Utilitarian ethics, effective altruism, and efficient distribution of resources

Teleological ethics refers to the system of moral reasoning that takes the consequences of an action as the primary basis for its judgement. Utilitarianism, which asserts utility maximisation as the greatest good, is one of the most vivid teleological ideas. Although it is not easy to trace the history of the utilitarian concept to its roots, Bentham (Reference Bentham and Rosen1834a, Reference Bentham and Rosen1834b) was perhaps the first modern scholar to formulate the principles of utilitarian ethics explicitly. According to Bentham, the pursuit of the greatest happiness is central to human motivation, and this fact is sufficient to establish the principle of ‘goodness as utility’. Empathy, compassion, and social instincts are explicitly interpreted as acts of individual self-optimisation: ‘But the pleasure I take in the prospect of giving pleasure to my friend, whose pleasure is it but mine?’ (Bentham, Reference Bentham and Rosen1834a: 148). This quote perfectly describes how most modern economists evaluate altruism and pro-social behaviour using the notion of social (or other-regarding) preferences.

Mill's (Reference Mill1863) contribution to utilitarianism is to refine and extend the principle of greatest happiness proposed by Bentham. Mill introduces the concept of the quality of pleasure and posits that individuals who have the capacity to experience both mental and physical pleasure will tend to prefer the former. Bentham (Reference Bentham and Rosen1834a) argues for the justification of utilitarian motivation based on the belief that it is inherent in human nature, whereas Mill (Reference Mill1863) advocates utilitarianism as a widely accepted moral principle because of its beneficial effect on the collective outcome.

Utilitarian ethics has significantly shaped the development of normative attributions in mainstream economics (Colander, Reference Colander2000). The maximisation of social happiness (sometimes described as the efficient use of scarce resources in the context of collective choice) is implicitly assigned a role as the basis for any normative judgement, although economics is claimed to be value-neutral (see Arrow, Reference Arrow, Arrow, Sen and Suzumura1997; Robbins, Reference Robbins1938). Of course, it would be a mistake to say that economics does not deal with various considerations that seem to have nothing in common with narrowly defined self-interest; on the contrary, they play a prominent role being conceptualised as economic goods. The notions of ‘utility’ and ‘social welfare’ are extremely complex domains that encompass a wide range of economic goods, such as altruism (the ‘warm glow of giving’ is something for which we sacrifice our own resources), leisure, justice, equality, and so on. Consequently, when these considerations appear in economic analysis, they are only important as long as they are valued (i.e. as long as they contribute to individuals' utility).

It is worth mentioning that utilitarianism is typically juxtaposed to egalitarian motives. Rawls (Reference Rawls1971) pointed out that aggregate welfare maximisation does not necessarily benefit the most deprived individuals, thus contradicting the idea of fairness defended by Rawls from the ‘original position’ standpoint. Sen (Reference Sen1972) points out that although utilitarianism gained a reputation as an egalitarian movement (perhaps because assuming identical preferences and diminishing marginal utility, distribution according to the marginal benefit means assigning more resources to the least wealthy individuals – see Brandt, Reference Brandt1979, for more details) its innate nature has nothing to do with equity (or equality) concerns. Stark et al. (Reference Stark, Kobus and Jakubek2012) point out that if individuals care about their position in the income distribution, utilitarian and egalitarian social planners will arrive at the same end state (indeed, assuming that all individuals are characterised by strand inequality aversion, the goals of utility maximisation and equality promotion will coincide). Galanis and Veneziani (Reference Galanis and Veneziani2022) demonstrate that distribution implemented by the benevolent utilitarian planner decreases income inequality over time, provided that individuals exhibit reference-dependent preferences – yet, the results are, to a great extent, constrained by the diminishing marginal utility of wealth assumption, thus not immune to Sen's (Reference Sen1972) critique.

Today, we are witnessing a new round in the evolution of the act-utilitarian spirit – effective altruism. Effective altruism implies that a society can be better off by incrementally redistributing an endowment. As Singer (Reference Singer1972) points out, the sacrifice of a luxury (e.g. lipstick) does not have the same moral significance as human suffering due to the lack of essential goods (such as food, medicine, and shelter). Therefore, whenever someone faces a choice between buying a new lipstick and donating to charity, charity is a moral obligation. Singer's (Reference Singer1972) argument implies a redistribution of endowments based on the principle of maximum marginal utility: whoever enjoys the most should get the most (obvious for any economist, such a pattern of altruistic giving is not only effective but also efficient – see more details in Appendix A).

The above premise is easy to challenge from the perspective of economic epistemology. Such a transaction requires an analysis of the marginal utilities of different agents associated with different goods or an interpersonal utility comparison (IUC). From the collective choice theory standpoint, IUC could imply that one's own preferences should be given more weight than those of others (Arrow, Reference Arrow1951; List, Reference List2003). Moreover, it is impossible to experimentally verify the relative values of the marginal utilities that different individuals associate with various goods (Myerson, Reference Myerson, Hurwicz, Schmeidler and Sonnenschein1983). IUC is not a valid concept for normative economics. Nevertheless, introducing IUC is the only way to allow welfare economics to move beyond trivial Pareto improvements, which is why most welfare economists do so (Hammond, Reference Hammond, Elster and Romer1991; Johansson-Stenman, Reference Johansson-Stenman1998). On the other hand, Harsanyi (Reference Harsanyi1978) is in favour of the ‘general possibility’ of the IUC on the grounds that under certain conditions (such as cardinal preferences and impartialityFootnote ²) it can be meaningful. Moreover, provided that individuals are rational in the Bayesian sense, the social welfare function takes the form of an arithmetic mean of individual utilities, which justifies utilitarian morality from the standpoint of rationality.

The reliance on the IUC in Singer's (Reference Singer1972, Reference Singer2009) normative attribution model can be justified by incorporating the objective criterion (or self-sufficient truth) as defined by Scanlon (Reference Scanlon1975). A meal will provide more benefit to a hungry person than a new lipstick will to anyone, and this statement can be qualified as a self-sufficient truth. The problem is that most effective altruists apply the same principle to much more complex situations, implying that an objectively better option can still be identified. Distributing malaria nets seems a brilliant, cost-efficient way of fighting malaria – until one figures out they are actually used for fishing, contributing to environmental degradation in Africa (Jones and Unsworth, Reference Jones and Unsworth2020). MacAskill (Reference MacAskill and Boonin2018) acknowledges that such ‘epistemological issues’ remain an open question to be resolved at some point in the future, which resembles Bentham's (Reference Bentham1823) felicity calculus exercises.Footnote ³ The impossibility of assessing subjective utility or predicting the remote consequences of an action can hardly be treated as secondary concerns that will inevitably be addressed at some point; rather, they represent the major flaws in utilitarian thinking.

For the most modern version of effective altruism, teleological orientation – the additional key component of utilitarian ethics – takes a rather extreme form. MacAskill (Reference MacAskill2022) advocates longtermism, proclaiming that it is our ultimate moral obligation to care for the welfare of all future generations. Although it is hard to argue with the above statement, being a true longtermist would require something more: a clear vision of the desirable ‘end state’, a belief that such a state is either favoured by the rest of society (or can be undoubtfully identified as objectively superior to all alternatives), and (last but not least) living in a world free of radical uncertainty.Footnote ⁴ Overall, longtermism mirrors a well-known ‘engineering’ approach to social organisation (Hayek, Reference Hayek1944).

It would be too ambitious to argue that there is no boundary between effective altruism and classical utilitarianism. The former is claimed to be more nuanced and complex (MacAskill, Reference MacAskill and Boonin2018). However, the definition of effective altruism proposed by MacAskill (Reference MacAskill and Boonin2018) highlights maximising, science-alignment, tentative welfarism, and impartiality, which should sound recognisable to anyone familiar with collective choice problems being discussed under the neoclassical economics shield. In addition, most of the hypothetical cases described by advocates of effective altruism typically resemble the familiar problem of redistribution based on the marginal utility criterion (Elder and Fischer, Reference Elder and Fischer2017; Gabriel, Reference Gabriel2016; Singer, Reference Singer1972, Reference Singer2009). The treatment of efficiency as the main normative criterion and the teleological orientation are innate to effective altruism and remain the key focus of this paper.

Deontological altruism and long-term resilience criterion

Deontological ethics is juxtaposed with teleological moral thinking in the sense that the former disregards the consequences of the act as the basis for its evaluation. Unlike utilitarianism (often described as a product of the French Enlightenment – see Hayek, Reference Hayek and Caldwell1945), deontology (as we understand it nowadays) can be traced back to ancient Greek philosophy (see Russell, Reference Russell1946).Footnote ⁵ Among modern philosophers, Kant (Reference Kant1785) is, perhaps, the most famous advocate of deontological ethics, who objects to consequentialist moral reasoningFootnote ⁶ and believes that all humans have specified moral duties, which they are obliged to follow because there is nothing to justify the violation of these duties.

Unlike effective altruism, altruism rooted in deontological reasoning might be tricky to define. Van Staveren (Reference van Staveren2001) asserts that ‘deontological ethics is about following universal norms that prescribe what people ought to do, how they should behave, and what is right or wrong’ (p. 23), aligning with Kant's ‘rule worship’. McNaughton and Rawling (Reference McNaughton, Rawling and Copp2007) postulate that ‘deontologists characteristically hold that we must not harm people in various ways’, although ‘deontology sometimes requires agents not to maximise the good’; the former premise sounds in line with deontological (although not Kantian) logic, whereas the latter one resembles teleological thinking. According to White (Reference White2009), deontology implies that ‘not all ethical judgements regarding actions can be made on the basis of outcomes or consequences’ (p. 300), assuming that in some circumstances, teleological reasoning can be justified. Sunstein (Reference Sunstein2014) affirms that ‘deontologists believe that some actions are wrong even if they have good consequences’. Hardt (Reference Hardt2020) argues that deontological norms are not absolute, and sometimes, violation of perfect duties can be justified. Our intuition is that ‘pure’ deontological reasoning (in the Kantian sense) requires a belief in fundamental moral rules; being religious is not crucial, but it certainly helps. Consequently, modern views of deontology include a teleological component, in the sense that moral duties should be consistent with general welfare goals to be justifiable.

To depict deontological altruism in simulations, we need to understand how individuals manifest it in social exchange. Sunstein (Reference Sunstein2014) describes deontological reasoning as a kind of ‘moral heuristics’: in situations of uncertainty and time pressure, we rely on ‘rapid, automatic, emotional processing’, following specific unconditional rules that take the form of formal (e.g. legally enforced) and informal (i.e. social normsFootnote ⁷) institutions. Thus, in the present context, deontological altruism is seen as the exercise of social norms by individuals, while the particular social interaction strategy represents a social norm as such. A big question is the extent to which social norms are actually unconditional; for example, Sugden (Reference Sugden2018) highlights that our tendency to follow social norms depends on whether others are observing us. However, even though social norms may be constrained by external approval or disapproval, they have the deontological component of acting in a certain way regardless of the expected consequences.

The deontological (heuristical) giving has been known since ancient times. Tithing is mentioned in the Old Testament; Judaism requires at least 10% of income to be given to charity (this practice is common among Muslims and Christians). Singer (Reference Singer2009) refers to this practice and argues that one can give a tenth of one's income to effective charitable foundations. Yet, ancient religious communities had little in common with modern charitable foundations that cherish the idea of effective altruism. The former served as orphanages, provided schooling and helped the poor by collecting and distributing donations. However, it would be more accurate to think of them as charities of ‘spontaneous order’ (in Hayek's sense) rather than the product of deliberate design with a clear end goal. Religious confessions provide communities with public goods and help to ensure organised collective action; they stay resilient because they do not have a central planner striving for the ‘optimal design’ of charity and other forms of human interaction (Gill, Reference Gill2020).

Human beings are social creatures; as long as they can feel the ties with their community and a proper sense of sociability, altruism can be effectively institutionalised (Kropotkin, Reference Kropotkin1904). Thus, although Singer (Reference Singer2009) attempts to fit tithing custom into the paradigm of effective altruism, there is no more profound connection between the two. Although we do not feel sufficiently confident to provide an explicit definition of deontological altruism, intuition dictates that it can be described as sacrificing a share of one's income for the sake of giving without concern for how efficiently the donation is used.

Our take on conceptualising ethical systems in action allows for drawing a borderline between utilitarian and deontological altruism. However, the distinction between deontology and virtue ethicsFootnote ⁸ is much less pronounced. Intuitively, there is a difference between following the ‘logic of duty’ and developing a virtuous personality through acting accordingly. Yet, the aforementioned difference refers to motivation, not action. The practice of tithing might arise from one's devotion to duty (expressed as a religious norm or social convention) or the desire to be a good person. Therefore, although virtue ethics represents a separate ethical system, it mostly remains beyond the scope of our interest.

Overall, we concede that deontological giving might lead to inefficient allocation of scarce resources, but argue that it might serve as a better giving pattern from another perspective, namely resilience and sustainability criteria. Gill and Thomas (Reference Gill and Thomas2023) also doubt the appropriateness of the normative criterion of allocative efficiency. Gift-giving inevitably leads to deadweight losses and represents, therefore, an undesirable practice from a mainstream economic perspective; cash transfers would be much more efficient. However, gift-giving makes sense once one abandons the mainstream economic view. Such custom can be seen as a symbolic sacrifice (sometimes involving the deliberate destruction of value) caused to develop mutual trust (primarily by demonstrating one's trustworthiness).

Giving gifts violates allocative efficiency but creates and maintains an environment essential for further cooperation (including market transactions). One would hardly believe that gift-giving is motivated by the desire to sustain the important social practice and thus contribute to social well-being in the long-run perspective. Instead, a giver follows a common practice – some heuristics – developed in the process of social evolutionary selection. Perhaps one might say that being an effective altruist requires the belief in the superiority of deliberate design, while deontological ethics implies following the rule, not necessarily realising its greatest purpose (or even the existence of such).

Simulation design

The simulation mirrors the Giving according to GARP (Andreoni and Miller, Reference Andreoni and Miller2002) experiment. The original experiment includes eight rounds; the participants are randomly assigned different partners during each round. All participants receive the same endowment (the number of tokens) to allocate between themselves and others under various ‘hold’ and ‘pass’ values. Under such a setting, participants face a trade-off between two economic goods: own pay-off and altruistic giving under various budget constraints. Consequently, the original study concentrates on testing social preferences for consistency with the GARP (see Appendix A).

The present study adopts a similar experimental design for a different purpose: evaluating the various giving strategies (including effective altruism and deontological altruism) based on multiple criteria. From the narrow choice-consistency perspective, deontological altruism violates the principles of rational choice (in contrast to effective altruism – see Appendix A). Besides, intuition dictates that a society of effective altruists should have higher aggregate wealth than the deontological altruists (results supporting this intuition are presented in further sections). From the mainstream perspective, effective altruism seems the most desirable form of social exchange from society's standpoint. Yet, it is worth examining the problem from a different perspective by observing the outcomes of interaction between agents following different giving strategies in various circumstances.

Our simulation was inspired by so-called ‘battle of algorithms’ studies exploring the relative performance of various decision-making rules (Axelrod, Reference Axelrod and Davis1987; Imhof et al., Reference Imhof, Fudenberg and Nowak2007; Lomborg, Reference Lomborg1996; Nowak and Sigmund, Reference Nowak and Sigmund1993; Wahl and Nowak, Reference Wahl and Nowak1999) in which pseudo-intelligent agents interact according to fixed rules constrained by their type. In the present study, agents' types are defined by their giving strategies; the decision-making framework (i.e. endowment alongside the hold and pass values) changes every round.

Each iteration of the simulation contains two loops. In the outer loop, endowment (in the form of tokens) is drawn from the range [10, 100] for a population of N for R periods (rounds), generating random matrix M[N, R]. Therefore, wealth distribution is not uniform at the beginning of the game. We specify eight rounds (analogously to the original experiment), although the number of rounds can be amended without any noticeable change in the results. In each round, each agent interacts with a new partner. The monomorphic populations consist of 1,000 agents; each additional type added to the society increases the population by 1,000 agents. In polymorphic populations, all the types are combined; because the partners are selected randomly, the agents can interact with representatives of various types (including their own). During the game, the population composition remains unchanged. Then, the hold (V _s[N, R] – ‘payment to self’) and pass (V _o[N, R] – ‘payment to others’) values are randomly picked from the range [1, 10]; these values are uniform for all the agents, regardless of their type.

It should be noted that although, technically, one is free to specify any range for the pass and hold values, the behaviour of effective altruists is sensitive to the ratio of the aforementioned, because it constitutes parameter f (see the detailed discussion in the next section). Therefore, f should be specified considering the maximum gap between the pass and the hold value. Otherwise, assuming that the parameter value is too high, effective altruists might donate nothing (and vice versa).

The inner loop generates agents' choices (i.e. the number of tokens to pass) under the budget constraints specified by rows of matrixes M[N, R], V _s[ ⋅ , R], V _o[ ⋅ , R] depending on the given agent type (the behaviour of each type is described in the next section). We use Monte Carlo simulations for the sake of robustness. In each of the 100 iterations, information about the total wealth of individuals and the entire society is collected, and the Gini coefficient is used to measure wealth inequality.

Giving strategies

The game design utilised in the simulation serves as a simplified model of social exchange. Therefore, to conceptualise effective and deontological altruism in the simulation, one should take the aforementioned ideas to the extreme and concentrate on their most distinct aspects. Teleological orientation and allocative efficiency are distinguishable features of effective altruism. In Giving according to GARP setting, such a decision-making principle can be only conceptualised through giving according to the marginal benefit rule (although in a more complex real-world environment, effectively altruistic charity might not even concern the proportion of income being donated – Côté and Steuwer, Reference Côté and Steuwer2023). Consequently, this paper does not attempt to criticise effective altruism in a holistic manner; instead, we address the implications of teleological reasoning and treating efficiency as the principal normative criterion exclusively.

Similarly, when referring to deontological altruism in simulation, we emphasise its unconditional and heuristic nature – a deliberate simplification of a more complex concept for simulation purposes. It should be stated clearly that we see deontological altruism as a spontaneously developed and constantly evolving phenomenon. Our natural inclination to give and help is cultivated through socialisation,Footnote ⁹ but this does not mean that we cannot learn or change a giving strategy depending on external environment constraints. At the macro level, mutual expectations and shared social norms may changeFootnote ¹⁰; at the micro level, individuals adjust their interaction strategies according to the signals they receive. As we are unable to include the above aspects in the simulation, we should nevertheless warn that our deontological altruists are quite dumb compared to their hypothetical and more realistic version.

In the simplified simulation setting, we distinguish between three types of agents, namely:

1. (1) Type 1: deontological altruists. Deontologically altruistic agents always pass the fixed portions of their token endowment, regardless of the hold and pass value. They pass t × M _R and hold (1 −  t) × M _R tokens in each round R. Two extreme attitudes can be distinguished: unconditionally selfish agents tend to pass nothing (t  →  0), whereas pathological altruistsFootnote ¹¹ tend to pass the entire endowment to other players (t  →  1).

2. (2) Type 2: effective altruists. Welfare-maximising effective altruists distribute their token endowment in line with the allocative efficiency principle. When the hold value exceeds the pass value, they hold all the tokens, and vice versa: when the pass value exceeds the hold value, they pass all the tokens. However, other sub-types might be more or less sensitive to efficiency considerations. The parameter f stands for a psychological multiplier indicating how many times the pass value must be greater than the hold value so that the agent is willing to give (we refer to it as the ‘efficiency considerations parameter’). The condition for transferring endowment is f ≤ V _o/V _s. Three essential strategies can be distinguished. Agents for whom parameter f approaches infinity (f → ∞ ) exhibit egoistic tendencies: they donate if the pass value is substantially higher than the hold value. Agents with f approaching zero (f → 0) feature pathological altruism because they only hold tokens if the hold value surpasses the pass value enormously. Welfare-maximising effective altruists operate on a trade-off principle: they are concerned with aggregate welfare maximisation only, implying that f  =  1.

3. (3) Type 3: zero-intelligence altruists. Zero-intelligence agents assign a random number of tokens to other players regardless of the hold and pass value trade-off, constrained solely by their token endowment (analogously to Sunder's, Reference Sunder1993, agents).

Interaction in monomorphic societies

In monomorphic societies, the agents interact with their type solely. Each society consists of 1,000 agents (this parameter was selected arbitrarily and can be amended without any implications for the results). The particular pattern of giving is evaluated based on the value of the endowment and its distribution; we utilise the cumulative distribution functions (CDFs) for this purpose (see Figure 1). The interpretation is as follows: for any value of endowment (x-axis variable), the function represents the proportion of the population (y-axis variable) with endowment below the aforementioned value. It is possible to say that one type stochastically dominates the other if, for any cumulative proportion of the population, such a type possesses the greater endowment (in this case, the endowment distribution of the dominant type is located to the right-hand side of the distribution of the dominated type). The results of the simulations in the form of wealth distributions featured by each ‘ideal type’ and society as a whole are constrained by the values of the parameters t and f. By manipulating these variables, one can create infinite options, and we cannot discuss (or even demonstrate) all of them in the present paper. Therefore, we present the selected results – the most interesting and illustrative ones in our view. However, one could check the results in monomorphic and polymorphic societies, assuming different values of the key parameters using the online appendix.Footnote ¹²

Figure 1. Wealth distributions in monomorphic societies of deontological altruists, effective altruists, and zero-intelligence altruists assuming different values of t and f parameters.

Note: In every panel, the x-axis represents the simulated wealth of society after the exchange, and the y-axis shows the proportion or percentage of data points that are less than or equal to the corresponding wealth values. The point where the curve crosses 0.5 on the y-axis (indicated by the black line) corresponds to the median. If the curve rises quickly, much of the wealth is clustered around lower values. A slower rise indicates wealth is more evenly distributed across the range. The ‘fat’ curve's tails indicate the unequal distribution and outliers. Comparing distributions of simulated societies: when lines diverge, it indicates differences in the distribution. The further to the right the line is, the more wealth a given society has. The parallel shift of a given distribution (A) about another distribution (B) to the right indicates first-order stochastic dominance: for every possible income level, the proportion of the population with income below that level is smaller in (A) than in (B).

The outcomes in the societies of zero-intelligence altruists (who select the number of tokens to be passed randomly) are treated as a benchmark for assessing the remaining types. In the first and the second panels, we design relatively selfish deontological and effective altruists (assuming that the former donate a relatively small proportion of their endowment and the latter require a substantially greater value of pass value compared to the hold value to donate their entire endowment to others). In the simulation displayed in panel 3 (corresponding to f = 1 and t = 0.5), effective and deontological altruists are designed to be indifferent between their own and others' pay-off (the total pay-off maximisation objective guides the former type, and the latter type passes half of the endowment). Panel 4 represents the scenario of pathological altruism among the effective and deontological agents.

Panel 1 shows that radically selfish deontological and effective altruistic giving produce similar results to zero-intelligence agents. However, effective altruists stochastically dominate zero-intelligence and deontological altruists in all other cases. In contrast, about half of the deontological altruists underperform even zero-intelligence agents in all but the first simulation. Interestingly (yet not surprisingly), welfare-maximising effective altruists (i.e. featuring f = 1) accumulate the greatest wealth compared to the effective altruists featuring higher or lower values of the ‘efficiency considerations parameter’.

Effective altruists dominate deontological altruists with similar levels of generosity in isolation. At the same time, however, the latter pattern of giving appears to be the most egalitarian. The distribution of changes in Gini coefficients in 100 iterations (see Appendix B, Figure B1) shows that the deontological pattern of giving reduces the degree of initial wealth inequality. In contrast, effective altruists experience increased inequality (although not as substantial as in the population of zero-intelligence agents).

It is worth mentioning that in one of the preliminary versions of the simulation, we assumed the uniform distribution of initial endowment. In such a setting, the isolated population of welfare-maximising effective altruists featured the lowest wealth inequality among all the groups ex-post. Therefore, in the ideal world of perfect equality of opportunity (captured by equality of wealth), where all individuals are concerned only with the common good (maximising aggregate wealth), equality and wealth are not competing but complementary concerns. Such a society would indeed be a true utopia. However, in a more realistic setting, where the distribution of endowments is uneven, effectively altruistic giving leads to increasing wealth inequality. Although this is not the primary objective of the paper, our robust simulation results show that the goals of total wealth maximisation and equality can be aligned in rare circumstances only (e.g. under the assumptions of Stark et al., Reference Stark, Kobus and Jakubek2012, or Galanis and Veneziani, Reference Galanis and Veneziani2022). In general, however, the utilitarian distribution leads to the anti-egalitarian outcome.

Interaction in polymorphic societies

The polymorphic societies consist of deontological altruists, effective altruists, and zero-intelligence altruists in equal proportions. The populations include 1,000 agents of each type; analogously to the monomorphic groups' analysis, the results are robust to the changes in the population size parameter N. The simulations presented in Figure 2 were designed according to the same logic as the simulations reported in Figure 1: our goal was to compare the performance of the deontological and effective altruists featuring a comparable degree of generosity. Allowing agents to interact with other types caused radically different outcomes. Although the shape of CDFs of relatively selfish effective and deontological altruists did not change significantly, zero-intelligence altruists are worse off being stochastically dominated by the aforementioned types (see panels 1 and 2 of Figures 1 and 2). Under t = 0.5 and f = 1, isolated effective altruists used to dominate deontological altruists and zero-intelligence agents; in polymorphic societies, they are dominated (compare panel 3 of Figures 1 and 2). Deontological altruists passing half of their endowment feature CDF similar to zero-intelligence altruists (see panel 3 of Figure 2). Finally, zero-intelligence agents stochastically dominate pathologically altruistic effective and deontological agents; however, deontological altruists perform better (see panel 4 of Figure 2).

Figure 2. Wealth distributions in polymorphic societies combining deontological altruists, effective altruists, and zero-intelligence altruists in equal proportions assuming different values of t and f parameters.

The trade-off between allocative efficiency and equality becomes apparent when analysing the polymorphic group as a whole, rather than focusing on the individual types (Appendix B, Figure B2). The society of ‘self-neutral’ effective and deontological altruists (i.e. agents featuring f = 1 and t = 0.5) exhibits the smallest increase in wealth inequality. At the same time, pathological altruism (i.e. f = 0.25 and t = 0.7) implies a higher level of cumulative wealth.

In the next step, we assess the effect of deontological agents' giving heuristics while assuming that effective altruists are concerned with welfare maximisation solely (implying that f = 1). The results are displayed in Figure 3. Utterly selfish deontological altruists passing only 0.01 of their endowment perform better than welfare-maximising effective altruists. The result is not surprising because selfishness represents a ‘predatory’ strategy (giving almost nothing, yet receiving donations from others). Yet, even zero-intelligence agents perform better than effective altruists (see panel 1). The outcome remains similar after increasing the proportion of endowment donated by deontological altruists to t = 0.2 (panel 2). Deontological altruists donating half of their endowment perform similarly to zero-intelligence agents, but effective altruists' position remains inferior (panel 3). In the case of pathological deontological altruism (t = 0.7), approximately half of the effective altruists still perform worse than deontological altruists, although zero-intelligence agents dominate both types (panel 4).

Figure 3. Wealth distributions in polymorphic societies combining deontological altruists, effective altruists, and zero-intelligence altruists in equal proportions assuming f = 1 for different values of t parameter.

For welfare-maximising effective altruists, the trade-off between efficiency and inequality in the whole society is not as sound as in the previously discussed simulation (see Figure B3 in Appendix B). Although the scenario of t = 0.5 and f = 1 still produces the most egalitarian outcome (i.e. the outcome associated with the slightest change in the Gini coefficient), the CDF is mainly located on the right-hand side of the CDFs corresponding to the remaining scenarios. Therefore, the society of ‘self-neutral’ deontological and effective altruists outperforms the societies consisting of ‘self-neutral’ (welfare-maximising) effective altruists and more selfish or more generous deontological altruists in terms of wealth and equality.

Finally, attempting to mirror the real-life example of deontological giving – the practice of tithing – we explore the societies where all the deontological altruists donate 0.1 of their endowment (see Figure 4). Relatively selfish deontological altruists outperform pathologically altruistic effective agents (panel 4), which should not come as a surprise. However, in such a setting, a substantially higher degree of selfishness among effective altruists provides a minor advantage: although selfish effective altruists dominate deontological altruists, the distance between the CDFs is barely visible (panel 1).

Figure 4. Wealth distributions in polymorphic societies combining deontological altruists, effective altruists, and zero-intelligence altruists in equal proportions assuming t = 0.1 for different values of f parameter.

Society as a whole (see Figure B4 in Appendix B) experiences the smallest increase in the Gini coefficient when both effective and deontological altruists are relatively selfish – i.e. when t = 0.1 and f = 2. Interestingly, a relatively low level of wealth inequality is achieved without considerable marginal wealth redistribution (which would require more generous deontological and effectively altruistic agents). Moreover, such a society stochastically dominates the population with welfare-maximising effective altruists (i.e. featuring f = 1).