"the vote that" is correct and usable in written English.
You can use it when referring to a specific vote. For example: "We have to take into consideration the vote that was cast by the majority."
"This was the vote that got rid of soft money".
A preview to the vote that could bring a Whole Foods grocery to Brooklyn.
He won 88.7% of the vote that was held in government controlled areas.
The campaign will change many times between this week and the vote that really matters, in November.
Now he relies on polls as he decides when to hold the vote that will make or break his leadership.
The election is in November, but the vote that counts is the Democratic primary two months before.
Presidential candidates usually capture a percentage of the vote that is about the same as their approval rating.
(Four was ultimately deemed necessary, because no one wanted to be "the vote" that turned the issue).
Four countries -- China, France, Malaysia and Russia -- abstained in the vote that established the new inspection commission.
It is legislation that was not put to the vote that better explains Abbott and Turnbull's criticisms of the Senate.
The big beneficiaries are groups like Rock the Vote that were formed to engage young people in politics.
