That's a complicated question. I live in the US, so my answers are based on that. Yes, I do vote. The system is set up to be fair, and I don't have proof that it's not fair.
There are a number of manipulations that can be used:
1) Fraudulent votes cast
2) Destruction of valid votes
3) Intimidation of voters to prevent them casting votes
4) Preventing valid voters from casting their ballots
There are also options that aren't as blatant such as gerrymandering. This is where politicians re-draw the boundaries of voting areas so that more seats are won for their own party.
Another issue that has come up throughout the years has been that of Voter ID laws. Critics of the proposed laws claim that requiring people to present identification is discrimination. Proponents say that it's not discrimination for people to prove who they say they are. The proponents state that it would cut down on fraudulent votes being cast as numerous times people have been caught on camera claiming to have votes multiple times.
Blockchain's Impact on Voting
Some claim that using blockchain technology could prevent or eliminate voter fraud. There is something to be said for that, but it's not as straightforward.
One of the best things that blockchain technology could do is to keep track of which votes had been cast. This would prevent multiple ballots from being cast by the same person. However, it will not prevent votes from being cast by unauthorized individuals. One issue that needs to be address is the number of votes being cast by deceased individuals. If properly managed, the voter registration ledgers could be set up to only include valid voters.
There would still be an issue of properly identifying the voters. If someone does not have to prove they are who they claim to be, they could still move from polling station to polling station claiming to be different individuals. They could even cast votes as real, valid voters who hadn't voted yet.
tl;dr Yes, blockchain technology could help with managing voting, but there are other issues to addressed before it would be a the magic bullet that some might claim it to be.