Polkadot is a decentralized blockchain platform to be launched in 2020. It will implement nominated proof-of-stake (NPoS), a proof-of-stake based mechanism where k nodes are selected by the network as validators to participate in the consensus protocol, according to the preferences expressed by token holders who take the role of nominators. This setup leads to an approval-based multi-winner election problem, where each nominator submits a list of trusted candidates, and has a vote strength proportional to their stake. A solution consists of a committee of k validators, together with a fractional distribution of each nominator's vote among them. We consider two objectives, both recently studied in the literature of social choice. The first one is ensuring the property of proportional justified representation (PJR). The second objective, called maximin support, is to maximize the minimum amount of vote support assigned to any elected validator. We argue that the former objective aligns with the notion of decentralization, while the latter aligns with the security level of the consensus protocol. We prove that the maximin support problem is constant-factor approximable, as we present several approximation algorithms for it, and prove a matching hardness result. Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party. Besides being of independent theoretical interest, our results enable the network to run an efficient validator election protocol that simultaneously achieves the PJR property and a constant-factor approximation for maximin support, thus offering strong theoretical guarantees on decentralization and security .
The property of proportional representation in approval-based committee elections has appeared in the social choice literature for over a century, and is typically understood as avoiding the underrepresentation of minorities. However, we argue that the security of some distributed systems is directly linked to the opposite goal of avoiding the overrepresentation of any minority, a goal which leads us to an optimization objective known as Maximin Support, closely related to the axiom of Proportional Justified Representation (PJR). We provide an inapproximability result for this objective, and propose a new election rule inspired in Phragmen's methods that achieves a) a constant-factor approximation guarantee for the objective, and b) the PJR property. Furthermore, a structural property allows one to quickly verify that the winning committee satisfies the two aforementioned properties, even if the algorithm is executed by an untrusted party who only communicates the output. Finally, we present an efficient post-computation that , when paired with any approximation algorithm for Maximin Support , returns a new solution that a) preserves the approximation guarantee, b) satisfies PJR , and c) can be efficiently verified to satisfy PJR . Our work is motivated by an application on blockchains that implement Nominated Proof-of-Stake (NPoS), where the community must elect a committee of validators to participate in its consensus protocol, and where fighting overrepresentation protects the system against attacks by an adversarial minority. Our election rule enables a validator election protocol with formal and verifiable guarantees on security and proportionality. We propose a specific protocol that can be successfully implemented in spite of the stringent time constraints of a blockchain architecture, and that will be the basis for an implementation in the Polkadot network, launched in 2020.
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Polkadot is a decentralized blockchain platform to be launched in 2020. It will implement nominated proof-of-stake (NPoS), a proof-of-stake based mechanism where k nodes are selected by the network as validators to participate in the consensus protocol, according to the preferences expressed by token holders who take the role of nominators. This setup leads to an
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multi-winner election problem, where each nominator submits a list of trusted candidates, and has a vote strength proportional to their stake. A solution consists of a committee of k validators, together with a fractional distribution of each nominator's vote among them. We consider two objectives, both recently studied in the literature of social choice. The first one is ensuring the property of proportional justified representation
committee elections has appeared in the social choice literature for over a century, and is typically understood as avoiding the underrepresentation of minorities. However, we argue that the security of some distributed systems is directly linked to the opposite goal of avoiding the overrepresentation of any minority, a goal which leads us to an optimization objective known as Maximin Support, closely related to the axiom of Proportional Justified Representation
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The second objective, called maximin support, is to maximize the minimum amount of vote support assigned to any elected validator. We argue that the former objective aligns with the notion of decentralization, while the latter aligns with the security level of the consensus protocol. We prove that the maximin support problem is
We provide an inapproximability result for this objective, and propose a new election rule inspired in Phragmen's methods that achieves a) a
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by an untrusting third party. Besides being of independent theoretical interest, our results enable the network to run an efficient
. Our work is motivated by an application on blockchains that implement Nominated Proof-of-Stake (NPoS), where the community must elect a committee of validators to participate in its consensus protocol, and where fighting overrepresentation protects the system against attacks by an adversarial minority. Our election rule enables a
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that simultaneously achieves the PJR property and a constant-factor approximation for maximin support, thus offering strong theoretical guarantees on decentralization and security .
with formal and verifiable guarantees on security and proportionality. We propose a specific protocol that can be successfully implemented in spite of the stringent time constraints of a blockchain architecture, and that will be the basis for an implementation in the Polkadot network, launched in 2020.