We've been through several scenario's.
Spam 1: User marks a link which is classed as spam.
In this scenario the user has burned their own marks, and people tend not to mark (read: upvote, like, share, tip) spam content, so in any ordered list it simply falls to the bottom out of view, and only clutters up their own account.
Spam 2: In a marking powered community, say forum, a user submits spam content.
In this scenario we have discussed a spam button, when another user clicks it some of their marks are staked against the action, if enough people click the spam button the content is automatically binned, and the marks staked on the spam button are returned to the users who clicked it. This acts as democratic semi-automated moderation, and whilst the people clicking the spam button are not rewarded monetarily, they have no increase in balance, they do gain reputation from the action since the marks are sent back to them. Conversely if somebody tries to be a bad moderator and mark legitimate content as spam, they have burned their own marks by doing so. Note this is many people agreeing something is spam, as opposed to pay to class something as spam.
Network: A troll starts trolling via web-scale marking.
The system I am working on models a federated social network, with social connections and public channels. This means that generally you only see public markings from people you view as reputable (or watch), and markings in generic public categories, or specific categories you follow. The system focuses on curating via marking, and passing reputation, there is no content creation or message channels to speak of. Therefore limit places to troll.
It appears that the marking system promotes good actions, since everything is attached to reputation, reputable actions are rewarded. In some ways it codifies altruism. We must however stay vigilant to ensure the system cannot be gamed.
Hopefully much more will be written on this topic, and each implementation will advance different approaches to common problems, then share what they have learned between systems.
Thank you for sharing the link, I will enjoy reading it later.
Second, do site-owners need to do something to implement marking? For example, would the NY Times need to cooperate with Bitmark in order to enable its commenters to mark one another? Could this be done in a permissionless manner, perhaps using a browser plugin?
They may implement marking, or integrate marking from another service. Where they have chosen to implement then they will have their own marking system working in their web applications, on their website. When they have chosen to integrate marking from another service, then we can expect the system to work in the same way as clicking "like", "share" or "tweet this", nothing complicated required. Hopefully with the passing of time comment systems such as disqus, and sharing services such as add this, will add mark-this buttons.
However, we can also enable marking via browser plugins, bookmarklets, and apps, so there's really no shortage of approaches, anything can be bootstrapped, both in real life and on the web.
Thank you for the well thought questions, and we look forward to discussing with you further in the future.