I've always enjoyed the concept of exponential costs for incremental gains. I've had the benefit of only really utilizing them in strong-identity systems (games) but I've considered some of the drawbacks of using them in weak-identity systems and come to a few ideas:
1) A participation barrier can be used to prevent identities from participating until they've overcome something. A simple example would be an age barrier (identity must exist for some period of time before participating) which prevents spinning up multiple identities on-demand to try to increase voting power. Ideally, in practice there would be multiple barriers that would be naturally-occurring for a real participating identity but too expensive to create/maintain several identities.
2) Similar to (1), have an ongoing cost to maintaining identities. Something such as a "subscription fee" may serve as a deterrent as the value of one identity needs to be weighed against the cost of maintaining it. This can be made additionally effective if the issue being voted on recurs every period rather than one-time (i.e. revisiting regulation votes every cycle instead of just voting once and having the regulation remain until stricken). For the normal participant, the value of this subscription could be offset by access to a non-scaling benefit - i.e. access to private content/events.
3) While the article focuses on the economics in terms of dollars there's the very real question of allowing votes to be purchased with other forms of currency that either complement or replace traditional currency. This is common in MMOs where you can have multiple characters (weak identities) each with their own in-game currency that can be acquired from in-game activities and may or may not be exchanged with real-world currency depending on the stance the owners of the game take.
Suffice it to say there aren't really silver bullets to "general purpose quadratic payments with weak identities" but you could create some limited-purpose constraints that are particular to the problem/community and make some strides from there.
1) A participation barrier can be used to prevent identities from participating until they've overcome something. A simple example would be an age barrier (identity must exist for some period of time before participating) which prevents spinning up multiple identities on-demand to try to increase voting power. Ideally, in practice there would be multiple barriers that would be naturally-occurring for a real participating identity but too expensive to create/maintain several identities.
2) Similar to (1), have an ongoing cost to maintaining identities. Something such as a "subscription fee" may serve as a deterrent as the value of one identity needs to be weighed against the cost of maintaining it. This can be made additionally effective if the issue being voted on recurs every period rather than one-time (i.e. revisiting regulation votes every cycle instead of just voting once and having the regulation remain until stricken). For the normal participant, the value of this subscription could be offset by access to a non-scaling benefit - i.e. access to private content/events.
3) While the article focuses on the economics in terms of dollars there's the very real question of allowing votes to be purchased with other forms of currency that either complement or replace traditional currency. This is common in MMOs where you can have multiple characters (weak identities) each with their own in-game currency that can be acquired from in-game activities and may or may not be exchanged with real-world currency depending on the stance the owners of the game take.
Suffice it to say there aren't really silver bullets to "general purpose quadratic payments with weak identities" but you could create some limited-purpose constraints that are particular to the problem/community and make some strides from there.