The criticism to direct democracy does not apply to PDI. Partido de Internet is NOT about direct democracy - it's about both direct and representative democracy. You get what you want when you want. The most probable use-case is you stablish a voting delegate, and then once in a while you check that your delegate is doing right. If there's an important voting you can always check the vote your delegate will proxy as yours, and if you don't agree you can emit a direct vote for a specific voting and continue delegating in the rest. And of course if that happens a lot, then you can change your delegate.
Oh and you cannot stablish a voting delegate and forget about it for years: the authorities in charge of the secrecy of the vote need to be many and will have a period of renewal, which could be say 2-4 years. When they change, the votes (including the delegations, which are treated as a special kind of vote, where the options are not YES/NO/ABSTENTION but DELEGATE 1,DELEGATE 2,etc) need to be re-emitted too. So in the end it can function as regular representative democracy where you vote (i.e. delegate) every 4 years, BUT you can change your vote at any time, and you can emit a direct vote if needed for important matters, working as direct democracy when the user wants only (which can be always, never, or anything in between). This is useful because some people always want to vote for X party, but in reality they don't agree 100% with it. For exmaple in spain 50+% voted for Partido Popular, but ~97% was against irak war promoted by Partido Popular. All of them could have voted NO had liquid democracy been in place.
People voting to a traditional party and then also voting in Ágora "virtual parliament" is a non-issue for us: we want more users, and those must naturally come from those voting traditional parties, so that's a "transitional" stage, and as marketing. If lots of people from another party try our system, we believe we will gain lots of people that otherwise wouldn't have known our system and wouldn't have a chance to vote to our party.