an agent who themself receives good grades than from an agent who themself receives poor grades.

GENERALIZED PEERRANK
====================

The PeerRank rule proposed so far does not incentivize agents to evaluate other agents or even themselves accurately. We therefore add an additional term to provide such an incentive. Suppose $\alpha$ and $\beta$ are parameters with $\alpha + \beta \leq 1$. Then we define the generalised PeerRank rule recursively by the following equation: $$\begin{aligned}
X^{n+1}_i & = & (1-\alpha-\beta) . X^n_i + \frac{\alpha}{\sum_j X^n_j} . \sum_j X^n_j . A_{i,j} + \\
 &  &  \ \ \frac{\beta}{m} . \sum_j 1-|A_{j,i}-X^n_j| \end{aligned}$$ This degenerates to the earlier form of the rule when $\beta=0$. The new term measures the normalised absolute error in the grades given by an agent. This is similar to the reward given in the recent mechanism for reviewing NSF proposals in the SSS program [@nsf1]. The agent “receives” a credit towards their grade of $\beta$ times this normalised error.

If $A_{j,i} = X^n_j$ for all $j$ then the grades assigned by an agent are exact and we add $\beta$ to their score. If $|A_{j,i} - X^n_j|=1$ for all $j$ then the grades assigned by an agent are completely wrong (either 