The Westminster system does not compel, either by law or by convention, a member to resign from his/her electorate and force a by-election upon resignation or loss of confidence as head of government. The decision is left up to the member, who may choose to do so after a satisfyingly long career or in an attempt to allow the party to present a fresh face without being encumbered by someone synonymous with past unpopular policies.
In Australia, very few Prime Ministers have resigned from parliament straight after having resigned as Prime Minister:
- Edmund Barton, the first Prime Minister, resigned in 1903 to join the newly established High Court.
- Andrew Fisher resigned as Prime Minister and from his seat without much explanation in 1915.
- Robert Menzies retired in 1966 after having been Australia's longest serving Prime Minister. He had earlier resigned as Prime Minister in 1941 but had stayed on in parliament.
- Malcolm Fraser resigned from parliament after losing the 1983 election.
- Bob Hawke resigned from parliament 3 months after losing to a leadership challenge from Paul Keating. At the time, he had been Australia's second longest serving Prime Minister.
- Paul Keating resigned from parliament after losing the 1996 election.
I'm not as familiar with the poliical history of other countries. Some examples of those who have not resigned from parliament straight after resigning as Prime Minister are John Major (UK), Margaret Thatcher (UK), Paul Martin (Canada) and Jenny Shipley (NZ).