Is the purpose of electing officials by vote to ensure that the people of the country are all represented? Or is it enough that they can be represented if they make the effort?

In some countries they fine people for not showing up to the polls, good idea or no? Should criminals be allowed to vote to ensure they are represented? What of the various and sometimes half-baked plans for limiting the number of eligible voters by adding requirements based on education, or on a community service requirement, or a "not on welfare" requirement?

Does the idea of getting "better" voters (even through a simple thing like not fining the apathetic people for not showing up) have any merit?