There is now no technical reason for the broad spending priorities of governments (x% on health, y% on education) to be decided by a professional political class rather than the populace as a whole. If you like the idea of democracy, electoral representation is, at best, a lossy compression of voters’ policy preferences. Multi-candidate ballots are low-bandwidth channels (on the face of it, a vote for Obama over McCain conveys log2(2)=1 bit of information), while the opinions of citizens over all political issues contain a huge amount of information. Elections work by exploiting redundancy in voters’ preferences. As everyone knows, political beliefs on different issues aren’t independent; they are often highly correlated, as with for example stances on abortion rights and attitudes towards global warming. The existence of mutual information between preferences (if someone wants x, there’s an increased likelihood that they also want y) allows the political signal to be compressed into party affiliation or support for some candidate. (The distribution of voter’s favourite “ideal points” in a multidimensional policy space thus maps roughly to a one-dimensional ideological spectrum, which forms the basis for the well-known median-voter theorem.)
This not-terrible system for transmitting popular wishes might have satisficed in the 19th century. But there’s just no point to it now, other than to protect the social privileges of certain groups.
We don't have direct democracy not only because we have only recently gained the ability to do it, but also because ever since Burke we have concluded that representative democracy is a superior system.
There are a number of reasons for this. In part we feel that the model parliamentarian is better informed than the general public, and is more likely to be sensitive to competing interests; in part because Arrow's Theorem says that it's theoretically impossible to guarantee that you can sum individual preferences into a general solution; in part because public opinion is not necessarily coherent or consistent. All of these are, however, largely irrelevant.
The insurmountable problem with direct democracy - with plebiscites, no matter how efficient, working from citizen's preferences - is that it mistakes the means for the end. The one absolute rule is that the king's government must be carried on. (That's an archaic formulation, but it does emphasize that the nation is more than simply the sum of the preferences of its citizens). Decisions have to be taken within reality-based constraints and within the constraints of previous decisions, and these decisions are governed by different standards of morality and desirability than the decisions we take as individuals; cf. Machiavelli.
The functions of a parliamentary system are
* to elect an executive
* to provide the personnel for the executive
* to provide sufficient legitimacy to that executive
* to blur and diffuse individual solicitations into a policy that's generally acceptable
It's a category error to say that what's important to the parliament as a parliament is important to the executive as an executive. The fact that in this country there's a partial coincidence between the members of each group only confuses the issue.