Consensus: Reputers

Reputers are rewarded based on their accuracy relative to consensus (formed by all reputers providing data for a topic) and stake, with added functionality to prevent centralization of rewards caused by reputers with larger stakes.

Problem: Runaway Centralization

1. Stake-Weighted Average:

• Reputers are actors who report how accurate certain predictions or inferences are against the ground truth.
• Normally, we might average the accuracy (or "losses") they report but give more weight to reputers with bigger stakes (more reputation).
• This means reputers with more stake have more influence on the consensus (agreed-upon truth).

2. Runaway Effect:

• The problem is that reputers with higher stakes will be closer to consensus, which they have more influence on, and get more rewards, which further increases their stakes.
• This creates a cycle where the rich get richer, leading to centralization. A few reputers end up controlling most of the influence and rewards, which is unfair and unhealthy for the system.

Solution: Adjusted Stake

1. Adjusted Stake:

• To prevent runaway centralization, we adjust how much weight each reputer's stake has when setting the consensus.
• Instead of using the full stake for weighting, we use an adjusted version that doesn’t let any one reputer dominate.

2. How It Works:

• The formula for adjusted stake ensures that if a reputer's stake goes above a certain level, it doesn’t keep increasing their weight in the consensus calculation.
• It levels the playing field, so reputers with smaller stakes still have some influence.

$\hat{S}_{im} = \min \left( \frac{N_r a_{im} S_{im}}{\sum_m a_{im} S_{im}}, 1 \right)$

Where:

• $N_{r}$​ is the number of reputers.
• $a_{im}$ is a listening coefficient, which is a measure of how much the network considers each reputer's input, and is optimized to maximize consensus among the reputers.
• $S_{im}$​ is the original stake.