Vejam que interessante este seminário online:

Dear participants of the Online Social Choice and Welfare Seminar,

Our next seminar will be next Tuesday (1 November).  Here are the details.

Time:  2PM GMT (10AM New York, 11AM Rio de Janeiro, 2PM Edinburgh, 3PM Paris, 5PM Istanbul, 7:30PM New Delhi, 11PM Seoul/Tokyo)

Speaker:  Murdoch James Gabbay (Heriot-Watt University)

Title:   “The semitopology of heterogeneous consensus”

Abstract.  Arriving at consensus is an old problem, to which blockchain systems add some particularities:
performance is at a premium,
the environment may be highly adversarial — and perhaps most significantly,
the system may be permissionless (any agent can join the network at any time) and heterogeneous (different parts of the network may have different computational power, connectivity, latency, and so forth).

We can make sense of this using the language of topology: a point is a participant, and an open set is a local quorum.  A quorum that reaches agreement may progress locally.  This has good performance: the system doesn’t need to synchronise or reach a global majority to progress.  It is also resilient: local adversarial behaviour may corrupt a local quorum, but the rest of the space may continue to operate.

Such a system is up and running in the Stellar payments network, and can be viewed here: <https://stellarbeat.io/>

The intersection of two quorums is not necessarily a quorum, so in fact we get a new notion of semitopology, which is like a topology but without the condition that intersections of open sets are open.  Semitopologies, like topologies, have rich mathematical structure, with explanatory power which includes the emergence of a kind of “Dictator set” — a subset of privileged participants that determine behaviour which is mathematically guaranteed to exist for any network.

What seems to be emerging is a kind of topological voting theory, with its own version of Arrow’s theorem and various other properties that we are still trying to make sense of.  Applications are to Stellar as currently implemented, and we see further applications in the design of blockchain governance, and specifically for DAOs (distributed autonomous organisations).

I hope that bringing this material to the attention of a social choice audience may lead to a fruitful exchange of ideas and insights, which might inform the new generation of permissionless systems emerging in the blockchain space and help them to be fair and humane, as well as efficient and resilient.
Working paper available here.

Reminder: On the seminar website you can find the video recordings, slides and supplementary materials for all past presentations, as well as information about future presentations.

Marcus Pivato
THEMA, CY Cergy Paris Université
(marcus.pivato@cyu.fr)
https://sites.google.com/site/marcuspivato