This happend this week in the Netherlands.
In Holland we have a "First Chamber". It consists of 75 people who are picked from 566 elected provincial politicians that got elected by the people of that province, by those same 566. The voting procedure consists of filling in a ballot with a red pencil.
For the goverment to pass law they come to an agreement with the "Second Chamber" and then pass it on to the "First Chamber" and need them to agree on these laws before they can make it a law. Basically it's the last hurdle for stopping a law.
During the election of the 75 politicians, one person from the opposition did not see a red pencil and decided to fill it with his own blue pen. His vote was marked invalid. When dividing the votes the party that lost the highest fraction after dividing gets this seat.
The result: his party got 5 seats instead of 6. That seat ended up on the government side. The government ended up short. They got 27 out of 75, but due to their being a minority government, they have an agreement with the PVV so they ended up with 27+10 out of 75. That's 1 seat short (could have been 2).
Now there is 1 party that has 1 vote called the SGP. No other parties are willing to help the government. And the SGP is a party that wants women back in the kitchen and gays neutered.
Yes, 1 vote can make a difference.