Taxemes are only one part of the Resilience system. Think about the blockchain. What Craig Wright did was to combine multiple different parts into a new type of system. I have attempted to do the same, and it takes some time to walk through the components.
Taxemes are the selection-system for tax-rates, which behaves similar to how trends spread. It decentralizes the governance of the tax-rate. They use an incentive-system (1) where inheriting a high-tax-rate Taxeme is rewarding, through what I have conceptualized as "branching schemes". (2)
The idea is roughly that when A buys something from B, the Taxeme extracts tax, and A then enters what I call a "branching scheme", where tax from any future transactions that extend from B would flow down the dividend pathway that was formed between A and B.
A's dividend pathway becomes active first after the Taxeme which taxed the transaction is destroyed. This happens once it has been forwarded by A to someone who consumed from A, and then eventually collides with an anti-Taxeme which has spread in the opposite direction (from sender to recipient instead of recipient to sender).
A is therefore incentivized to pay-it-forward and to spread the Taxeme, in turn forming new branching schemes that extend from A. (3)
Dividend pathways gain a width proportional to the Taxeme that was active when they formed. Dividend pathways compete with other dividend pathways in the same branching scheme. Dividend pathways are used up as tax flows through them. (4)
References
3, https://steemit.com/ethereum/@johan-nygren/on-chronological-branching-processes
4, https://steemit.com/ethereum/@johan-nygren/the-resilience-protocol-darwinian-basic-income
History
I've improved the designs over time, and most of the concepts originate from 2012. I built a demo of dividend pathways in 2014 (1), and coined the word Taxeme in 2015 (2), deployed the Proof-of-Individuality (POI) project in 2015 (3), designed the anti-Taxeme concept in 2016, and built a demo of Taxemes on Ethereum in 2016 (4)
1, http://graph.basicincome.co
3, https://steemit.com/proofofindividuality/@johan-nygren/proof-of-individuality-poi-poc3
4, https://medium.com/@resilience_me/try-out-proto-taxemes-c0d27f3ae36a#.ybnccbxac