Group Informed Consensus
Group informed consensus is a measure of the extent to which an opinion group in the conversation agrees (by vote) in response to a particular comment. It is designed to counter "tyranny of the majority" by optimizing for comments which are as favorably viewed as possible across participant groups in the conversation.
Derivation
For any group of participants, you can estimate the probability that a random participant drawn from that group will agree with a particular comment by counting up the number of agrees, and dividing by the total number of votes.
It can be helpful to add 1 to the first of these numbers, and 2 to the second, so that in the absence of any vote data, our estimate defaults to 1/2. These "psuedocounts" act as a naive prior to smooth out the estimates for low vote data, and importantly prevent the system from dividing by zero.
If one multiplies these estimated probabilities for each group in the conversation, we get a number that will be highest for comments every group tends to agree with. We call this product the group informed consensus metric.
Intuition
This metric is designed so that even a single small group united in opposition against a comment can prevent it from having high group informed consensus, even if all the other groups are in unanimous support. High group informed consensus is more likely going to select for an option with 70-80% favorability across all groups than for a couple of large opinion groups to simply have their way on an issue (tyranny of the majority).
Discussion
It's important to note that this metric can vary significantly based on what the chosen opinion groups look like. This highlights the importance of carefully considering what clustering algorithms we use to identify opinion groups from the vote data, and suggests an angle for considering how trade offs between different clustering algorithms are evaluated.