It is said that in a democracy rule is determined by numbers. Numbers count. This is odd, as mathematically this may be a very poor solution. Say in a 2-party vote there is a 50% chance of winning. But winning what? You're most likely to favour the party with the most appealing promises at the time of election. If we say, for simplicity's sake, that what a party promises only prepresents the first of four years of government, this in effect this represents only a fourth of your vote, so 25%. Combined with the 50% chance of winning, we're now at 12.5%.
Let's furthermore remember that you vote for the party which has more policy proposals you concur with than the other party, not that you agree with all of them. So if we say you only agree with half of them, another 50%comes off the 12.5%, making it 6.25%. Bearing in mind that politicians lie and make promises to gain votes, that not all those promises actually get implemented, your representation is reduced by say another 50%. Half of 6.25% is 3.125%. In short, in very crude terms, mathematically speaking only about 3% of your beliefs are represented in the government you vote in.
The above is not very scientific and is based on various possibly erroneous assumptions. Nevertheless, most would agree that the level of representation one gets through voting is very low. Whether is is really 3% or as high as 20% it is still low. The situation is completely different in a direct democracy where youn can vote on each issue, issue by issue, independently of any party line. But in a representative democracy you have to gamble on a party, and you may find it only represents about 1% - 5% of your views. Is it any wonder then if you feel disengaged?