WE economy: Potential of mutual aid distribution based on moral responsibility and risk vulnerability

Reducing wealth inequality is a global challenge that requires the transformation of the economic systems that produce inequality. The economic system comprises: (1) gifts and reciprocity, (2) power and redistribution, (3) market exchange, and (4) mutual aid without reciprocal obligations. Current inequality stems from a capitalist economy consisting of (2) and (3). To sublimate (1), the human economy, to (4), the concept of a “mixbiotic society” has been proposed in the philosophical realm. In this society, free and diverse individuals mix, recognize their respective “fundamental incapability,” and sublimate them into “WE” solidarity. Moreover, the economy must have a moral responsibility as a co-adventurer and consider its vulnerability to risk. This study focuses on two factors of mind perception—moral responsibility and risk vulnerability—and proposes a novel wealth distribution model between the two agents following an econophysical approach, whereas the conventional model dealt with redistribution through taxes and institutions. Three models are developed: a joint-venture model in which profit/losses are distributed based on their factors, a redistribution model in which wealth stocks are redistributed periodically based on their factors in the joint-venture model, and a “WE economy” model in which profit/losses are distributed based on the ratio of each other’s factors. A simulation comparison reveals that WE economies are effective in reducing inequality, resilient in normalizing wealth distribution as advantages, and susceptible to free riders as disadvantages. However, this disadvantage can be compensated for by fostering fellowship and using joint ventures. This study presents the effectiveness of moral responsibility and risk vulnerability, complementarity between the WE economy and joint economy, and the direction of the economy in reducing inequality. Future challenges include developing an advanced model based on real economic analysis and economic psychology and promoting its fieldwork for worker coops and platform cooperatives to realize a desirable mixbiotic society.


Introduction
Wealth inequality and disparity have become major social issues around the world.According to the World Inequality Report 2022, the top 1% richest people account for 38% of the world's wealth [1], and according to the World Economic Forum, only 8 men of the top have the same wealth as the poorest 3.6 billion people [2].The global Gini index has reached 0.7 [1], well above the warning level 0.4 for social unrest [3].Solving the inequality problem is an urgent issue because social unrest creates a vicious cycle that lowers productivity, increases inequality, and further fuels social unrest [4].
The United Nations Sustainable Development Goals include, as Goal 10, reducing inequality, promoting social, economic, and political inclusion, and fiscal and social policies that promote equality, and as Goals 1, 2, 8, and 16, eradicating poverty, zero hunger, inclusive economic growth, and fair and inclusive institutions, respectively [5].At the World Economic Forum, a gathering of political and business leaders, the reduction of inequality is also on the main agenda [6].To achieve these goals, it is essential to formulate policies and institutions based on the economic relationships that produce inequality-that is, the mode of wealth exchange.
The economist Polanyi has identified three modes of economic relations: (1) reciprocity, (2) redistribution, and (3) market exchange [7].Anthropologist Graeber presents (2') hierarchy, (3') exchange, and (4') foundational communism as three moral principles involved in economic relations [8], and philosopher Karatani presents four modes of exchange: (1") reciprocity, (2") plunder and redistribution, (3") commodity exchange, and (4") advanced recovery of reciprocity [9].Of these, (1)(1') is a human gift economy with an obligation of return, (2)(2')(2") is a power economy with tax collection and redistribution, (3)(3') (3") is a market economy with non-human exchange of goods and money, and (4')(4") is a human mutual-aid economy without an obligation of return and sublimated from a gift economy.The capitalist economy that produces the current inequality is a combination of a power economy and a market economy [8,9], and Graeber and Karatani advocate a transformation to a (4') (4") human economy as a prescription for the inequality problem.Note that the Islamic economy is a combination of redistribution based on the morals of the Islamic code instead of power (waqf, sadaqah, and zakat) and a joint economy that prohibits interest (mudaraba, murabaha, and salam) [10,11].It is a capitalist economic alternative and a possible stepping stone to a human economy [8].
Philosopher Deguchi introduces the concept of a "mixbiotic society," a further development of the symbiotic society, as a social vision corresponding to (4')(4") above [12].This is a society in which free and diverse individuals, "I," mix with each other, recognize their respective "fundamental incapability" and sublimate them into "WE" solidarity [12,13].In a mixbiotic society, individuals entrust and cooperate with each other in a "WE" community.Regarding the human economy in a mixbiotic society-I call it the "WE economy"-Deguchi states in his book [14]:  Good WE: Fellowship, equality, hollowness without power center, cooperativity, voluntary participation, softened WE.
 Bad WE: Totalitarianism, exclusivism toward the outside, peer pressure toward the inside, hardened WE.
 Good WE are coadventurers who participate while accepting the risk together.
 WE members qualify as coadventurers (risk takers) in that they have vulnerability and frangibility.
 Coadventurers in the same boat may have economic class divisions, but they are on equal footing as a community of destiny.
 Coadventurers are weighted according to their moral responsibility, but the weighting is only a quantitative differentiation of the received profit and the associated risk (latch).
 The risk-return allocation is increased or decreased but not monopolized, and everyone receives a return for the amount of risk taken.
To summarize Deguchi's discourse, two things are important in the "WE Economy": moral responsibility and risk vulnerability.Here, the dimensions of mind perception are informative.According to psychologists Gray and Wegner, mind perception can be divided into two main dimensions: agency (capacities such as selfcontrol, morality, and memory) and experience (capacities such as hunger, fear, and pain) [15].Then, as shown in S1 Fig in the Supporting information, characters such as a fetus, a baby, a girl, an adult man, an adult woman, a man in persistent vegetative state, and a dead woman are mapped on a two-dimensional plane.Agency corresponds to moral agent (giver of moral action: moral responsibility) and experience to moral patient (recipient of pain: risk vulnerability) [16,17].Based on these, the WE economy make the coadventurers undertake risk (latch) in accordance with their moral responsibility and allocates returns in consideration of its responsibility and risk vulnerability.
What potential does the WE economy have for reducing wealth inequality?In examining this, I use an econophysical approach.According to reviews in this field, various wealth distribution models have been proposed based on the analogy of kinetic energy exchange of gaseous particles and other dynamics, and wealth distributions and inequalities such as exponential, power, gamma, and delta distributions have been considered [18,19].Recent examples of studies have examined income and inheritance taxes [20], social class and inheritance [21], tax exemptions for the poor [22], contributions of surplus stock [23], interest business, joint ventures and redistribution [24], and redistribution and mutual aid [25].Among these models, to compare with the WE economy as coadventurers, it seems appropriate to refer to the joint-venture model, which is the most similar to this in the way wealth is distributed.
Therefore, in this study, I formulate a new mathematical model of the WE economy based on moral responsibility and risk vulnerability referring to the above joint-venture model [24], and simulate wealth distribution and inequality.Then, by comparing joint ventures and WE economies, I aim to gain insights to lead the capitalist economy, which generates inequality, to the WE economy.The remainder of this paper is organized as follows: In the Methods section, I first cite the conventional jointventure model and then present a redistribution model based on moral responsibility and risk vulnerability in the joint-venture model and a distribution model based on responsibility and vulnerability in the WE economy.The Results section presents simulation results for the wealth distribution and the Gini index of inequality.The Discussion section discusses, based on the results, the real-world applicability of the joint ventures with redistribution and the WE economies as alternatives to capitalist economies.Finally, future challenges include the research issues and empirical fieldworks.

Moral responsibility and risk vulnerability
Firstly, using the agency and experience scores by Gray and Wegner shown in S1 Fig [15] in the Supporting information, I establish values for moral responsibility and risk vulnerability.Excluding a fetus, a man in persistent vegetative state, and a dead woman, who are not involved in economic activities, a baby, a girl, an adult man and an adult woman roughly ride on a straight line on a two-dimensional plane.From baby to adult, agency, which corresponds to moral responsibility, roughly changes from 0.2 to 0.8, and experience, which corresponds to risk vulnerability, roughly changes from 1 to 0.8.The age-specific population distribution includes a stationary type with a constant population of each age group, an expansive type with a large population of young people (population growth), and a constrictive type with a small population of young people (population decline) [26].Here I assume the stationary type, not the expansive type with short life expectancy or the constrictive type with extreme aging.
That is, assuming an even distribution of the number of people from babies to adults, the moral responsibility   and risk vulnerability   of the  -th agent (  = 1, 2, ⋯ , ) among  agents can be expressed as shown in Eq (1).Note that   is a multiplication of   and   .

Joint-venture and redistribution models
First, as an econophysical model, I refer to the basic joint-venture model presented in the literature [24] (called the JV-B model).In the JV-B model, two agents  and  ( ≠ , ,  = 1, 2, ⋯ , ) are randomly selected at time  among  agents.
Both agents have wealth   () and   (), respectively, and a common savings rate .Both agents contribute their wealth, excluding savings, to the joint venture, and wealth is distributed according to the wealth contributed by each agent and the profit/loss ratio  .The wealth   ( + 1) and   ( + 1) of the two agents  and  at time  + 1 are expressed as shown in Eq (2), respectively.
In the JV-B model, all wealth excluding savings was contributed to the joint venture.But in the joint-venture model in this study, I model the two agents  and  contributing wealth according to their moral responsibilities   and   (called the JV-M model).That is, two agents  and  contribute wealth and (1 − ) •   •   (), respectively, and wealth is distributed according to the profit/loss rate .The wealth   ( + 1) and   ( + 1) at time  + 1 are expressed as shown in Eq (3), respectively.collected from the  agents is redistributed to each agent according to its moral responsibility ratio   ∑    ⁄ .The wealth   ( + ∆) of agent  at time  + ∆ after redistribution is expressed as shown in Eq (4).
In the JV-M-M model, redistribution was made according to moral responsibility, but for comparison, I model redistribution according to agent 's risk vulnerability   (called the JV-M-R model).In the JV-M-R model, the wealth collected from  agents is redistributed to each of them according to their risk vulnerability ratio   ∑    ⁄ .The wealth   ( + ∆) of agent  at time  + ∆ after redistribution is expressed as shown in Eq (5). ( Similar to the JV-M-M and JV-M-R models, I model the redistribution according to both moral responsibility   and risk vulnerability   of agent  (called the JV-M-MR model).In the JV-M-MR model, the wealth collected from  agents is redistributed to each according to the ratio   ∑    ⁄ using   =   •   in Eq (1).The wealth   ( + ∆) of agent  at time  + ∆ after redistribution is expressed as shown in Eq (6).

WE economy models
In the JV-M model, wealth is distributed according to the wealth (1 − ) shown in Eq (7), respectively.
In the WE-M-M model, redistribution was made according to moral responsibility, but for comparison, I model redistribution according to agent 's risk vulnerability   (called the WE-M-R model).In the WE-M-R model, the wealth contributed by the two agents  and  according to their moral responsibilities   and   is distributed according to their risk vulnerability ratios   (  +   ) ⁄ and   (  +   ) ⁄ .The wealth   ( + 1) and   ( + 1) at time  + 1 are expressed as shown in Eq (8), respectively.

Impact of free riders
I now refer to the JV-M model in Eq (3) and the WE-M-M model in Eq (7) to examine the impact of free riders who are not cooperative in joint ventures and WE economies.Assuming that one agent  of the two agents  and  contributes wealth only by multiplying its moral responsibility   by the ratio   , Eqs (3) and ( 7) can be rewritten as Eqs (10) and (11), respectively.For convenience, I call to the model combining Eq (10) with the redistribution in Eq (4) as the JV-M-M-FR model and the model in Eq (11) as the WE-M-M-FR model.Note that the redistribution in the JV-M-M-FR model does not take into account the impact of free riders, because the redistribution is considered to be institutionally done for everyone.

Calculation of Gini Index
The Gini index is a well-known parameter for assessing wealth inequality [27] and is calculated by drawing a Lorenz curve and an equal distribution line [28].There are various inequality indices calculated from Lorenz curves [29], but here I use the most common Gini index.By the operation (  ()) in Eq (12), the wealth   () ( = 1, 2, ⋯ , ) of the  agents at time  is sorted from smallest to largest, and the -th wealth from smallest is set as   (), and the Gini index  is calculated.
The Gini index  = 0 if the wealth of the  agents is equally distributed, and  = 1 if it is delta-distributed (all wealth is concentrated in only one agent).In other words, the more unequal the distribution is, the larger the Gini index is.

Results
To begin, common parameters for the simulations of the joint-venture model, the redistribution model, and the WE economy model are set.The number of agents is  = 1,000 (which does not affect the relative calculation of wealth distribution or Gini index), and time is run from  = 0 to 10 6 in increments of 1.The initial distribution of the wealth of the  agents at time  = 0 is equally   (0) = 1 ( = 1, 2, ⋯ , ) (this will be discussed later).The savings rate is  = 0.25, referring to the world's gross savings (as a percentage of GDP) [30].With respect to the profit/loss ratio , while the average return of the stock index is about 8%, there are large fluctuations exceeding ±10% [31], compared to an average return of only about 2% for investors [32].In other words, to account for the fact that business profits and losses fluctuate both positively and negatively, here I set a uniform random number in the range −0.1 ≤  ≤ 0.1 for every time  for the profit/loss rate  .For the redistribution period   and transfer rate  of the joint-venture model, I use the combination   = 10 4 and  = 0.5, where the Gini index  is relatively small, referring to the literature [24].and ( 5), the wealth contributed according to moral responsibility was redistributed according to risk vulnerability, resulting in an imbalance between the contribution and redistribution of wealth.there is almost no difference in the distribution of wealth  in both models.This is because, as can be seen in Eq (10), in the joint venture model, the effect of a free-rider agent only spills over to that agent itself.In contrast, the WE-M-M-FR model in Figs  3B.This is because, as can be seen in Eq (11), in the WE economy model, the reduction in the free-rider agent's wealth contribution affects both of the two agents.
This indicates that WE economies have the disadvantage of being more susceptible to free riders than joint ventures.respectively.With respect to the impact of free riders, the Gini index  is slightly smaller in the JV-M-M-FR model (dark blue) than in the JV-M-M model (blue).This is due to the reduced contribution of free-rider wealth, which reduces the impact of profits and losses.This has been shown in the literature [23,25] as a proportional relationship between the amount of contributions and the Gini index (i.e., the Gini index decreases as the amount of contributions is reduced).The Gini index  of the WE-M-M-FR model (dark green) is larger than that of the WE-M-M model (green).This has already been explained as the reason for the difference between Figs 5C and 5D relative to Figs 3A and 3B.we are currently in a transition from a money economy to a credit economy [8].The results of this work will support Graeber's vision and encourage a transformation from the capitalist economy, which currently produces inequality, to a humanistic mutualaid economy.
The resilience of the WE economy and joint ventures/redistribution based on moral responsibility to the distribution of wealth shows that it has the potential to break the vicious cycle of social unrest, as described at the beginning of the Introduction section, and stabilize society.Furthermore, a distribution of wealth based on both moral responsibility and risk vulnerability tilts toward people who are more vulnerable.This will contribute to a more inclusive society by, for example, helping children taking the future, young people leading the next generation, and the socially vulnerable.
However, WE economies have the disadvantage of being more susceptible to free riders than joint ventures with redistribution.This can be viewed, in other words, as a governance issue in a coadventurer or community of destiny.Economist Ostrom cites collective choice of operating rules, effective monitoring, and graduated sanctions as design principles for the commons [35].Of these, there is a fear that monitoring and sanctions will lead to the bad WE (totalitarianism, peer pressure) indicated by Deguchi, but collective choice of operating rules, including free riders, or consensus building to recognize each other's moral responsibility, will be important.
Economist Bowles, in his quite book "The Moral Economy," presents the trilemma of Pareto efficiency, preference neutrality, and voluntary participation, and cites limiting preference neutrality as a solution to this trilemma [36].The limitation of preference neutrality is, for example, the moral sensitization of free riders and the fostering of fellowship and cooperation.Once this is done, both respect for voluntary participation and the efficiency of the WE economy will be ensured, as indicated by Deguchi.Moreover, since societies and communities are multi-layered, an apparent free-rider in one community can move to another based on the voluntary participation.
Given the disadvantages of WE economies, even if they are compensated for by collective choice and restrictions on preference neutrality, WE economies would be suitable for relatively small-scale local societies and communities with common moral and social norms.This is because WE economies require mutual recognition of moral responsibility and risk vulnerability.Specific examples include worker cooperatives [37], where workers hold labor, investment and management, and platform cooperatives [38,39], which are based on joint ownership and democratic decisionmaking by users and workers.As an implementation of the WE economy through information technology, initiatives such as the Social Co-Operating System [40], which combines an operational loop that promotes cooperative behavior with a collegial loop that supports consensus building, would be useful.
In societies larger than WE economies, joint ventures with redistribution based on moral responsibility would be complementary and effective.In other words, it would constitute a multi-layered network of WE economies and joint ventures/redistribution, and perform the joint ventures/redistribution between the WE economies.However, the redistribution should be based on norms and morals, as in the Islamic economy, rather than on hierarchies as shown by Graeber [8] or plunder by power as shown by Karatani [9].The Islamic economy is highly compatible with the WE economy in that it emphasizes a real, face-to-face, and mutual-aid economy and balances self-interest and altruism through various institutions [10,11].Just as Islamic societies triggered a shift to a credit economy in the Middle Ages [8], so too in modern times the Islamic economy could be a stepping stone to a shift to a capitalist economic alternative.
Note that the simulations were conducted using moral responsibility and risk vulnerability riding on a straight line on a two-dimensional plane based on the literature [15], but the basic relationship and trends between WE economies and joint ventures/redistribution should not change even if both are distributed on the plane.It is known that the mind perception changes with mental states [41,42] and with nonhuman objects [43,44].In the future, it is expected that artificially intelligent agents with morality will emerge [14].Although the mind perception is expected to change depending on the context of economic actors, economic activities, and social relations, the fundamental importance of the WE economy should remain the same.
This study only models the basic WE economy and the joint ventures/redistribution, and the absolute values of the parameters and calculation results do not necessarily reflect the real economy.However, because it is a basic model that discards details, it essentially presents the effectiveness of moral responsibility, the complementarity of the WE economy and the joint economy, and the direction of economic transformation toward reducing wealth inequality.As future challenges, there remain analytical studies based on modeling and parameterization that reflect the real economy, psychological research on the mind perception in economic activities, empirical research through fieldwork on economic activities based on moral responsibility, and social movements to spread the WE economy and transform a money economy into a credit economy.
Next, I formulate a redistribution model for the JV-M model (called JV-M-M model) by referring to the redistribution model in the literature [24].In the JV-M-M model, each of the  agents contributes wealth  •   •   () according to its transfer ratio  and moral responsibility   every redistribution period   , and the wealth ∑   •   ()  =1 Similar to the WE-M-M and WE-M-R models, I model distribution according to both the moral responsibilities   ,   and risk vulnerabilities   ,   of the two agents  and  (called the WE-M-MR model).In the WE-M-MR model, using   =   •   in Eq (1), the wealth contributed by the two agents  and  according to their moral responsibilities   and   is distributed according to their ratios   (  +   ) ⁄ and   (  +   ) ⁄ .The wealth   ( + 1) and   ( + 1) at time  + 1 are expressed as shown in Eq(9), respectively.

Figs
Figs 1A and 1B show the calculation results for the JV-B model of

Fig 2
Fig 2 shows the calculation results for the combinations of joint-venture

Fig 3
Fig 3 shows the calculation results for the WE economy models.Figs 3A and 5C and 5D has a wider distribution of wealth  than the WE-M-M model in Figs3Aand

Fig 6
Fig 6 shows the results of the Gini index calculation.Fig 6 shows the change