Understanding the long-term evolution of social inequality is a crucial goal in social science. While significant progress has been made in studying inequality across entire societies, both modern and ancient, less is known about inequality within specific societal segments, particularly among elites. Intra-elite inequality can destabilize societies, highlighting the importance of long-term perspectives to understand these dynamics. This paper addresses this gap by focusing on relational wealth inequality—an individual's endowment with social ties and networks—within the upper societal segment of prehistoric Central Europe. The study utilizes a unique dataset of approximately 5000 single-funeral burial mounds from the first four millennia BCE, with burial mound volume serving as a proxy for relational wealth. The assumption is that larger mounds reflect greater ability to mobilize resources and networks. While acknowledging the localized nature of these networks, the researchers posit a supra-regional network connecting these communities, supported by archeological evidence. The analysis employs inequality indices, such as the Gini index and Generalized Entropy Measures, to quantify inequality within this upper societal segment. Additionally, the study examines the temporal changes in the size of this segment by analyzing the proportion of individuals buried in mounds compared to those in flat or collective burials.

The paper reviews existing literature on the evolution of social inequality, highlighting the advancements in understanding inequality across entire societies in modern, preindustrial, and ancient contexts. It emphasizes the need to shift the focus from overall societal inequality to examine inequality within specific societal segments, particularly elites. The importance of understanding intra-elite inequality and its potential destabilizing effects on societies is discussed. Existing research often focuses on material wealth, whereas this study focuses on relational wealth as an equally important dimension of elite power and influence. The limited availability of long-run data on intra-elite inequality is highlighted, underscoring the novelty of the current study's contribution.

The research employs a novel dataset comprising approximately 5000 single-funeral burial mounds from Central Europe, spanning the first four millennia BCE. Burial mound volume is used as a proxy for the relational wealth of the deceased individual. The researchers acknowledge the limitations of this proxy and justify its use by referencing ethnoarchaeological evidence suggesting a link between mound size and the deceased's ability to mobilize resources via social networks. Since burial mound volume data is not directly available, the researchers employ a method to estimate volume based on the measured ground area and assumed shapes (round or rectangular) of the mounds. They use a non-linear transformation of the ground area to estimate volume, assuming a hemispherical shape for round mounds and a cuboid shape for rectangular mounds. To ensure data accuracy and minimize bias caused by variable dating intervals, the researchers limit their analysis to burial mounds with dating intervals not exceeding 600 years. The data is further divided into 200-year intervals for temporal analysis. Inequality is measured using the Gini index and Generalized Entropy Measures. Due to the heavy-tailed distributions in the data, the researchers employ permutation tests to assess the statistical significance of differences in inequality estimates between different time periods, choosing this method over bootstrapping for its robustness with heavy-tailed data. The study also examines the size of the upper societal segment by calculating the proportion of individuals buried in mounds over the total number of burials (including flat and collective burials).

The analysis reveals two key findings. First, a wave-like pattern is observed in the share of individuals buried in mounds, indicating fluctuations in the size of the upper societal segment over time. These fluctuations consist of two phases: an initial phase with a relatively small number of individuals buried in mounds and a subsequent phase with a significantly larger number. The second key finding is consistently high levels of inequality in relational wealth among the individuals buried in mounds, with a clear increasing trend over time, particularly in the last 1200 years BCE. The wave-like pattern in the size of the upper societal segment repeats multiple times throughout the analyzed period (3800 BCE - 200 BCE), with each cycle characterized by two phases: Phase 1, where only a few individuals achieve prominent status in emerging regional networks, and Phase 2, where disruptive events like migrations or environmental changes lead to the expansion of the upper societal segment. This pattern is linked to technological advancements (like animal traction, metallurgy), changes in trade networks, and climatic or demographic shifts. The study presents a detailed breakdown of these four repeating patterns, relating them to specific archeological developments and changes in network structures. The analysis uses the Gini index to measure inequality. The results illustrate significant differences in inequality levels between different time periods and phases within the identified cyclical patterns. These variations in inequality are analyzed in conjunction with population dynamics, inferred from the total number of burials, to understand the broader societal contexts.

The findings demonstrate a long-term trend of increasing inequality in relational wealth within the upper societal segment of prehistoric Central Europe, interwoven with cyclical fluctuations in the size of this segment. The observed patterns suggest a complex interplay between technological innovation, environmental changes, and sociopolitical transformations. Technological advancements and the expansion of trade networks initially concentrate wealth and power in the hands of a few individuals, leading to high inequality. However, disruptive events and broader adoption of technologies subsequently lead to periods of increased social mobility and a larger upper societal segment, albeit with persistent high inequality. The study's focus on relational wealth provides a unique perspective, demonstrating that social networks and power dynamics play a crucial role in shaping inequality, not solely material wealth. This research supports existing theories suggesting a link between technological innovation and social complexity. However, it adds a nuanced understanding of the non-linear dynamics of inequality, highlighting both increasing trends and periods of fluctuation. Potential indicators of conflict, such as increasing prevalence of weaponry and fortified settlements, are mentioned, emphasizing the need for further research into the relationship between social inequality and violence.

This study offers valuable insights into the long-term dynamics of inequality in prehistoric Central Europe. By focusing on relational wealth and analyzing temporal changes in both inequality levels and the size of the upper societal segment, the research reveals a complex interplay of factors shaping social stratification. The wave-like patterns observed suggest that technological advancements and disruptions create cyclical changes in social mobility and inequality. Future research should investigate the role of conflict and violence in shaping these patterns, further explore different dimensions of wealth, and conduct regional analyses using the dataset's spatial granularity.

While the study uses a large dataset and sophisticated statistical methods, several limitations are acknowledged. The reliance on burial mound volume as a proxy for relational wealth might introduce biases. The estimation of burial mound volume based on assumed shapes could also affect the accuracy of the results. The temporal resolution of the data could be further enhanced, and a deeper examination of the role of conflict and violence in shaping the observed patterns is warranted.