I live in a third-world country (Greece). The problem is not fraud. They don't need that. Corrupted politicians (ruling for 40 years here, without any real problems) buy votes prior to the elections. From 20 (EUR) to 50 per vote. Now that we're in the middle of a financial crisis even 12 to 15 per vote could work. In the villages you can get an entire family to vote (~ 4-5 votes) for 2Lt of fresh oil. In the cities are either bought or exchanged for a future job as a public servant (hard to do these days, but still...)
This. I live in Serbia and it's the same thing. They approach you as you're entering a voting location and offer you as little as €20 in exchange for a vote, and they ask you to take a smartphone photo of the voting piece of paper (dunno the right term in English) as proof.
Not to draw discussion to political affairs, but literally nobody I personally know has ever expressed nothing but contempt for the currently leading party here, yet they have amassed over 50% of all the votes on the latest elections. I suspect a lot of it was via these methods. So a fraud-intolerant voting system would help, but not tremendously so.