I think one of main problems in stock pump and dump schemes is that market participants, not trusting each other, should decide what to pump and when. This is a variant of Byzantine Generals Problem. Often, the solution relies on a leader who tweets stock picks (see stocktwits.com), and if enough people trust him, pump and dump will succeed. But this has a centralization problem: the leader could be tempted sell his picks to paying customers before the announcement is made, or he can be arrested by authorities, because pump and dump is illegal of course.

Now imagine a "pumpdump" blockchain, miners would mine for the solution and for the right to announce their P&D stock pick. Miners are incentivised to select good P&D candidates, because if no one joins, their mining effort will be wasted. That blockchain doesn't have to have a separately valued "coin" associated with it, the incentive here is to get others follow your pick and benefit at the "dumping" stage.