Hashgraph algorithms actually do not really need a Proof of Work algorithm, the voting itself can be realized by the graph itself with a relative minimal cost, the only issue that remain how the system should avoid Sybil attacks. Here one of the idea might be to use some kind of a tokens for voting and the token distribution can be controlled in a way. One of the idea for the voting token distribution can be simply a consortium network scenario, the other one is a something similar to a Proof of Stake.
However the voting token distribution can be controlled with the help of a Proof of useful Work algorithm as well. Everyone who did some amount of useful work get tokens in the system to vote. Such a mechanism provide several advantages comparing to classical Proof of Work of a Blockchain system. In Hashgraph Proof of Work we do not need rounds, so the work itself must be not scalable to blocks, it might vary and take largely different amount of time frames. On the other hand, the proof of work should not be competitive as in Bitcoin for example where the fastest wins and the rest of the efforts will be lost. Here, practically every piece of work will be regarded with tokens, so they are considered as valid.
Certainly, there remain some open question. On the one hand, how can be proved that the amount of work was really done. On the other hand, it must be analysed by game theoretical perspective if maintaining the system is a Nash equilibrium.