Merit-Based Sortition in Decentralized Systems

TL;DR

This work introduces a simple algorithm for 'merit-based sortition', in which the quality of each participant influences its probability of being drafted into the active set, while simultaneously retaining representativeness by allowing inactive participants an infinite number of chances to be drafted into the active set with non-zero probability.

Abstract

In decentralized systems, it is often necessary to select an 'active' subset of participants from the total participant pool, with the goal of satisfying computational limitations or optimizing resource efficiency. This selection can sometimes be made at random, mirroring the sortition practice invented in classical antiquity aimed at achieving a high degree of statistical representativeness. However, the recent emergence of specialized decentralized networks that solve concrete coordination problems and are characterized by measurable success metrics often requires prioritizing performance optimization over representativeness. We introduce a simple algorithm for 'merit-based sortition', in which the quality of each participant influences its probability of being drafted into the active set, while simultaneously retaining representativeness by allowing inactive participants an infinite number of chances to be drafted into the active set with non-zero probability. Using a suite of numerical experiments, we demonstrate that our algorithm boosts the quality metric describing the performance of the active set by $>2$ times the intrinsic stochasticity. This implies that merit-based sortition ensures a statistically significant performance boost to the drafted, 'active' set, while retaining the property of classical, random sortition that it enables upward mobility from a much larger 'inactive' set. This way, merit-based sortition fulfils a key requirement for decentralized systems in need of performance optimization.

Figures (4)

• Figure 1: Merit-based sortition simulation for an initial set of eight participants, illustrating the construction and performance of the active set ${\cal A}_i$ as a function of time. Left: Each color represents a different participant, and the line style reflects the (in)activity as indicated by the legend. Line segments connecting two epochs where a participant changes from inactive to active show as solid, whereas those connecting a transition from active to inactive show as dotted. Middle: Correlation between the median quality metric of each participant (reflecting their ability or performance) and the fraction of the 1000-epoch duration of the simulation for which this participant is active. Colors match those in the left-hand panel. Right: EMA of the mean instantaneous quality metric across the active set ${\cal A}_i$ for merit-based sortition (solid line) and random sortition (dotted line) over the full duration of the simulation. The panel titles list the number of initial participants, the number of active participants, and the percentile.
• Figure 2: Merit-based sortition simulation for an initial set of 80 participants, illustrating the construction and performance of the active set ${\cal A}_i$ as a function of time in a crowded ecosystem. Left: Each color represents a different participant, and the line style reflects the (in)activity as indicated by the legend. Line segments connecting two epochs where a participant changes from inactive to active show as solid, whereas those connecting a transition from active to inactive show as dotted. Middle: Correlation between the median quality metric of each participant (reflecting their ability or performance) and the fraction of the 1000-epoch duration of the simulation for which this participant is active. Colors match those in the left-hand panel. Right: EMA of the mean instantaneous quality metric across the active set ${\cal A}_i$ for merit-based sortition (solid line) and random sortition (dotted line) over the full duration of the simulation. The panel titles list the number of initial participants, the number of active participants, and the percentile.
• Figure 3: Merit-based sortition simulations for evolving participant pools. Colors indicate participants in order of their first participation (light to dark). Columns correspond to the same panels as in \ref{['fig:default']} and \ref{['fig:large']}. The panel titles list the type of evolution (from top to bottom, these are growth, shrinkage, and dynamically evolving), the number of initial participants, the number of active participants, and the percentile.
• Figure 4: Set of sortition simulations showing how the added value of merit-based sortition over classical, random sortition depends on the percentile $P$, for a dynamically evolving participant pool. Left: Time-averaged mean instantaneous quality metric ${\cal T}_i$ across the active set ${\cal A}_i$ as a function of $P$. The solid line indicates the results for merit-based sortition, and the dotted line represents classical (random) sortition. Right: Statistical $z$-score (the absolute difference between both lines in the left panel, normalized by the standard deviation of the mean underlying, unsmoothed instantaneous quality metrics) as a function of $P$, demonstrating a highly statistically significant ($>2\sigma$) improvement with merit-based sortition relative to classical sortition for $P=20{-}40\%$, and a mild ($>1\sigma$) improvement for $P=10{-}85\%$.