It is often lamented that the modern system of elections is broken, at least when one means simple universal franchise for selecting office-holders. Some of the complaints against the system are age-old, such as the observation that he who promises everything to everyone (regardless either of capacity to deliver or of any negative consequences of trying to deliver) has an unfair advantage. However, in recent times, the system has suffered increasingly from additional woes. In today's world of sound-bites, mass-media fascination, and saturated attack campaigning, it has become increasingly dysfunctional--those we choose to lead us often effectively win elections by an auction process, victory going to the highest bidder, with grotesque amounts of wealth expended on campaigns which are all about subliminal manipulation and have next to nothing to do with the actual merits of the candidates. Worse, the system often selects for individuals of sociopathic or psychopathic tendencies, and frequently maintains them in office indefinitely by means of gerrymandered voting districts--a perfect recipe for unwholesome control and domination by entrenched special interests.
Traditional alternatives, however, have not fared much better: hereditary monarchy, military dictatorship, and so on strive for the Platonic ideal of the "enlightened despot," but this proves to be a mirage; for a society to play no role at all in the selection of its leaders leads nowhere productive in the long run. For every Augustus, you get any number of Neros. Limited-franchise republics (restricting the vote to a certain class of society, such as in apartheid South Africa or Israel) have their own issues with the creation of permanent classes of disenfranchised sub-citizens; there is a tendency for such underclasses to fall into poverty and exploitation, and a substantial portion of the population feels (correctly) that they have no stake in society as it exists. In addition to social-justice issues, this is destabilizing for a society.
There is, however, another idea out there, and quite an old one at that; some have alleged that it actually was implemented in ancient Greece, though other historians disagree with this claim. Whatever the historical reality might have been, the system as described has two stages. A candidate wishing to stand for a public office must submit first to some sort of pre-screening test. At the minimum, this must weed out those aspirants who are obviously unfit for duty due to such things as mental handicaps, illness, emotional instability, insufficient understanding of the requirements of the office, and so on. This could take the form of a written examination, or some other type. (one can also imagine variants where the stage 1 screening is more stringent to varying degrees.)
In the second stage, the winner is selected from the candidate pool by means of a lottery or equivalent random process. Since there is no way to influence the outcome of a lottery by campaigning or psychological tactics, campaigns would be pointless, and it would be far more difficult to win an office by sheer force of money spent; having a powerful party organization behind one would not ensure victory. Since the probability of one person's winning a lottery more than once is quite low. there would be no need for explicit term limits, and geographical district boundaries would also have little effect on the probability of winning. Because most persons would be eligible to stand for office, there would be broad participation and stake in the system.
This idea, of course, is not immune to potential problems of its own. For example, it does not dovetail well with the prevailing parliamentary model on which most republics are constructed, dependent as it is on dominant party factions or simple coalitions to function smoothly; nor is there any obvious equivalent to the snap elections which happen when a parliament is dissolved (a US-style congressional system might be a better match, but this paradigm is unfamiliar to most of the world.) There is also the issue of whether the impartiality of the first stage could be adequately secured; if a way is found to corrupt this stage of the process, then the system fails quickly. Yet elections themselves are often rife with corruption or error, so the question to ask is which process is easier to secure against corruption.
It is interesting to contemplate whether he system outlined above might be a better match for the political realities of the 21st century than the existing electoral system. At the very least, it would appear to be less expensive than traditional voting, and to spare us all the bombardment of obnoxious campaign advertisements that occur all too regularly.