It could work like this: before an election, each political party would lay out its governing principles - what services it will provide, how its taxes will be structured, what social policies it will pursue, and so forth. After the election, each voter pays taxes to the party they voted for, and receives that set of services - cultural and educational subsidies, for example, or unemployment benefits - until the next election. This would require doing away with secret ballots. On some things, parties may choose to band together to govern specific services - military defence, for example, or monetary systems - where economies of scale are important.It's federalism without the geographic constraints, possible only either in tiny or technologically-saturated nations. It would turn voting into a sort of game--play with the same cards, but different rules when you switch election cycles. In one sense, it's the most legitimate form of government possible. (Somewhere, a 21st-century Thomas Hobbes is having a heart attack, while his Rousseauian counterpart furiously scribbles on a napkin.)
There'd have to be a way to cap the number of political parties for practicality's sake, lest the solipsists and anarchists gum up the works. I'd imagine it'd also raise the stakes for voter fraud, with people appearing in multiple virtual jurisdictions. For instance, someone would claim allegiance to the Flat Tax party while signing up for free flu shots from the Universal Health Care party. And then there's the prospect of a society completely fragmented on partisan lines, with its desires, needs, and values more ephemeral than ever.
Still, it's an intriguing combination of democratic legitimacy and market efficiency, and a few years hence, when we're all avatars in a digital lifescape, it just might work.