There are a lot of requirements surrounding an executive committee meeting (also see questions on convening executive committee meetings and notice requirements).
Chairperson’s role: The chairperson (or if the chairperson is not there someone else who the executive committee chose to chair the meeting) must chair the meeting and assist the executive committee make its decisions.
The chairperson does not have a casting vote but does have the power to decide if a motion is out of order (ie. it is illegal).
Quorum: Before a meeting is able to start there must be a quorum.
A quorum is:
A decision is made by a majority vote either in favour or against a particular motion (if the vote is equal, the motion fails).
In addition an executive committee can hold a meeting where nobody turns up, provided a valid notice is given to each member (with the required motions) and the majority of members approve the motion(s) in writing to the secretary (by way of a voting paper).
In some cases the executive committee will be unable to make a decision:
Adjournment: an executive committee can adjourn a meeting if they pass a resolution to adjourn (for example, to invite an expert to attend the meeting like lawyers, accountants or engineers).