Fair and Representative Jury Selection for Decentralized Justice
Pages 244 - 248
Abstract
With the increasing number of decentralized applications in the blockchain ecosystem, there is a growing demand for a fair dispute resolution method that accurately represents blockchain network users. Existing crowdsourced blockchain arbitration platforms rely on weighted random jury selection based on token staking. Such mechanisms may lead to a predictable choice of jury members and raise concerns about fairness. Moreover, such juries may not represent the entire user population. To address these concerns, we introduce the Fair-Spread family of algorithms. The Fair-Spread prioritizes spread maximization strategies to improve network members’ representation and emphasizes unpredictable jury selection with the workload balance of jury duty across multiple trials. Our work introduces novel metrics for evaluating jury quality, considering factors such as fairness, network coverage, and diversity during jury selection. We assess the performance of the Fair-Spread algorithms on different network graphs and recommend specific algorithms within the Fair-Spread family for various jury selection contexts.
1 Introduction
Blockchain is a decentralized and distributed ledger system that eliminates the need for intermediaries by providing a secure platform for recording and verifying data. Current dispute resolution protocols, like Kleros and Aragon, rely on weighted randomness selection based on stakes, introducing a bias towards network users with larger token holdings [4, 5, 17, 18]. Selecting jurors based on stakes in a blockchain system offers advantages such as utilizing stakes as collateral, giving rewards, and incentivizing users to vote with the majority or truth. However, solely relying on stake-based selection can lead to centralization, as users with more tokens gain disproportionate influence [20]. In such scenarios, decisions are driven by wealthier individuals rather than a representative group. A balanced approach that considers stake-based participation alongside other factors may be necessary to address these issues to establish a fair and inclusive dispute resolution model in blockchain networks. Our approach involves selecting a representative jury composed of a diverse group of jurors and achieving maximum coverage or reach in its connections to other unselected users within the blockchain network. Our main contribution is an algorithmic framework that integrates two disparate aspects of jury selection: fairness and representation. These concepts have been studied in isolation. While Kleros and other jury selection systems are inherently random due to a random selection process based on stakes [4, 5, 17, 18], they overlook the underlying user interactions through network graphs, introducing bias to the selection process and resulting in a lack of representation. On the flip side, many classical selection algorithms (such as facility location and k-center [23]) applied to the network graph may yield well-representative juries but could unfairly burden a small set of selected members with jury responsibility across multiple trials. Our work seeks to integrate these two disparate requirements within a single framework. Unlike existing solutions, we utilize the underlying blockchain transaction network graph to select jury members. Transaction behaviors can unveil social relationships when user entities engage in frequent or significant transactions. Blockchain transaction-related features can be used to build a transaction network graph to select a crowdsourced jury [10, 21, 24]. We also present novel metrics to assess the quality of the jury formed. We have conducted extensive experiments to compare the proposed algorithms’ performance against the defined metrics and offer recommendations for selecting the most suitable algorithm based on specific requirements.
2 Related Work
We study the problem of jury selection within a transaction network graph. In this graph, nodes represent potential jury candidates, and the patterns resulting from social interactions through transactions contribute to shaping the network graph for jury selection. Social networks can be analyzed to gain detailed insights into the patterns of interaction, helping us understand how communities emerge [13, 19]. It is worth noting that social network graphs often exhibit power-law degree distribution characterized by many nodes with low degrees and a small number of nodes with high degrees, similar to wealth concentration in blockchain networks [20]. Fischer et al. [10] outline the entity identification problem involving identifying real-world entities in Bitcoin. The work considers seven heuristics from [15], and by analyzing the Bitcoin network’s transaction graph, an address correspondence network is formed by inserting links whenever at least one heuristic aligns. Similarly, in the case of Ethereum, some studies, such as [21], consider Ethereum Transaction Behavior, while others, like [24], propose heuristics using Ethereum deposit addresses, multiple participations in airdrops, and token authorization mechanisms to construct the network graph. The selection problem has been extensively studied in the literature [14, 23], with variations closely related to the jury selection problem. The Jury Selection Problem, defined in [3], is to assemble a jury within a given budget constraint, particularly for decision-making tasks and known ground truth to evaluate jury quality. While [3] focuses on the majority voting strategy, [26] introduces a broader approach that explores various voting strategies to optimize jury quality. However, this selection process proves challenging in a setting where the ground truth is unknown, making it difficult to measure the effectiveness of the jury. As blockchain transactions are often conducted pseudonymously with users represented by cryptographic addresses rather than real-world identities, it also becomes difficult to acquire user attributes. Our work differs from [3] and [26] as we do not rely on trial outcomes to assess the jury’s quality. We define metrics based on the underlying transaction network graph to measure the fairness and representation of the selected jury through diversity and coverage. Additionally, our model does not consider other user attributes and applies to pseudonymous networks like blockchain.
3 Jury Selection: Model and Metrics
Consider the blockchain network users as the nodes of an undirected, unweighted transaction network graph G = (U, E). Consider a subset V⊆U from the network users, where V denotes the set of all eligible users for the jury selection. Each node represents a transaction network user and is a potential jury member. An edge e = (i, j) ∈ E indicates that i and j are socially related and neighbors.
Let Pij be the set of all the paths from i to j in G (with no repeated nodes or edges). For any pair (i, j) ∈ U × U, dij is the distance of the shortest path between i and j, which represents the strength of the relationship between the two nodes as a distance measure. We can formally definewhere |p| denotes the number of edges in the path p. Thus, smaller dij indicates a stronger relationship between the two endpoints.
\begin{equation}d_{ij} \triangleq \min _{p \in P_{ij}} |p|\end{equation}
(1)
The nodes i, j ∈ U are neighbours if there exists and edge between them.
\begin{equation}\mathcal {N}(i) \triangleq \lbrace j \in U \mid (i,j) \in E, i \ne j \rbrace\end{equation}
(2)
A trial is a process of selecting a jury J⊆V, where |J| = k for a given fixed value of jury size k with 0 < k ≤ |V|.
We introduce the following metrics to measure the quality of the selected jury J. The objective is to select J that meets a subset or the entirety of the metrics as per requirements.
3.1 Measures of spread
Measures of spread assess the coverage and diversity of the jury selection. The Coverage Metrics, includes two specific measures. Farthest Node Cover ensures that the jury J is a good representation of all members in U. The metric aims to minimize the maximum distance between jury members and other nodes in the network. The goal is to minimize C(J).The second measure, Fractional Node Coverage, considers the number of nodes K(r) covered within a radius r from some j ∈ J. Fractional node coverage is defined as the fraction of nodes K(r) covered relative to the total nodes in the network. The aim is to maximize F(r).The second set of metrics is the Diversity Metrics. Maximum Shortest Path ensures that the selected jurors have weak relationships with each other by maximizing the distance between jurors, thus promoting diversity within the jury pool. For high diversity, S(J) is maximized.Finally, Unique Coverage aims to maximize overall coverage by selecting a jury J that covers the maximum number of unique nodes. Overlapping coverage results in redundant node coverage by the set J. The objective is to select a jury J that maximizes U(J). Let \(\mathcal {N}(a)\) and \(\mathcal {N}(b)\) represent the neighborhood set of a and b as per definition 3.2.
\begin{equation}C(J) \triangleq \max _{i \in U} \min _{j \in J} d_{ij}.\end{equation}
(3)
\begin{equation}F(r) \triangleq \frac{K(r)}{|U|}.\end{equation}
(4)
\begin{equation}S(J) \triangleq \min _{i,j \in J, i \ne j} {d_{ij}}.\end{equation}
(5)
\begin{equation}U(J) \triangleq \sum _{a,b \in J} \mathcal {N}(a) \cup \mathcal {N}(b).\end{equation}
(6)
3.2 Fairness Criteria
The Fairness Criteria are set to support the principle of equality in the jury selection process. The process must ensure the distribution of the jury workload evenly among eligible users over multiple trials, such that no specific group of jurors is consistently called for jury duty and no subset of jury members is repeatedly ignored. We consider the vector \(\mathcal {V}\) of the frequency of occurrence for all elements v ∈ V in the jury over t ∈ T trials. To ensure workload balancing across multiple trials for jury duty, we consider the following two metrics. First, equality. For effective load balancing of jury duty, the vector \(\mathcal {V}\) should exhibit low standard deviation, ensuring a more even and consistent distribution of the workload. We define equality asand aim to minimize E(J), the standard deviation of \(\mathcal {V}\). Second, disparity. The disparity in juror selection is defined as the difference between the highest and lowest values in the vector \(\mathcal {V}\), capturing the difference in workload between the most and least loaded jurors. We define disparity asand aim to minimize Q(J).
\begin{equation}E(J) \triangleq \sigma _{\mathcal {V}}\end{equation}
(7)
\begin{equation}Q(J) \triangleq \mathcal {V}_{\text{high}} - \mathcal {V}_{\text{low}}\end{equation}
(8)
4 Fair-Spread Family of Algorithms
Our work presents the Fair-Spread family of algorithms \((\mathcal {F})\) that outputs jury J from the blockchain transaction network graph U, with the eligible set of users V. The Fair-Spread consists of two components: fairness assurance \((\mathcal {A}_f)\) and maximizing spread strategies \((\mathcal {A}_s)\). Fairness assurance algorithms focus on the fair selection of nodes by addressing equality and disparity. Three methods are used for fairness: Random Seed, Random Candidate Pool, and Probabilistic Selection. To enhance jury coverage and representation, two spread maximization strategies based on coverage and diversity are applied: Betweenness Centrality (\(\mathcal {B}\)) and Greedy Coverage-based Selection (\(\mathcal {G}\)). The selection algorithm is developed by choosing one from each of these categories. The Fair-Spread family of algorithms is represented as \(\mathcal {F} = (\mathcal {A}_f, \mathcal {A}_s)\). To address the challenges associated with random number generation in blockchain, we recommend using oracles. Oracles are trusted external services that can generate randomness off-chain and deliver it to the blockchain with cryptographic proof, ensuring fair generation [1]. This method, along with fallback mechanisms and robust security practices, effectively mitigates associated risks. To address random number generation challenges, we recommend using oracles to generate randomness off-chain and provide cryptographic proof to ensure fairness [1]. This approach, combined with fallback mechanisms and strong security practices, mitigates associated risks.
4.1 Fairness Assurance Algorithms
Within fairness assurance, we introduce three algorithmic variations designed to uphold fairness assurance. Random Seed Selection (\(\mathcal {S}\)), randomly selects t seeds from a set V where t < k, with the remaining k − t juror nodes chosen based on spread maximization strategies \(\mathcal {B}\) or \(\mathcal {G}\). Random Candidate Pool Selection (\(\mathcal {C}\)), creates a candidate pool by random sampling, where the pool size c is a fraction of nodes selected from V. Network nodes in this candidate pool become eligible for jury selection based on the spread maximization strategies \(\mathcal {B}\) or \(\mathcal {G}\). Probabilistic Selection (\(\mathcal {P}\)), selects nodes randomly with probability p, while with probability 1 − p, nodes are chosen based on spread maximization strategies \(\mathcal {B}\) or \(\mathcal {G}\).
4.2 Spread Maximization Strategy Algorithms
Spread Maximization strategies are incorporated to contributing to the quality of the jury. Two strategies are presented for spread maximization within the selected set, namely Betweenness Centrality(\(\mathcal {B}\)) and Greedy Coverage-based selection(\(\mathcal {G}\)). The Greedy Coverage strategy works by marking nodes that are neighbors to the currently selected jurors in J as covered, and then adding nodes to J based on a greedy approach that prioritizes nodes with the highest count of uncovered neighbors, ensuring unique coverage. The coverage set, denoted as \(\mathsf {Cov}_i\) for all i ∈ V − J, includes nodes directly connected to i. The given input set J represents the set of nodes selected by fairness assurance algorithm until the call to \(\mathcal {G}\). The node that has the highest unique coverage is selected in set J. The Betweenness Centrality strategy involves selecting nodes for J based on their betweenness centrality scores. Nodes with the highest scores among the eligible candidates are added to J. While our study emphasizes betweenness centrality [11, 12], other centrality measures may also be used depending on specific requirements [6, 25]. The input set J represents the nodes selected by the fairness assurance algorithm until the call to \(\mathcal {B}\).
4.3 Jury Selection Across Multiple Trials
In addition to the fairness and maximization strategies introduced by the Fair-Spread family of algorithms, we present memory-less and memory-enhanced procedures to select jury members across multiple trials. Memory-enhanced procedures aim to achieve unpredictability in juror selection while ensuring a balanced jury duty allocation across multiple trials by minimizing the selection frequency of any subset of jury members in subsequent trials. Memory-less Trial procedure considers all nodes in V in every trial. It does not retain any memory of selected nodes in previous trials, making all nodes in V eligible for selection in every trial, t ∈ T. Memory-enhanced Trial procedure maintains a history of the nodes that have been selected in trial t ∈ T. This selection memory is used in the subsequent trials. The selected set J1 in trial t1 ∈ T becomes inactive for a certain number of rounds \(w \in \mathbb {Z}\). In our work, the inactive window w is generated randomly and lasts for a short number of trials. At trial t1 + w, the nodes in J1 become active again and will be eligible for selection in the next round.
5 Experiments
The experiments were conducted using Ubuntu version 22.04. The hardware configuration involved Intel Xeon Gold 6248R CPU processor operating at a clock speed of 3.00GHz with 1TB memory. The system operated on a 64-bit \(x86\_64\) architecture. The Python version used was 3.10.12, with NetworKit library version 10.1 for network analysis and operations [22]. The experiments consist of three types of network models: Barabasi-Albert network graph model [2] to generate random scale-free networks using preferential attachment mechanisms based on the degree to represent the Rich getting Richer phenomena in blockchain [20]; Lancichinetti–Fortunato–Radicchi (LFR) model [16], producing benchmark networks with known communities and power law distributions for degree and community size; and Erdős–Rényi model [8, 9], to generate random graphs with a given probability for edge creation. The Barabasi-Albert network is constructed with 15,000 nodes, featuring preferential edge attachment of 3. The LFR network comprises 15,000 nodes with average and max degrees set to 50 and 250, respectively. The power law exponent for the degree distribution is -3, while for the community size distribution, it is -1.5. Additionally, the fraction of inter-community edges incident to each node is set to 0.2, and the minimum and maximum sizes of communities in the graph are 50 and 250, respectively. The Erdős–Rényi graph is generated with 15,000 nodes and a 0.2 probability for edge creation. For these experiments the jury size is set to 25, and algorithmic parameters are defined as follows: radius (2) for the fractional node coverage metric, pool size (0.25), seed size (10), and probability (0.7). The experiments are conducted in three rounds, each comprising 2,000 iterations. Unless otherwise specified, the experiments use the above properties.
5.1 Comparison with Pure-Random strategy
To establish baseline comparison, we assess Fair-Spread algorithms against pure-random selection to examine their performance in jury selection. In pure-random selection, nodes are chosen randomly from the set of eligible jurors without considering weights due to stakes or any specific strategy. We observe that the performance of pure-random selection in terms of coverage and diversity metrics is lower compared to the Fair-Spread algorithms. The Figure 1 illustrates the performance of the Barabási-Albert network model with pure-random and memory-enhanced selection for the unique coverage metric. The Random Candidate Pool-Greedy coverage selection algorithm covers the maximum number of unique nodes in the network and the pure-random selection covers the lowest number of unique nodes. This discrepancy arises because pure-random selection does not ensure the inclusion of nodes with higher unique coverage in the jury, leading to uncovered regions in certain parts of the network.
Figure 1:
5.2 Memory-less and Memory-enhanced Trials
The experiment depicted in Figure 2 compares Memory-enhanced and Memory-less Trial procedures for six Fair-Spread algorithm variations on the Barabasi-Albert network. As stated in 3.2, we wish to minimize the Q(J) and E(J) values. Our experiments show that the memory-enhanced approach outperforms the memory-less one in disparity and equality metrics, achieving improved workload balance and unpredictability in jury formation.
Figure 2:
5.3 Network Size Variation
Table 1 illustrates the performance of the Memory-enhanced Random Candidate pool with greedy coverage selection for the Barabasi-Albert network graph across various network sizes and preferential edge attachment values. This observation allows us to assess performance on sparse and dense graphs recorded across different metrics. We note that, as the network size increases, the performance in terms of the fairness criteria metric reduces as providing an opportunity for each node in the network to be in the jury becomes challenging. Additionally, with increasing preferential edge attachment values, we observe that as the graph becomes dense, the fractional node coverage increases, and the farthest node coverage decreases due to more connections. The diversity in the selection increases with increasing network size, while in a sparse graph, the reduced number of connections leads to a decrease in node reachability.
Table 1:
| Fairness Criteria | Coverage | Diversity | ||||
|---|---|---|---|---|---|---|
| Size | Q(J) | E(J) | F(r) | C(J) | U(J) | S(J) |
| (2500,2) | 0.0048 | 46.27 | 0.57 | 2.329 | 0.121 | 3.48 |
| (5000,2) | 0.0044 | 34.55 | 0.48 | 2.481 | 0.088 | 3.29 |
| (7500,2) | 0.0044 | 28.86 | 0.40 | 2.626 | 0.072 | 3.37 |
| (10000,3) | 0.0044 | 25.03 | 0.58 | 2.324 | 0.087 | 2.89 |
| (15000,3) | 0.0044 | 20.49 | 0.54 | 2.414 | 0.074 | 2.83 |
| (20000,5) | 0.0044 | 17.88 | 0.77 | 2.113 | 0.097 | 2.47 |
| (50000,10) | 0.0056 | 11.37 | 0.95 | 1.939 | 0.113 | 2.02 |
5.4 Ethereum Transaction Network Graph
To evaluate the performance of the Fair-Spread family of algorithms, we fetch the publicly available Ethereum blockchain dataset in Google BigQuery to construct a transaction network graph [7]. The table bigquery-public-data.crypto\(\_\)ethereum.transactions contains all transactions across blocks, and each transaction has a source address, a target address, the transferred amount of Ether, and an array of input bytes. We utilize the table to construct a transaction network graph, where nodes correspond to addresses from the dataset. An edge exists between nodes if a transaction occurs between the respective addresses, as indicated by an entry in the table with either address as the source or target. The graph is constructed with 30 days of transaction between 2023-09-01 and 2023-09-30 and consists of 6,985,341 nodes and 14,325,646 edges. We conduct experiments on the obtained Ethereum transaction network graph to measure the performance of the algorithms for the defined metrics. Our experiments show that the Random Candidate Pool-Greedy Coverage strategy outperforms other Fair-Spread variations in terms of diversity and coverage metrics. To further evaluate our algorithm, we compare its performance against the pure-random selection of jurors. The Fair-Spread family of algorithms performs better than a pure-random selection in forming a jury that is both fair and representative across multiple trials. The enhanced performance of Fair-Spread is attributed to the preference for randomly choosing nodes with fairness assurance algorithms and then selecting the node with higher unique coverage or betweenness centrality scores in every iteration. Figure 3 shows the comparison of fractional node coverage values between pure-random selection and candidate pool selection with greedy coverage selection for various jury sizes, incorporating a memory-enhanced procedure. The comparison demonstrates the effectiveness of using a transaction network graph for selecting a jury that is both representative of the network and diverse in its composition. As seen in the Figure 3, as the jury size increases, the fractional coverage of nodes also increases.
Figure 3:
6 Conclusion and Future Works
We address the jury selection problem of crowdsourced arbitration platforms on decentralized networks, like blockchains. Introducing the Fair-Spread family of algorithms, we improve upon existing dispute resolution methods by leveraging blockchain transaction network graphs for selection. The Fair-Spread family includes variations that ensure fairness and maximize the spread of the jury for network representation within a single trial and consistently across multiple trials. Employing a memory-enhanced procedure ensures fairness through the unpredictability of jury selection and balances the workload of jury duty throughout the process. Our novel metrics assess jury quality in terms of fairness, coverage, and diversity. Furthermore, our experiments show that the Fair-Spread algorithms select a representative jury compared to pure-random selection. Using Ethereum transactional data, we validate our approach, providing recommendations for Fair-Spread variations based on specific selection requirements.
The following are potential future directions for this research. First, while our current work provides extensive experimental results, we aim to study theoretical models and prove theorems to substantiate the insights obtained from our experiments. Additionally, such theoretical explorations could broaden the scope of our contributions to other application contexts. Second, our current work builds an unweighted transaction network graph; however, incorporating weights and directions could capture the strength and nature of relationships more effectively. Thus, we plan to explore weighted and directed versions of blockchain transaction social network graphs. We plan to develop and deploy a dispute resolution Decentralized Application that leverages the Fair-Spread family of algorithms.
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January 2025
460 pages
ISBN:9798400710629
DOI:10.1145/3700838
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