In proportional party-list voting systems, each party is entitled to a fraction of the seats in proportion to its vote count. This fraction is always rounded up or down according to some rule of "apportionment". Inevitably, some parties get their proportional share rounded down, while others get their proportional share rounded up. This may be considered unfair.
An alternative to these apportionment rules is to give each party a fractional seat. For example, if there are 435 seats to allocate, and one of the parties wins 10% of the votes, then the first 43 candidates in its list will get a whole seat, and the 44th candidate will get 0.5 seat. This candidate will get 0.5 of the salary of a parliament member, and have 0.5 voting power.
Apparently, this method seems fairer than rounding up or down. What are its downsides?