The work within the PRAGMA project regards (a) various ways of facilitating
the use of multiwinner elections, and (b) building the ``map of elections''
for preference data analysis. Below we provide the project's main achievements.
One important issue regarding multiwinner elections is explaining the
results to both voters and the candidates. Indeed, many multiwinner
rules, such as the single transferable vote rule (STV), do not even
have a naturally defined score, and those rules that do, such as
Proportional Approval Voting (PAV) only provide scores for the whole
committees and not for individual candidates. Hence, within PRAGMA we
have developed a number of techniques for explaining why particular
candidates were or were not selected. These techniques are
particularly useful in participatory budgeting scenarios: We evaluate,
e.g. how many additional votes a project needed to be funded, how
much it cost should have been decreased, which other projects stood in
its way, how it would perform if we added some random noise on top of
the cast votes, etc. Altogether, our methodology provides a
multidimensional evaluation of project performance. While our
techniques often involve solving computationally challenging problems,
we have provided a number of techniques to deal with this
issues. Following this line of research, we have also studied several
game-theoretic models, which guide which candidates and projects
should be nominated in an election, to be successful (in case of
participatory budgeting, we also analyzed how to choose project
costs).
In terms of data analysis, the most important achievement of the
PRAGMA project is developing the ``map of elections'' framework. The
idea is to collect election instances (either those from repositories
of real-life ones or generated synthetically), compute distances
between them, and, based on that, analyze similarities between
them. This, however, requires so-called isomorphic distances, which
are invariant to candidate and voter identities. Within PRAGMA, we
have developed and analyzed such distances, and used them to analyze
elections. One of the imporant recent achievements in this respect is
providing distances that work seamlessly over elections of different
sizes. This way we were able to provide maps of large fractions of
elections from PrefLib and PabuLib databases, which are the most
important collections of real-life elections in computational social
choice.
