Hi all, recently I have been doing a lot of research related to weighted voting systems, cooperative games, and the calculation of power indices, including the Banzhaf power index.
I am fairly certain these notions are very useful for analyzing on-chain governance systems, as most of them tend to be weighted majority games, including Aragon. I also think there are interesting applications to valuation of governance tokens.
Here is the discussion of computation of these indices in an efficient manner, including open source code!
Here is my first post on the topic, applying the analysis for MolochDAO:
I’ll also be publishing a more in-depth analysis and for some real token supplies, including ANT in the coming days.
If you are interested in this topic and would like to discuss more, hit me up on Twitter @jbrukh.
This is awesome! Thank you so much for sharing. The more research and analysis into voting and decision making the better
Wow… the banzhaf index for MolochDAO is really eye opening. Whales have a much higher ability to sway votes than anyone else. Also interesting to think that while whales sway votes directly through token holdings, they also sway votes indirectly due to the fact that people act differently if they know whales are active in the decision making process.
Yeah, this is actually a vulnerability in weighted voting.
Measures like the Banzhaf index assume they know nothing about how people are actually likely to vote and produce the metric based on the structure of the system alone. The result is that everyone is assumed to be equally likely to vote yes or no.
If a voter publishes their preferences ahead of the vote, then they change the “prior” probability of the voting distribution. This expectation also changes the calculation of who is a dummy (disenfranchised) which may cause some people to abstain where they would have otherwise voted. But of course since nothing binds anyone to vote their stated preferences, this may create attacks vectors on the system.
