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The largely dominant meritocratic paradigm of highly competitive Western cultures is rooted on the belief that success is mainly due, if not exclusively, to personal qualities such as talent, intelligence, skills, smartness, efforts, willfulness, hard work or risk taking. Sometimes, we are willing to admit that a certain degree of luck could also play a role in achieving significant success. But, as a matter of fact, it is rather common to underestimate the importance of external forces in individual successful stories. It is very well known that intelligence (or, more in general, talent and personal qualities) exhibits a Gaussian distribution among the population, whereas the distribution of wealth — often considered as a proxy of success — follows typically a power law (Pareto law), with a large majority of poor people and a very small number of billionaires. Such a discrepancy between a Normal distribution of inputs, with a typical scale (the average talent or intelligence), and the scale-invariant distribution of outputs, suggests that some hidden ingredient is at work behind the scenes. In this paper, we suggest that such an ingredient is just randomness. In particular, our simple agent-based model shows that, if it is true that some degree of talent is necessary to be successful in life, almost never the most talented people reach the highest peaks of success, being overtaken by averagely talented but sensibly luckier individuals. As far as we know, this counterintuitive result — although implicitly suggested between the lines in a vast literature — is quantified here for the first time. It sheds new light on the effectiveness of assessing merit on the basis of the reached level of success and underlines the risks of distributing excessive honors or resources to people who, at the end of the day, could have been simply luckier than others. We also compare several policy hypotheses to show the most efficient strategies for public funding of research, aiming to improve meritocracy, diversity of ideas and innovation.

Humanity has been fascinated by the pursuit of fortune since time immemorial, and many successful outcomes benefit from strokes of luck. But success is subject to complexity, uncertainty, and change — and at times becoming increasingly unequally distributed. This leads to tension and confusion over to what extent people actually get what they deserve (i.e. fairness/meritocracy). Moreover, in many fields, humans are overconfident and pervasively confuse luck for skill (I win, it is skill; I lose, it is bad luck). In some fields, there is too much risk-taking; in others, not enough. Where success derives in large part from luck — and especially where bailouts skew the incentives (heads, I win; tails, you lose) — it follows that luck is rewarded too much. This incentivizes a culture of gambling, while downplaying the importance of productive effort. And, short-term success is often rewarded, irrespective, and potentially at the detriment, of the long-term system fitness. However, much success is truly meritocratic, and the problem is to discern and reward based on merit. We call this the fair reward problem. To address this, we propose three different measures to assess merit: (i) raw outcome; (ii) risk-adjusted outcome, and (iii) prospective. We emphasize the need, in many cases, for the deductive prospective approach, which considers the potential of a system to adapt and mutate in novel futures. This is formalized within an evolutionary system, comprised of five processes, inter alia handling the exploration–exploitation trade-off. Several human endeavors — including finance, politics, and science — are analyzed through these lenses, and concrete solutions are proposed to support a prosperous and meritocratic society.

While wealth distribution in the world is highly skewed and heavy-tailed, human talent — as the majority of individual features — is normally distributed. In a recent computational study by Pluchino et al. [Talent vs luck: The role of randomness in success and failure, Adv. Complex Syst. 21(03–04) (2018) 1850014], it has been shown that the combined effects of both random external factors (lucky and unlucky events) and multiplicative dynamics in capital accumulation are able to clarify this apparent contradiction. We introduce here a simplified version (STvL) of the original Talent versus Luck (TvL) model, where only lucky events are present, and verify that its dynamical rules lead to the same very large wealth inequality. We also derive some analytical approximations aimed to capture the mechanism responsible for the creation of such wealth inequality from a Gaussian-distributed talent. Under these approximations, our analysis is able to reproduce quite well the results of the numerical simulations of the simplified model in special cases. On the other hand, it also shows that the complexity of the model lies in the fact that lucky events are transformed into an increase of capital with heterogeneous rates, which yields a nontrivial generalization of the role of multiplicative processes in generating wealth inequality, whose fully generic case is still not amenable to analytical computations.

This paper further investigates the Talent versus Luck (TvL) model described by [Pluchino et al. Talent versus luck: The role of randomness in success and failure, Adv. Complex Syst.21 (2018) 1850014] which models the relationship between ‘talent’ and ‘luck’ on the impact of an individuals career. It is shown that the model is very sensitive to both random sampling and the choice of value for the input parameters. Running the model repeatedly with the same set of input parameters gives a range of output values of over 50% of the mean value. The sensitivity of the inputs of the model is analyzed using a variance-based approach based upon generating Sobol sequences of quasi-random numbers. When using the model to look at the talent associated with an individual who has the maximum capital over a model run it has been shown that the choice for the standard deviation of the talent distribution contributes to 67% of the model variability. When investigating the maximum amount of capital returned by the model the probability of a lucky event at any given epoch has the largest impact on the model, almost three times more than any other individual parameter. Consequently, during the analysis of the model results one must keep in mind the impact that only small changes in the input parameters can have on the model output.

The role of luck on individual success is hard to be investigated empirically. Simplified mathematical models are often used to shed light on the subtle relations between success and luck. Recently, a simple model called “Talent versus Luck” showed that the most successful individual in a population can be just an average talented individual that is subjected to a very fortunate sequence of events. Here, we modify the framework of the TvL model such that in our model the individuals’ success is modelled as an ensemble of one-dimensional random walks. Our model reproduces the original TvL results and, due to the mathematical simplicity, it shows clearly that the original conclusions of the TvL model are the consequence of two factors: first, the normal distribution of talents with low standard deviation, which creates a large number of average talented individuals; second, the low number of steps considered, which allows the observation of large fluctuations. We also show that the results strongly depend on the relative frequency of good and bad luck events, which defines a critical value for the talent: in the long run, the individuals with high talent end up very successful and those with low talent end up ruined. Last, we considered two variations to illustrate applications of the ensemble of random walks model.

This paper analyzes the Talent versus Luck model, which examines the impact of talent and luck on an individual’s career success. The original simulation-based model demonstrated that the distribution of capital has a heavy tail, and the most successful individuals are not necessarily the most talented. While the implications of the original model are intriguing, those findings were based solely on numerical calculations, and it was unclear how generally valid they are. Challet et al. generalize the original model using an analytical approach and successfully clarify the relationship between talent, lucky events, and capital when talent is constant and follows a uniform distribution. We reformulate a simplified model and derive more general propositions about the relationship between luck and talent in individual success by introducing the new concept of luck of outcome in addition to the luck of opportunity in previous models. We show that the capital distribution generated from a simplified talent versus luck model follows a lognormal distribution even when the talent is subject to a normal distribution. Moreover, we specify the relationship between the inequality of the distribution, which is indicated by the Gini coefficient, and the parameters of talent distribution.

The three main claims of the discussion are that (i) values and perspectives integral to Judaism are especially congenial to liberal democracy as a political order and had a role in early modern theorizing about the liberal state, (ii) they are also congenial to the market as a basic economic arrangement on account of how Judaism regards the dignity, accountability and independence of the individual, and (iii) while there is no guarantee that the market will benefit everyone it is defensible on the basis of how it constructively interacts with the pluralistic civil society that a liberal order makes possible. Judaism’s core notions of voluntariness and concern for others can contribute to a morally endorsable form of market activity.