Section 23 of the Constitution provides:
Questions arising in the Senate shall be determined by a majority of votes, and each senator shall have one vote. The President shall in all cases be entitled to a vote; and when the votes are equal the question shall pass in the negative.
This section clearly refers to a simple majority, that is, a majority (half plus one) of the senators present and voting. A simple majority is distinguished from an absolute majority in the Constitution by the requirement in section 128 that a bill for amending the Constitution must be passed by each House of the Parliament by an absolute majority. An absolute majority is also prescribed for the passing of a bill at a joint sitting of the two Houses in the event of further disagreement between the Houses over the bill after simultaneous dissolutions under section 57 of the Constitution. An absolute majority is a majority of the whole number of senators.
The provision in section 23 whereby the President has a deliberative vote only and not a casting vote is designed to preserve the equality of representation of the states. If the President had been given a casting vote, the state represented by the senator who happened to be President would have either an additional vote (if the casting vote were in addition to a deliberative vote) or the power to decide issues when the other senators were equally divided (if the President had a casting vote only).