A Computational Clarification of the "Veil of Ignorance": Transformation of Income Expectation Distributions via Bayesian Inference and the Justification of Principles of Justice
Introduction: The Redefinition of Justice and the Contemporary Challenges of the "Veil of Ignorance"
John Rawls's "A Theory of Justice," published in 1971, is a landmark in post-war political philosophy and remains the starting point for discussions on "justice as fairness" to this day. The core of Rawls's theory lies in his critique of the utilitarian "greatest happiness for the greatest number," which can sometimes force sacrifices upon the minority, and his proposal of the "difference principle (maximin principle)," which maximizes the benefits for the least advantaged.
The device used to derive this principle is the "veil of ignorance." This is a thought experiment that posits individuals placed in an "original position" where they have no knowledge of their own talents, social status, assets, or religious and moral beliefs. Behind this veil, it is assumed that individuals, considering the risk of being at the very bottom of society, will act in a risk-averse manner and choose rules that take into account the most disadvantaged.
However, this theory has long been accompanied by a decisive criticism: the "veil of ignorance" is a psychological state unattainable by real human beings, and there is no objective method to determine whether such a state has been "achieved." This paper aims to model this philosophical black box using "Bayesian inference," a framework from cognitive science and computational statistics, and to elucidate its formation process through numerical simulation.
Chapter 1: The "Veil of Ignorance" as a Computational Model
1.1 Limitation and Operationalization of Information
To treat the "veil of ignorance" scientifically, it is necessary to limit the abstract "omniscient ignorance" to measurable variables. In this study, this information is narrowed down to "expectations of future personal income." The probability distribution an individual constructs regarding their future income serves as the indicator of "self-cognition" in this model.
1.2 Learning Process via Bayesian Inference
Changes in individual cognition are described by Bayesian inference. We track how an individual's predictions are updated (formation of a posterior distribution) when objective external information, such as the income data of others, is provided against prior expectations (prior distribution). Under this framework, the veil of ignorance is defined as the state where the income expectation distribution, determined by representative values from the posterior distribution of each inferred parameter, becomes "uninformative," which can be posited as the variance of the income expectation distribution becoming extremely large.
Chapter 2: Simulation Design and Results—The Conflict Between "Self-Conviction" and "Macro Reality"
This chapter details how an individual's subjective income expectations transform when they come into contact with objective income data of society as a whole, using the constructed Bayesian inference model. In particular, we focus on the asymmetry between "optimism" and "pessimism" as initial states and analyze the structural factors that make reaching the "veil of ignorance" difficult.
2.1 Experimental Setup: Operationalization of Prior Distributions
The "virtual participants" in the simulation are assumed to have a specific prior distribution regarding their future income.
Optimistic Expectation Condition: A state where the mean of the prior distribution is significantly higher than the median income of real society, and the variance is small. This expresses a strong, privileged conviction that "I will certainly belong to the elite class."
Pessimistic Expectation Condition: A state where the mean is at a low level close to the welfare standard, and the variance is similarly small. This expresses a strong resignation that "I cannot escape from the bottom of the inequality."
Against these, we sequentially presented income data of others randomly sampled from the actual social income distribution (generally considered to follow a log-normal distribution) and observed the transition of the posterior distribution.
2.2 Optimistic Expectation Condition: Gradual Decline and Increased UncertaintyWhen macro income data (most of which are lower than their own expectations) were presented to subjects who were convinced of high income, the mean value of the posterior distribution gradually shifted downward due to Bayesian updating.What is noteworthy in this process is the change in "variance (fluctuation of conviction)." By recognizing the existence of a vast number of others with lower income than themselves, the subject loses the certainty of the hypothesis that "only I am privileged." As a result, the tails of the income expectation distribution widened, and uncertainty increased. However, in the computational model, the distribution did not become completely flat (uninformative) even after repeated observations.This is because the initial "obsession with high income (strong prior distribution)" functions as a kind of anchor, resisting correction by objective data. This result suggests that reaching the "veil of ignorance" as Rawls described requires not just the mere presentation of information, but a more powerful psychological detachment that forcibly resets one's own attributes.
2.3 Pessimistic Expectation Condition: Insensitivity to Change and the "Constancy of Despair"
On the other hand, more unique results were obtained in the condition where low income was expected. Macro data naturally includes a lot of data on income brackets higher than the subject's own expectations. However, the mean value of the posterior distribution did not shift significantly upward, and the stability of its position was striking.
Furthermore, regarding variance, although it increased slightly after observing the first few pieces of data, it quickly converged and plateaued. This represents the "robustness of negative bias." Predictions of low income are processed in a way that even when observing average social data (values higher than one's own), one thinks, "That is someone else's story and does not apply to me," making it difficult to be a factor that widens one's own prediction distribution (i.e., approaching the veil of ignorance).
This "fixation of pessimism" can be interpreted as a mathematical backing for "learned helplessness" in social psychology, highlighting a psychological situation where the disadvantaged cannot even hold uncertainty (i.e., expansion as possibility) regarding their own future.
2.4 Considerations on the Reachability of an "Uninformative Distribution"
From the results of this simulation, it was found that there are two barriers to reaching the "veil of ignorance (a global uninformative distribution)" in the pure sense.
One is the wall of confirmation bias; for subjects with a strong sense of self, data about others is easily processed as an "exception" and is unlikely to have enough impact to flatten the distribution.
The other is information asymmetry; optimistic individuals are forced to accept "downward uncertainty," while pessimistic individuals tend to reject "upward uncertainty."
Ultimately, humans cannot completely escape the obsession of "who they are" through the mere cognition of macro information. It can be said that the "failure" of this model (not reaching an uninformative state) paradoxically proves just how powerful an assumption the "veil" set by Rawls was.
Chapter 3: Redefining the 'Veil of Ignorance'—From 'Oblivion of Self' to 'Structuring of Society'
The simulation in Chapter 2 demonstrated that the initial biases held by individuals are extremely robust, and that the mere introduction of external information cannot completely reset predictions to a blank slate. However, this result does not signify the failure of Rawls's theory. Rather, it provides the key to reconstructing the concept of the 'veil of ignorance' in a more dynamic form that aligns with actual cognitive mechanisms.
3.1 Distinguishing between 'Ignorance of Self' and 'Knowledge of General Laws'
In 'A Theory of Justice,' Rawls states that even behind the veil, one is well-versed in 'general principles concerning human society (macro laws).' Applying this requirement to a computational model reveals a new interpretation. The perspective is that even if the income expectation distribution does not reach a 'completely flat (uninformed)' state through Bayesian inference, the process of asymptotically approaching the 'shape of the macro income distribution (log-normal distribution)' is the formation of a substantive veil of ignorance.
3.2 From Local Self to Statistical Self
When an agent under optimistic conditions observes macro data and the distribution approaches the shape of society, the agent is not predicting 'the individual that is me,' but rather 'myself as a random sample extracted from society.'
In other words, the 'veil of ignorance' in a computational sense is a state where the 'subjective income expectation distribution' and the 'objective social income distribution' become statistically indistinguishable. At this point, the individual abandons specific subjective convictions and accepts a statistical prediction: 'I will become someone in this society (someone who, on average, is at this position, and who has a certain probability of being in the lowest stratum).'
3.3 The Nature of the 'Uncertainty' that Leads to the Difference Principle
Under this redefinition, agreement with the difference principle becomes a consequence of 'rational risk management' rather than 'fear.' An agent with an expectation distribution close to the macro income distribution recognizes with mathematical reality the 'probability of being placed in the most disadvantaged situation in society.' When one's own predictions are 'synchronized' with the reality of society, a rational individual is compelled to choose the 'lifting of the bottom' as their own survival strategy.
3.4 Summary: Operationalized Justice
With the redefinition in this chapter, the 'veil of ignorance' has transformed from an unmeasurable psychological state into a computable index: 'the degree of convergence of subjective predictive distributions toward the macro distribution.' This signifies an intellectual process of correctly positioning oneself as an 'interchangeable point' within the large distribution that is society—that is, the acquisition of 'statistical humility.'
Chapter 4: Conclusion and Prospects—The Future of Consensus Building Opened by the Operationalization of Justice
This study has clarified a portion of the cognitive mechanisms behind John Rawls's 'veil of ignorance,' one of the most abstract concepts in political philosophy, by situating it within the framework of a computational model known as Bayesian inference.
4.1 Summary of This Study
The greatest insight gained through the simulation is the re-conceptualization of the veil of ignorance not as an 'empty state of knowing nothing,' but as **'a dynamic process in which one's subjective biases dissolve into and synchronize with the macro reality of society.'**
Whether dreaming of high income or resigning oneself to low income, by being repeatedly exposed to the objective external information of the macro income distribution, individuals rewrite their income expectations into 'a single sample of society as a whole.' It was suggested that the acquisition of this 'statistical self' is the cognitive foundation that rationalizes agreement with the difference principle—that is, the choice to 'maximize the benefits of the most disadvantaged.'
4.2 Digital Transformation (DX) of Political Philosophy
The method presented in this study brings 'measurability' and 'operability' to political philosophy. Discussions that were previously left to the individual's imagination—such as 'if one were behind the veil... '—can now shift to quantitative discussions, such as 'how much macro information, presented over what duration, causes the variance of self-prediction to exceed a threshold and leads to the formation of an agreement on principles of justice.' This is an important step toward the scientific foundation of justice theory.
4.3 Future Developments: Possibilities for Social Implementation
The methodology proposed in this study is not limited to mere simulation, but is expected to have wide-ranging applications in research and real-world society, such as the following:
Design of Fair Consensus Building (Mechanism Design): In discussions on tax reform or social security systems, architecture design to mitigate subjective biases and elicit a 'fair consensus' closer to global optimization by providing participants with macro statistical information along with appropriate visualizations.
Countermeasures against Algorithms and Information Polarization: The 'echo chambers' created by modern social media excessively sharpen individual prior distributions, distancing them from the veil of ignorance. By applying this model to analyze how exposure to diverse information can re-form a 'veil of cognition,' we can explore remedies for society.
Comparative analysis of senses of justice across cultures and social strata: By varying parameters such as prior distributions and learning rates, we compare and examine the 'thresholds of justice' that differ by country and cultural sphere.
In Conclusion
The 'justice as fairness' that Rawls dreamed of need no longer be a mere armchair theory in the modern era, where digital technology and computational science have flourished. Only when we break out of the small shell of our own attributes and project ourselves as an uncertain element within the distribution of society as a whole can empathy for others be sublimated into a 'rational social contract.' The 'operationalization of the veil of ignorance' proposed in this study should serve as a compass for transforming subjective conflicts of belief into a process of objective information sharing and inference, thereby helping to build a more just society.