Semi-PR systems are those which inherently translate votes cast into seats won in a way that falls somewhere between the proportionality of Proportional Representation (PR) systems and the majoritarianism of plurality-majority systems.
The three Semi-PR electoral systems used for legislative elections are the Single Non-Transferable Vote (SNTV), Parallel (or mixed) systems, and the Limited Vote (LV).
SNTV Systems
In SNTV systems, each elector has one vote, but there are several seats in the district to be filled, and the candidates with the highest number of votes fill these positions. This means that in a four-member district, for example, one would on average need only just over twenty percent of the vote to be elected. This allows for the election of minority-party candidates, and improves overall parliamentary proportionality (see Single Non-Transferable Vote).
Parallel Systems
Parallel systems use both PR lists and plurality-majority ('winner-take-all') districts (see Parallel). However, unlike Mixed Member Proportional (MMP) systems (see Single Transferable Vote), under Parallel systems the PR lists do not compensate for any disproportionality within the majoritarian districts. Parallel systems have been widely adopted by new democracies in Africa and the former Soviet states (see The Global Distribution of Electoral Systems).
LV Systems
The LV falls between SNTV and the Block Vote, as there are multi-member districts, and winning candidates are simply those who poll most votes. Voters have fewer votes than there are seats to be filled, but more than one vote (see Limited Vote).
See case studies on Japan Japan - Electoral Reform, Russia Russia - An Evolving Parallel System and Jordan Jordan - Electoral System Design in the Arab World.