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Longman Dictionary of Contemporary English
free vote
noun
EXAMPLES FROM CORPUS
▪ It called for a free vote on marijuana, and also for possible referendums on abortion and the restoration of capital punishment.
▪ Members are traditionally allowed a free vote and can not be instructed by their party to follow a line.
▪ On a free vote the amendment was carried by 292 votes to 246, a majority of forty six.
▪ The issues of Maastricht - single currency, sovereignty and legal structure - deserve thorough scrutiny and a free vote.
▪ Who is really winning will not be known before the free vote on the embryo Bill in the new year.
Wiktionary
free vote

n. (context politics English) In a Westminster parliamentary system and other democracy systems, a vote by members of a legislative body in which the members are permitted by their respective political party to vote as they individually see fit, without direction from their political leaders.

Usage examples of "free vote".

Will this City be no longer able to stand, is our dominion at an end, if a free vote is allowed to the Roman people so that they may entrust the consulship to whomsoever they will, and no plebeian may be shut out from the hope of attaining the highest honour if only he be worthy of the highest honour?

And then you have a free vote and everybody talks about how wonderful democracy is.

But this has come about through a free vote and reflects the considered opinions of both races.

It was the Nation that by the exercise of a free vote put him in power and kept him there.