Add mean-median interpolation for incentive

docs/consensus.md

@@ -281,7 +281,15 @@ We set validation reward ratio at $\xi=0$, $0.25$, and $0.5$ and respectively ob
 This means that network security improves as the validation reward ratio is increased, although a significant server incentive ratio still needs to be maintained to ensure overall high utility.
 
 #### Median-mean interpolation (μ)
-Median consensus is unaffected by highly deviating minority stake, and is the primary layer of defence via adjustment of server incentive. However, if we also cut validator bonds at median consensus, honest minority servers with legitimate reasons for deviating weights may experience an unfair double penalty: (i) reduced server incentive to share in, and (ii) reduced bonding with servers.
+Median consensus is unaffected by highly deviating minority stake, and is the primary layer of defence via adjustment of server incentive. Mean consensus ($\mu=1$) for both the incentive and validator reward adjustment is more prone to skewing by minority self-weighting, and we see a decrease from 87\% honest utility requirement down to 73\% when switching to median consensus.
+
+<p align="center">
+ <img src="img/mu_all_100.svg" width="330">
+ <img src="img/mu_all_50.svg" width="330">
+ <img src="img/mu_all_0.svg" width="330">
+</p>
+
+However, if we also cut validator bonds at median consensus, honest minority servers with legitimate reasons for deviating weights may experience an unfair double penalty: (i) reduced server incentive to share in, and (ii) reduced bonding with servers.
 
 To address this, we can relax the median to a mean consensus for cutting the weights for the bonds calculations, according to ratio $\mu\in[0, 1]$. We see that this has relatively little impact on the overall security guarantees, only increasing honest utility requirement from 73\% to 75\%. However, the relief for honest minority validators would likely also be limited with this adjustment.
 
@@ -291,6 +299,7 @@ To address this, we can relax the median to a mean consensus for cutting the wei
  <img src="img/mu_0.svg" width="330">
 </p>
 
+
 ### Reproduce Consensus Plots (Runpod)
 
 This guide demonstrates how to reproduce consensus retention profile plots on a minimal Runpod CPU instance.