Phragmen’s method and how it affects staking in (N)PoS Blockchains

As part of my interest to understand Blockchains, I look at sophisticated terms and try to simplify them – so I could understand their role better, and help others to do so too. As I learned from the best, writing is the best way to do it, so I give my first try in this blog post!

In this specific post, I’m going to touch an interesting elections method invented by a Swedish mathematician, and explain how it’s used in the Polkadot Blockchain. If you’re not familiar with Polkadot, I suggest visiting Polkadot.network before reading this.

Phragmen’s method – and how it affects DOT holders

Phragmen’s method, is one of the methods helping to design the Polkadot’s validators elections process. We’ll touch the most important points about it in regards to participating in the network as a DOT holder.

What is Phragmen’s method in Polkadot?

Phragmen’s method is used to implement the idea of equal-representation in the validator elections and ensure that an appropriate power balance is achieved. This implementation inside NPoS is echoing the original idea of Edvard Phragmen to correct minority representation in the political environment. His method presented an idea in which the number of seats assigned to each party was proportional to the votes given to them, instead of having all the seats given to the most popular party. That achieves a situation giving more representation to minorities.

Before getting into the specifics of this method and how it’s relevant for DOT holders, it’s essential to get to know the types of participants in the protocol and understand their roles.

Roles of a DOT holder in Polkadot

A DOT holder can participate in the network as one having one of a few roles. The most relevant ones impacted by Phragmen’s method are validators and nominators. The others who complete the symbiotic circle are the collators and fishermen.

  1. The collators are the “right-hand” of the validators as they are accountable to a significant part in the process of blocks production. The two are highly dependent on each other. Collators run a “full-node” and hold necessary information to execute transactions and author new blocks, then pass them to the validators to implement the final production.
  2. The fishermen are the “police” of the network, as they are incentivized to chase bad actors to receive bounties, similarly to a police’s work. A fisherman has to lock a small DOT bond in the system to prevent possible misbehavior from their side and time-waste of the validators, who validate their work and provide computational resources.
  3. The validator‘s work is to verify that blocks are appropriately secured and validated. A validator locks a significant DOTs bond in the system, similar to a deposit, and as the fishermen do. That’s a term needed to prevent misbehavior and encourage higher security service standards. If a validator misbehaves or presenting faulty service to the network repeatedly, the bond is burned. On the flip side, providing a reliable service gets a validator rewarded for the work of running node operations.

By design, the Polkadot maximum capacity for validators’ participation in the protocol is at the thousands. Because of that, there’s an election process in place to select the strongest validators that can lock the strongest bonds. By that, validators essentially put more skin in the game and likely to provide a reliable service. A validator can provide this bond independently or with help from nominators.

  1. A nominator can help validators get into the pool by electing them with DOTs, essentially delegating their stakes to a combined bond, which increases the chances to get into the validator operations pool. That is because there is a significant requirement for DOTs in the validator’s bond. For a nominator, this means he/she can indirectly participate in the network’s validator operations and increase his/her bond size without running a full-node. In practice, a nominator can delegate DOT tokens to his favorite validator, and in exchange, get a proportional stake in the rewards of this validator. For example, if Bob nominated 25 DOTs to validator X, who is total DOTs at stake are 100, he would be getting 25% of the validator’s reward(minus validator fee). It does not matter how many validators Bob is nominating, as he still has a proportionate stake at each one of them. A nominator can nominate up to 16 validators.

Phragmen’s method in the validator elections

In Polkadot’s validator election process, Phragmen’s method presents a mechanism that automatically adjusts the stakes(votes) backing a validator pre and post-elections. The goal is to achieve a situation where minority validators have improved chances to get elected and vote equally — essentially balancing over/under representations of a validator to participate in the operations. Also, all stakes are always valid because delegated stakes must end up at a validator’s bond that passes the elections process.

In this process, some validators need the nominators to have an increased bond to pass the elections, as their bond size isn’t big enough. Given that, there is a high likelihood of competition among validators to recruit their nominators.

Takeaways for DOT holders

There are several crucial points every DOT holder should consider when participating in the network, particularly in regards to validators and nominators given the implications of the Phragmen’s method.

  • Choosing a validator – a nominator should put appropriate thinking in choosing the right validator/s. While participation in the network as a nominator is relatively low-risk, it’s important to remember that there’s still a chance that a validator’s bond will decrease due to service failure. Phragmen’s method is reducing some of that risk when it’s doing the rough equalization among validator’s stakes, so the risk spreads, yet it’s important to realize it still exists.
  • Effective participation – A nominator should keep in mind that in an event where he/she is nominating a set of validators, and one(or a few) of them does not pass the elections process, the delegated stakes pass over to the others according to Phragmen’s method. Meaning there’s no “waste” of voting power in the system, and a nominator should not worry about his/her stakes not effectively delegated.
  • Post nomination – Validators stakes adjust during the election process according to Phragmen’s method in NPoS. It means that a nominator should keep in mind their stakes in a validator’s bond can adjust by the system as a default, and might not end up entirely in there post-election. That isn’t affecting the rewards, as all validators are getting paid equally in Polkadot.
  • For Validators – With Phragmen’s method, validators now have even more opportunities to be chosen by the system to secure the network, with less significance to their original bond size. That’s because nominators can easily “buy” a stake in their bond that is adjusted between all validators – meaning one validator can benefit in some cases from other validators and their nominator’s stakes.

Conclusion

Phragmen’s method in Polkadot provides an essential mechanism to make the validator’s election system more balanced. It evens out the rewards and power among chosen validators and provides a flexible scheme for minority holders to stake their tokens and be part of the validator operations. In the Polkadot protocol, each role in the network has it’s crucial responsibilities, and it’s vital to ensure an effective collaboration system is in place. With validators having one of the essential roles in the network, Phragmen’s method allows a significant mechanism for them to collaborate, work, and get rewarded equally. That’s a critical element of the protocol’s roles scheme, and it’s goals.

Phragmen’s method is a notable part of NPoS and the protocol’s design goal to attract a large sum of DOT token holders to participate in securing the network. With Phragmen’s method implemented in the protocol, token holders have more possibilities to take part in the network as the security layer is shared, and risk is appropriately adjusted among all participants.

Sources and further reading:

Click to access PolkaDotPaper.pdf

https://research.web3.foundation/en/latest/polkadot/NPoS/index.html

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