A Model for Ambition
How ambitious should you be? Some people exhort us to shoot for the stars, while others believe that greater success requires setting realistic goals. Now researchers have developed a mathematical model that offers some answers [1]. They found that better outcomes are always attained when people aim for better-than-average results, but that being too ambitious can come with a higher penalty than being too cautious. The researchers believe that the model could help guide people in a diverse range of real-world situations, such as looking for a job or building a business.
The model, developed by Ekaterina Landgren at Stanford University and her colleagues, is based on a mathematical concept known as optimal search: determining the best way to secure the maximum reward given the available time and resources. Such models have been used to understand the foraging behavior of animals, to design navigation systems for autonomous robots, and to guide search-and-rescue operations. These models are normally optimized around one specific task, but Landgren and her colleagues developed a general framework that can be applied to various human pursuits in which decisions can influence success.
In their model, an “agent” repeatedly draws at random from a set of options—each having a certain value—hoping to accumulate the maximum reward over time. It could represent a job seeker aiming to secure a higher salary, an entrepreneur trying to create a successful company, or a politician campaigning to boost their popularity. A distribution function gives the probability of receiving each possible reward value. In the simplest case, the function is a normal bell-shaped (Gaussian) distribution.
At each time step of the model, the agent must choose whether to stick with its current reward or to try for a more valuable one. If the current reward exceeds the statistical mean of the distribution by more than a predefined “satisfaction threshold,” the agent stops receiving random rewards and accrues the same level of reward for the remaining time steps. If the satisfaction threshold is not reached, the agent draws another reward in the next time step.
Varying the satisfaction threshold allowed the researchers to explore the effects of ambition: An agent with a low threshold will settle for less but may miss out on a greater reward, while one with a higher threshold will continue trying for a better reward that may or may not be attainable. To find the optimal amount of ambition, they computed the rewards that agents with different satisfaction thresholds accumulated over a fixed number of time steps. These simulations showed that the optimal satisfaction threshold is always higher than the mean reward, but that setting it too high can be more detrimental to the final outcome than setting it too low.
Next, Landgren and colleagues examined the effect of social comparison. Instead of comparing with the mean, the agent now compares its reward with the average obtained by a peer group of 100 agents with different satisfaction thresholds in the previous time step. They found that any form of social comparison is costly, lowering the optimal satisfaction threshold and reducing the cumulative reward. But the negative impact is heightened when the agent compares its rewards only with peers that have received more valuable rewards, which makes the agent less satisfied with its outcomes and more likely to miss achievable gains. “Upward social comparison can harm success by distorting your perception of what’s possible,” Landgren says.
The researchers also analyzed specific real-world scenarios that are described by different reward distributions. In business development, for example, the wealth distribution of private companies is skewed by a small number of extremely successful “unicorns.” In such right-skewed distributions, the optimal satisfaction threshold is lower than for a Gaussian distribution, suggesting that budding entrepreneurs should rein in their ambitions.
The reverse is true for left-skewed distributions, which describe, for example, the downward drag of deep recessions on economic growth data. In this case the model suggests that policymakers should pursue more ambitious strategies to maximize growth rates. “The key is understanding the distribution of outcomes in your particular domain and adjusting your expectations accordingly,” Landgren says. The researchers now plan to use the model to explore domains where its predictions could produce actionable results, such as job hunting or applying for admission to universities.
Thomas Hills, an expert in behavioral and cognitive science at the University of Warwick in the UK, says that this “innovative” work shows that the concept of optimal search is universal, applying across many different scenarios where ambition must be balanced against risk.
–Susan Curtis
Susan Curtis is a freelance science writer based in Bristol, UK.
References
- E. Landgren et al., “Optimal ambition in business, politics, and life,” Phys. Rev. E 113, 054317 (2026).