Don't follow the leader: how ranking performance reduces meritocracy

Abstract

In the name of meritocracy, modern economies devote increasing amounts of resources to quantifying and ranking the performance of individuals and organizations. Rankings send out powerful signals, which lead to identifying the actions of top performers as the 'best practices' that others should also adopt. However, several studies have shown that the imitation of best practices often leads to a drop in performance. So, should those lagging behind in a ranking imitate top performers or should they instead pursue a strategy of their own? I tackle this question by numerically simulating a stylized model of a society whose agents seek to climb a ranking either by imitating the actions of top performers or by randomly trying out different actions, i.e. via serendipity. The model gives rise to a rich phenomenology, showing that the imitation of top performers increases welfare overall, but at the cost of higher inequality. Indeed, the imitation of top performers turns out to be a self-defeating strategy that consolidates the early advantage of a few lucky-and not necessarily talented-winners, leading to a very unequal, homogenized and effectively non-meritocratic society. Conversely, serendipity favours meritocratic outcomes and prevents rankings from freezing.

Keywords: agent-based modelling; meritocracy; performance measurement; serendipity.

Figure 1.

Sketch of the model. At the beginning of a time step, agent i is playing action j, which awards a pay-off π_j. With probability equal to the individual pay-off P_ij = α_ij π_j (see equation (2.1)), the agent keeps playing the same action, and with probability 1 − P_ij switches to a new action, which is determined either via imitation or via serendipity. With probability q, the agent adopts the action being played by a (randomly selected) better ranked agent, while with probability 1 − q the agent selects a new action at random.

Figure 2.

From left to right panels show results of a single simulation run of the model for q = 0.1, q = 0.5 and q = 0.9, respectively. Top (bottom) panels show the trajectories of the top (bottom) 10 agents based on the ranking at the final time T = 500. The y-axis shows the numbers associated with the actions being adopted, which go from 1 to M = 1000 in no particular order. As it can be seen, in the q = 0.5 simulation the top agents tend to lock in on action 186, while in the q = 0.9 top agents lock in on action 516.

Figure 3.

(a) Total utility U(T) as a function of the parameter q. (b) Gini coefficient (see equation (3.1)) of the agents’ utility distribution as a function of q. (c) Utility accumulated by the bottom (blue circles) and top (purple diamonds) 10% of the agents in the ranking. In all panels circles/diamonds represent average values, while error bars represent 95% confidence level intervals obtained over 500 independent simulations. In all cases, simulations were run with N = 200 and M = 1000, and all values were measured at time T = 500.

Figure 4.

(a) Kendall correlation between the agents’ total utility and their fitness, as defined in equation (3.2) (blue circles) and equation (3.3) (purple diamonds), as a function the parameter q. (b) Society’s homogenization, defined as the fraction δ(T) of the actions being played by at least one agent at the end of a simulation as a function of q. In both panels circles/diamonds represent average values, while error bars represent 95% confidence level intervals obtained over 500 independent simulations with N = 200, M = 1000 and T = 500.

Figure 5.

Change in ranking position (defined as the change Δm_i of the quantity in equation (3.4) over a time interval) for agents of a society with N = 200 and M = 1000, averaged over 500 independent simulations. In all panels, the change in ranking position is computed for each agent individually over consecutive sets of Δt = 100 simulation steps, and plotted as a function of the agent’s position in the ranking m_i at the beginning of the interval Δt. As indicated by their labels, the panels refer to quantities computed across simulations at times t = 100, 200, 300, 400. Solid lines refer to averages, whereas the shaded regions denote 90% confidence level intervals.