BY Election and Additional Member System (AMS-PR)
Some electoral systems with MMPR enforce a by-election for a leaving constituency-MP without new calculation of list seats.
There is no new calculation of the number of list seats for each party, making a change in the constituency changing the party composition in parliament. The Party winning the by-election ends up better as PR, the party winning in the first place ends up worse then PR proportion (and is therby punished for the win of constituency on mean election day).
For the party winning the constituency seat in the first place is this win in reality a loss. On the mean election day, the constituency seats won reduce the number of list seats to reach PR. This means, there is no real advantage for the party in winning a constituency in the first place (Exception: overhang seats). By winning a Constituency Seat on mean election day a party risks loosing it by by-election, a not won Constituency Seat gives a change of winning an additional seat through a by-election.
The new composition is not PR in disfavour for the party winning first. It does not reflect the number of party votes any more.
All seats of a party, list seats but also specialy constituency seats are justified by party votes. Constituency MPs are thereby elected twice, by constituency vote and by party vote.
A By-Election with new calculation of list seats seems at tghe end more senasless, because we end up with an exchange of candidates within a party only (Or possibliy without any possible change at all).
This is of course true for the mean election itself, but there it is hidden by the fact, that all MPs are elceted simultanously.
By Elections with new list seat calculation are only seen, if there must be a second going to vote for the mean election.