In last Sunday's New York Times magazine, the economists that brought us Freakonomics argued that a rational individual should abstain from voting. According to them, virtually no election is decided by a single vote so the cost for voting is never compensated by any payoff. Their conclusion of why we (or some of us) actually do vote is because of the social esteem gained by being seen voting by our peers. They predict that internet voting may actually reduce voter turnout because we would no longer get this social payoff.
It seems to me that using social prestige as the basis for selecting a leader is a shaky way to maintain a democracy. The real intent of an election is to determine which candidate is favoured by the majority of the populace. For the most part, our current method accomplishes this task (insert your favourite Florida 2000 joke here) although it has two main problems.
The first is that making everyone vote to determine who is preferred is wasteful. In statistics, this is known as an overpowered experimental design. We only need to sample a fraction of the population to obtain an estimate of the election result. The error on the estimate scales with the square root of the sample size. In an election, when enough people have voted so that the error in the estimated result is less then the eventual margin, additional polling won't give you any new information. This is why a single vote doesn't matter.
In a practical sense, this is already what we do because only a fraction of the population votes. However, the fraction that votes is not guaranteed to be a representative sample of the population. Any bias in how the sample is selected will bias the estimate. This leads to the second problem with elections. In a close election, who shows up to vote could skew the results. One facet of election strategy is to enhance the turnout of your voters and suppress that of your opponent's. This never seemed very democratic to me.
If we really wanted to elect leaders based on what the true majority wishes then an election is not the optimal method. What we really should be doing is to scientifically select a sample of the population to vote. Of course deciding on how to choose this sample will never be perfect. There will also be some misrepresentation (like underrepresentation of homeless people) but I think we can certainly do better than what we have now. If we wanted to be really efficient we could even use a bootstrap method to estimate the error compared to the estimated margin of victory on the fly. Now, I'd like to see some brave politician suggest this scheme.