likely than their conservative
counterparts to use words relevant to Care, Fairness, and Ingroup but less
likely to use words relevant to Authority and Purity. This is consistent with
the general trends documented for these ideological camps on different
measures [8].

Even though the MFD is useful for linguistic analyses of moral foundations,
the dictionary is currently available only in English, and thus it is unknown
to what extent we can generalize the findings to the linguistic communities
outside of the English-speaking world. This is a problem because it is
plausible that the contents—as well as the roles of different moral
foundations—would vary across cultures. For instance, evidence shows that
people living in Western cultures tend to emphasize Care and Fairness in their
moral judgments, whereas non-Western people tend to rely more on Ingroup and
Purity [9]. The use of the MFD translated into different languages might
reveal similar differences in communication and discourses. An accumulating
body of evidence concerning cultural differences would also be important in
the context of criticism about the potential bias in morality research that
leans toward the so-called WEIRD (Western, Educated, Industrialized, Rich, and
Democratic) cultural samples [13, 17, 2]. Furthermore, social media platforms
provide an excellent arena for analyzing human behavior in a natural setting,
and some recent research has successfully applied natural language processing
(NLP) to social media data to quantify people’s moral behaviors [27, 23].
Particularly notable are the findings by Dehghani et al., who identified a key
role of Purity in social networking [4], and the work by Kaur and Sasahara
[19] showing that although Care was the most dominant, Purity was the most
distinct moral foundation in online conversations. Unfortunately, this
evidence is also limited to English texts, because there is no publicly
available dictionary that can be applied to texts written in languages other
than English [6, 15].

To overcome this limitation, we describe here how we developed a Japanese
version of the MFD (J-MFD) using a semi-automated method. The J-MFD is
publicly available online, and hence our methodology can serve as a useful
model for further attempts to develop moral dictionaries in other languages.

## Methods

### Strategy for J-MFD Development

The translation of a dictionary is beset with at least two difficulties. It is
difficult to maintain consistency between translation outcomes via multiple
translators because the accuracy of rendering from one language to another
depends on a translator’s linguistic ability. Moreover, the translated
outcomes are subject to change and require constant updates because the actual
use of the translated dictionary in text analysis may lead to a better
translation and because language itself culturally evolves.

To resolve the first issue, we took advantage of computational methods and
online linguistic resources and corpora. This collection of tools and data
allowed us to produce as many translations as possible and ensure accurate
translations while reducing human errors. To resolve the second issue, we
released the J-MFD to the public so that researchers worldwide could freely
use it and report issues, if any, on our website. These comments could be used
for future updates.

### Development of J-MFD

We translated the original MFD into our J-MFD via two online linguistic
resources and two corpora with the aid of computational methods. The original
MFD contains 324 English moral terms with 11 categories corresponding to
“Virtue” or “Vice” (violates); each is associated with one of the five moral
foundations (i.e., Care, Fairness, Ingroup, Authority, and Purity) as well
with a more general or abstract category of morality (i.e., Morality General)
[8]. Care is henceforth denoted as Harm in accordance with the notation of the
MFD. The moral terms consisted of 156 words (e.g., impair) and 168 word stems
(e.g., justifi*, which covers justification, justifier, etc.) There were some
words associated with multiple categories such as “impair” (Harm Vice and
Purity Vice); other words were associated with only a single category, such as
“justifi*” (Fairness Virtue alone).

Figure 1: Overview of a semi-automated method for J-MFD development. Automated
procedures are indicated by downward arrows, and manual procedures are
indicated by upward arrows.

Our development followed five steps. First, our programs automatically
collected all words that contained each of the word stems in the MFD by web
scraping OneLook—an online dictionary metasearch engine
(https://www.onelook.com) (Fig. 1A$\to$C). For example, “justifi*” with the
“Filter by commonness: Common words” option in Onelook returned 11 possible
words for the word stem (“justifiable”, “justifiableness”,
“justifiably”,“justifies”, etc). This procedure identified 891 words from all
of the word stems in the MFD.

Next, we manually eliminated 58 words that were unrelated to morality (Fig.
1C$\to$D). The remaining words comprised a list of moral words for
translation.

Third, the remaining words were translated into Japanese via Weblio—an online
dictionary and encyclopedia designed for Japanese speakers
(https://ejje.weblio.jp). This process was also performed by web scraping,
which allowed us to cover possible translation equivalents in Japanese (2044
words) (Fig. 1D$\to$E).

Fourth, we took a frequency-based approach for word selection using two
Japanese corpora: Japanese words based on the Balanced Corpus of Contemporary
Written Japanese (BCCWJ) and the Tsukuba Web Corpus (TWC). BCCWJ is a corpus
of contemporary written Japanese that contains 104 million words randomly
sampled from books, magazines, newspapers, business reports, blogs, Internet
forums, textbooks, and legal documents [21]
(https://pj.ninjal.ac.jp/corpus_center/bccwj/). The TWC is a large corpus that
contains 1.1 billion Japanese words obtained from 3.5 million Japanese web
pages (http://nlt.tsukuba.lagoinst.info). We adopted the top ten most frequent
Japanese words for every word stem and the top five for every word in BCCWJ
and TWC, thereby filtering out words rarely used (Fig. 1E$\to$F).

Finally, we adjusted the category assignments for each Japanese word after
removing words unrelated to morality and words that failed in backtranslation
using online dictionaries (Fig. 1F$\to$G). More specifically, we merged
Japanese words whenever possible, using word stem representation. For example,
“違反する” (Ihan-suru, or “violate”) is a verb and “違反” (Ihan, “violation”) is its
noun form; these words can be merged to “違反*” (n.b. “する” (suru, “do”) to make
a compound verb). Similarly, an adjective “安全な” (Anzen-na, “safe”) and its
noun form “安全” (Anzen, “safety”) can be merged to “安全*.” After the merge
procedures, we examined whether Japanese moral word candidates can be back-
translated to corresponding English words using online dictionaries. As a
result, 23 words that failed this test were removed, and we were left with 741
Japanese moral terms, for which we adjusted the moral categories. This
adjustment was necessary because multiple words (or word stems) with different
moral categories could be translated into the same single Japanese word (or
word stem); hence, a single Japanese word could belong to multiple categories.
Among these categories, the central one (or ones) needed to be selected based
on native Japanese knowledge and the definition of moral categories. For
instance, “safe*”, “protect*”, “shelter”, “secur*”, “defen*”, “guard*”,
“preserve”, and “obey*” all can be translated to “守る”; and “obey*” can fit in
both Authority Virtue and Harm Virtue. Because the core meaning of “守る” is a
Harm Virtue, we assigned it to Harm Virtue based on the judgment of three
native Japanese speakers.

## Results

### Japanese Moral Foundations Dictionary (J-MFD)

Table 1 shows the number of words for each category and the total number of
words in the J-MFD. As shown, the semi-automated procedures featured more
words in Ingroup Virtue and Authority Virtue than in others. This seems to
reflect Japanese culture, in which group harmony and hierarchy are more
appreciated than individual interests. Example words from the J-MFD are listed
in Table 2.

Table 1: The number of words for each category in the J-MFD. | Harm
---
Virtue
| Fairness
---
Virtue
| Ingroup
---
Virtue
| Authority
---
Virtue
| Purity
---
Virtue
| Morality
---
General
51 | 42 | 98 | 129 | 89 | 43
| Harm
---
Vice
| Fairness
---
Vice
| Ingroup
---
Vice
| Authority
---
Vice
| Purity
---
Vice
Total
93 | 33 | 43 | 53 | 87 | 718
Table 2: Examples of moral words in J-MFD Words in J-MDF (Romaji) |  Counterparts in MFD |  Moral Category
---|---|---
安全* (Anzen*) |  safe* |  Harm Virtue
友情* (Yujo*) |  amity, fellow*, comrad* |  Harm Virtue, Ingroup Virtue
殺す (Korosu) |  kill, kills, killed, killing, destroy |  Harm Vice
傷 (Kizu) |  hurt*, wound*, stain*, blemish |  Harm Vice, Purity Vice
平等* (Byodo*) |  egalitar*, evenness, equal* |  Fairness Virtue
誠実* (Seijitsu*) |  constant, honest*, loyal*, integrity |  Fairness Virtue, Purity Virtue
差別* (Sabetsu*) |  discriminat*, segregat* |  Fairness Vice
不法*(Fuho*) |  injust*, lawless*, illegal*, wrong* |  Fairness Vice, Authority Vice
国民* (Kokumin*) |  nation* |  Ingroup Virtue
忠誠* (Chusei*) |  loyal*, allegian* |  Ingroup Virtue, Authority Virtue
個人* (Kojin*) |  individual* |  Ingroup Vice
不義 (Fugi) |  disloyal*, adulter* |  Ingroup Vice, Purity Vice
従順* (Jujun*) |  obedien*, submi*, duti*, complian* |  Authority Virtue
謙虚* (Kenkyo*) |  submi*, modesty |  Authority Virtue, Purity Virtue
扇動* (Sendo*) |  sedidi*, agitat* |  Authority Vice
反逆* (Hangyaku*) |  treason*, traitor*, treacher*, rebel* |  Authority Vice, Ingroup Vice
きれい* (Kireina) |  pure*, clean*, pristine |  Purity Virtue
信心* (Shinjin*) |  devot*, piety, pious, holy |  Purity Virtue, Ingroup Virtue
冒涜* (Botoku*) |  profan*, desecrat* |  Purity Vice
背教* (Haikyo*) |  apostate, renegade, pervert |  Purity Vice, Ingroup Vice
価値* (Kachi*) |  worth*, value*, good |  Moral General
正直* (Shojiki*) |  honest*, integrity, upright, upstanding |  Fairness Virtue

The J-MFD and a computer program for Japanese word segmentation are publicly
available online ({https://github.com/soramame0518/j-mfd/}). Note that
Japanese texts are continuous strings of words and are not punctuated by blank
spaces; thus, word segmentation is required for Japanese texts before using
the J-MFD.

### Validation of the J-MFD

To validate our J-MFD, we compared the mean frequencies of the dictionary
words for the five moral foundations that were included in the descriptions
about moral issues reported by Japanese participants. More specifically, 386
Japanese participants (238 men and 148 women; $M_{\rm age}=35.22$, $SD=12.30$)
were recruited online using the Internet crowdsourcing service Macromill
(https://www.macromill.com). Participants read brief explanations of Haidt’s
five moral foundations (see Supporting Information) and listed as many
situations as possible that they thought followed and violated the five moral
foundations.

The situations resulted in 16,033 sentences in total after eliminating the
responses that were incomprehensible with respect to their meaning or were not
related to morality (e.g., “I can’t understand the meaning of the question”).
Each sentence in these descriptions of situations was segmented into words,
and five pools of morally relevant words (i.e., Harm-related, Fairness-
related, and so forth) were constructed. For each of these pools, we computed
the frequency ratio of appearances of J-MFD words associated with each moral
foundation. To take an example of the word pool produced from the Harm-related
context (Virtue and Vice combined), we separately counted the numbers of times
that the Harm-related words, Fairness-related words, and so forth contained in
the J-MFD appeared in each participant’s descriptions. To obtain ratio scores,
we divided those word counts by the size of the pool and by the total number
of dictionary words associated with each moral foundation. Figure 2 shows the
mean frequency ratio for each foundation in the J-MFD obtained from the Harm-
related word pool. A one-way ANOVA showed a main effect of moral foundations,
indicating a significantly higher frequency of Harm words than that of words
from the remaining foundations. We repeated the same analyses for the
remaining pools (i.e., Fairness-, Ingroup-, Authority-, and Purity-related),
and similarly found the highest frequency ratios in each pool for the
corresponding moral foundation, with the main effects of foundation (F
(4,1328) $=$ 52.95, p $<$ 0.001) (See Figs S1-S4 in Supporting Information).
These results demonstrate the validity of our J-MFD.

Figure 2: Mean percentages of dictionary words per participant used in
descriptions about the situations that the participants thought followed and
violated the Harm foundation (see Figs. S1-S4 for the other foundations).

### Relationships between Moral Descriptions and MFQ scores

We collected self-reported responses to the Moral Foundations Questionnaire
(MFQ) [9] from the same Japanese sample to examine relationships between self-
reported moral situations and MFQ scores in Japanese. This is important to
show the applicability as well as the further validation of the J-MFD. To
measure MFQ scores in Japanese, we used the 30-item version of the Japanese
MFQ that was back-translated with the approval of the authors of the original
MFQ (available at www.moralfoundations.org and in [18]). The Japanese version
of the MFQ was found to have a five factor model as the MFT predicted [14] and
has been used in other research on morality among the Japanese people (e.g.,
[28]).

Our assumption here was that people who have a high MFQ score on a certain
moral foundation (e.g., Harm) may have a better-organized schema for the
corresponding foundation. Thus, when asked to describe situations about the
foundation, they could describe it more easily and appropriately than those
who have a low MFQ score. This assumption can be tested by measuring for each
of the five moral foundations, (1) how many situations they listed (Virtue and
Vice combined), (2) how many words they used to describe the situations, and
(3) how many foundation-related words they used to describe the situations. It
should be noted that the task of mentally representing morality gets more
specific in the order of (1), (2), and (3): to achieve high performance in
(3), a more foundation-specific schema is required for choosing appropriate
words related to the corresponding foundation. The measurement of (3) with the
J-MFD is indispensable for examining the above-mentioned assumption. We
investigated whether (1), (2), and (3) would correlate with MFQ scores for the
corresponding moral foundations.

As for (1), the correlation of MFQ scores and the number of situations
described by participants was significant for most of the foundations (Harm: r
$=$ .25, p $<$ .01; Fairness: r $=$ .16, p $=$ .01; Authority: r $=$ .14, p
$<$ .01; Purity: r $=$ .22, p $<$ .01) except the Ingroup foundation (r $=$
.07, p $=$ .19). As for (2), the correlation of MFQ scores and the number of
total words included in participant-made situations was significant for all
five foundations (Harm: r $=$ .29, p $<$ .01; Fairness: r $=$ .20, p $<$ .01;
Ingroup: r $=$ .12, p $=$ .02; Authority: r $=$ .15, p $<$ .01; Purity: r $=$
.22, p $<$ .01). As for (3), the correlation of MFQ scores and the number of
J-MFD words included in participant-made situations was significant for the
Harm and Fairness foundations (r $=$ .12, p $=$ .02; and r $=$ .11, p $=$ .04,
respectively), while there was no significant correlation for the other three
foundations (Ingroup: r $=$ -.02, p $=$ .67; Authority: r $=$ .04, p $=$ .49;
Purity: r $=$ .06, p $=$ .21). According to the results of (1)–(3), the
correlation between self-reported moral descriptions by Japanese people and
MFQ scores was consistent for the Harm and Fairness foundations but not for
the other foundations. The implications of this finding are discussed in the
next section.

## Discussion

This work proposed a semi-automated method for translating the Moral
Foundations Dictionary (MFD) and developed and validated its Japanese version
(J-MFD). The J-MFD will be updated with revision via collaborative efforts by
its users ({https://github.com/soramame0518/j-mfd/}). Our method is beneficial
for developing other language versions of the MFD, which are needed because
multilingual versions allow us to test the Moral Foundations Theory (MFT) in
different languages and compare diverse cultures using the same basis of the
MFT [11, 12].

We showed that the J-MFD allows us to correctly categorize moral-relevant
situations in Japanese-written texts into the corresponding moral foundations,
which serves as validation of the J-MFD. Furthermore, our correlation analyses
showed that (1) the number of situations, (2) the number of words, and (3) the
number of J-MFD words all consistently correlated with the MFQ score in the
Harm and Fairness foundations, which implies the existence of a better-
developed schema. People were able to describe Harm- and Fairness-related
sentences easily (i.e., (1) and (2)) and accurately (i.e., (3)). However, such
consistent patterns across (1) to (3) were not observed in the Ingroup,
Authority, and Purity foundations, which suggests the lack of specific schema
for these foundations. A possible explanation for these results is that Harm
and Fairness foundations are more fundamental than the other foundations and
are better quantified in the MFQ. In contrast, the Ingroup, Authority, and
Purity foundations may be more culture-dependent, and the MFQ, as it stands,
may inaccurately measure these foundations, and therefore, may need a
modification specific to Japanese culture. These interpretations are
consistent with prior research findings, which show that Harm and Fairness are
central to moral judgment cross-culturally [10, 25] while Ingroup, Authority,
and Purity are susceptible to political ideology, ethnicity, culture, and
religiosity [1, 3, 8, 16, 20, 29]. Altogether, while our study shows that the
J-MFD is a valid tool for morality research in Japanese culture, it also
highlights the need for further research to scrutinize the causal relationship
of MFQ scores and the use of moral-relevant words in multilingual settings,
not only in Japanese.

It is important to note the overrepresentation of male participants in our
sample, which featured 238 males and 148 females. Previous research using
internationally diverse samples have found that females were more likely to
show higher scores on the Harm, Fairness, and Purity foundations than males,
with males scoring higher than females on the Ingroup and Authority
foundations in the MFQ [9]. In our sample, females rated higher only on Harm
($M_{\rm women}=24.67$ vs. $M_{\rm men}=23.76$), and males showed higher mean
scores on Fairness ($M_{\rm women}=22.28$ vs. $M_{\rm men}=22.46$), Ingroup
($M_{\rm women}=19.54$ vs. $M_{\rm men}=20.55$), Authority ($M_{\rm
women}=20.07$ vs. $M_{\rm men}=20.79$), and Purity ($M_{\rm women}=21.17$ vs.
$M_{\rm men}=21.94$). These inconsistent patterns for Fairness and Purity may
have been caused by the lack of female participants. Also, our results from
correlation analyses could be affected by the imbalanced number of males in
the sample. Future research with a gender-balanced ratio of participants would
be necessary.

This work contributes to interdisciplinary collaborations in morality research
across academic fields. First, the MFT can be tested using NLP with the J-MFD
by analyzing languages that people express online [7]. In addition to the
word-counting approach conducted in this study, NLP allows the J-MFD to be
used for word co-occurrence analysis [5] and latent semantic analysis [27,
19]. Second, the J-MFD can be used in combination with a Japanese emotion
dictionary because specific emotions are often associated with moral judgment
[22]. Third, morality matters in the business world as well; thus, it is
important to investigate morality from the perspective of both
leaders/employees in organizations and consumers [7, 26].

Finally, the J-MFD allows future research to scrutinize theoretical frameworks
about the standards of moral judgment in various fields of study; this would
enrich cross-cultural research by facilitating comparison of morality-related
texts in English and Japanese. We are aware that the J-MFD—as well as the
original MFD—is not an inclusive dictionary; thus, we had to combine Virtue
and Vice categories for words with low occurrence frequency. Both dictionaries
might be improved by adding more relevant words [4, 19]. The expansion of
moral words in the J-MFD is critical to improving accuracy in measuring
morality from written texts—that is one of our key future goals.

## Author Contributions

Conceived and designed the experiments: AM, KS, MK. Analyzed the data: AM, KS,
YT. Wrote the paper: AM, KS, MK.

## Funding

This research was supported by JSPS/MEXT KAKENHI Grant Numbers 15H03446 and
JP17H06383 in #4903, JST PRESTO Grant Number JPMJPR16D6, and JST CREST Grant
Number JPMJCR17A4. The funders had no role in study design, data collection
and analysis, decision to publish, or preparation of the manuscript.

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