COWPEA (Candidates Optimally Weighted in Proportional Election using Approval voting) is a method of proportional representation that uses approval voting and gives elected candidates differing weights in parliament or the body into which they are elected.
The weight each candidate gets in parliament is the same as the probability that they would be elected in the following lottery:
Pick a ballot at random and list the candidates approved on this ballot. Pick another ballot at random, and strike off from the list all candidates not also approved on this ballot. Continue until one candidate is left and elect this candidate. If the number of candidates goes from >1 to 0 in one go, ignore that ballot and continue. If any tie cannot be broken, then elect the tied candidates with equal probability.
COWPEA can also be used to calculate the proportion of seats to be allocated to each party in an approval-based party-list proportional election and can be used with the Kotze-Pereira transformation for a score voting variant.
COWPEA is monotonic and passes Independence of Irrelevant Ballots (IIB). The universally liked candidate criterion (ULC) is inapplicable since such a candidate would take all the power within the parliament. However, the COWPEA-Lottery method, which elects candidates according to the above lottery individually and with equal weight, passes monotonicity, IIB and ULC, which is very rare among proportional methods, but it is non-deterministic.