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Speaker Denison's rule is an explanation given by a 19th century Speaker of the British House of Commons, John Evelyn Denison, as to why the Speaker casts their vote in most cases in favour of, rather than against, a government, where they have the casting vote.

The principle is simple. No chairman should allow himself or herself to use their casting vote to take a decision which the House of Commons cannot subsequently overturn. Speaker Denison's argument was:

1. A vote against a government automatically terminates a government's position vis-a-vis a House of Commons by forcing either its resignation or a parliamentary dissolution. That decision automatically terminates either the Government's existence, or terminates the House of Commons by causing a general election. So either way, a vote against a government cannot then be rescinded by the House of Commons.
2. A vote for a government keeps it in existence for the time being, but leaves open the option that a House of Commons may vote against the Government at a later stage.

So whereas Number 1 cannot be overturned and is definitive, Number 2 is overturnable. Hence a Speaker's vote in favour of a government (or a Bill) allows a different decision to be taken later on, whereas a vote against would preclude the House from voting on the issue later on. The bottom line is simple: Vote to maintain the status quo for the moment, allowing the members if they wish to overturn that decision later on.

Speakers in the British House of Commons had traditionally cast their votes without explaining their reasons why. Speaker Denison explained the logic. Speaker Denison's rule is now a guiding principle by which chairpersons cast their vote in the event of a tie, in many bodies. However every chairperson is free to ignore the rule and vote on their own criteria. In practice most neutral chairpersons in most bodies use Speaker Denison's Rule as a guiding principle to keep the option open by which the membership may overturn the decision at a later stage.