  Many democratic political parties hold primary elections, which nicely
reflects their democratic nature and promote, among other things, the
democratic value of inclusiveness. However, the methods currently used for
holding such primary elections may not be the most suitable, especially if some
form of proportional ranking is desired. In this paper, we compare different
algorithmic methods for holding primaries (i.e., different aggregation methods
for voters' ballots), by evaluating the degree of proportional ranking that is
achieved by each of them using real-world data. In particular, we compare six
different algorithms by analyzing real-world data from a recent primary
election conducted by the Israeli Democratit party. Technically, we analyze
unique voter data and evaluate the proportionality achieved by means of cluster
analysis, aiming at pinpointing the representation that is granted to different
voter groups under each of the algorithmic methods considered. Our finding
suggest that, contrary to the most-prominent primaries algorithm used (i.e.,
Approval), other methods such as Sequential Proportional Approval or Phragmen
can bring about better proportional ranking and thus may be better suited for
primary elections in practice.
