What is the basis for weighted reward, calculated from both total and my effective balance?

Question: What is the basis for weighted reward, calculated from both total and my effective balance?

In this blog post, I will explain what is the basis for weighted reward, calculated from both total and my effective balance. Weighted reward is a way of distributing rewards among participants in a network, such as a blockchain or a distributed ledger. The idea is to reward participants according to their contribution to the network, measured by some metric, such as stake, work, or reputation.

One way to calculate weighted reward is to use both total and effective balance as inputs. Total balance is the amount of tokens or coins that a participant owns in the network. Effective balance is the amount of tokens or coins that a participant has locked or committed to the network, for example, by staking or delegating. Effective balance reflects the participant's commitment and risk-taking in the network, while total balance reflects the participant's wealth and potential influence in the network.

The formula for weighted reward can vary depending on the network design and parameters, but one possible formula is:

weighted reward = base reward * (effective balance / total balance) ^ alpha

where base reward is the amount of rewards that a participant would receive if they had equal effective and total balance, and alpha is a parameter that determines how much weight is given to effective balance relative to total balance. If alpha is zero, then weighted reward is equal to base reward, regardless of effective balance. If alpha is one, then weighted reward is proportional to effective balance. If alpha is greater than one, then weighted reward increases faster than effective balance.

The rationale for using this formula is to incentivize participants to commit more of their tokens or coins to the network, thus increasing their effective balance and their weighted reward. This can enhance the security and performance of the network, as well as reduce the concentration of wealth and power among a few participants. However, this also introduces some trade-offs and challenges, such as liquidity, volatility, and fairness, which I will discuss in more detail in the next section.

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