So it IS compulsory and you actually have to "be counted" - how do you know they still don't use your name for some kind of vote?
All voting is by pen/pencil and paper. If you turn up and have your name crossed of the electoral roll then no-one else can vote using your name. Once you receive the voting papers, which are initialled when you have your name ruled through,you go to a booth, mark it (or not if you refuse to vote) and then drop it yourself into the appropriate box for counting after the polls close. Counting is watched/checked by party scrutineers.
I believe we get the government they want us to have. Did you know that in our "Democracy" the majority of people could vote for a candidate, yet that candidate could still lose? Do you folks have an "electoral college"? That's a complicated way of making sure that only certain votes have any real weight, and is a system that is open to abuse.
First, we don't elect our head of state because we are still a constitutional monarchy. We have nothing equivalent to your electoral college, nor do we have your system of primaries. We do have an upper house, the Senate, which is very similar to yours. Senators have a fixed 6 year term and half retire every three years. Each state elects 6 senators for every half senate election and the seats are allocated by proportional representation using a preferential voting system.
We also have a lower house, the House of Representatives, which has a maximum term of 3 years but the PM can call an early election if he/she wants to. One representative is elected from each electorate using a preferential system. Counting of preferences only happens if no candidate gets at least (50% + 1) of the primary votes.
Whichever party wins the majority of lower house seats gets to form government and its leader is appointed Prime Minister by the Queen's representative, our Governor General (a mostly ceremonial position). The party can change leaders at any time and then we have a new prime minister. This has happened in the last month when our first ever woman PM was challenged and defeated by someone from her own party. The irony is that three years ago she did the same to him.
We are due for a new election later this year but the date has not yet been set by the new PM. Even though the last three years have been tumultuous, with a minority government surviving only with the support of a handful of independent MPs, and with scandals surrounding various MPs, including The Speaker of the House, we are still facing a reasonably close election. Politics down here is anything but dull.