  Elections are the central institution of democratic processes, and often the
elected body -- in either public or private governance -- is a committee of
individuals. To ensure the legitimacy of elected bodies, the electoral
processes should guarantee that diverse groups are represented, in particular
members of groups that are marginalized due to gender, ethnicity, or other
socially salient attributes. To address this challenge of representation, we
have designed a novel participatory electoral process coined the Representation
Pact, implemented with the support of a computational system. That process
explicitly enables voters to flexibly decide on representation criteria in a
first round, and then lets them vote for candidates in a second round. After
the two rounds, a counting method is applied, which selects the committee of
candidates that maximizes the number of votes received in the second round,
conditioned on satisfying the criteria provided in the first round. With the
help of a detailed use case that applied this process in a primary election of
96 representatives in Switzerland, we explain how this method contributes to
fairness in political elections by achieving a better "descriptive
representation". Further, based on this use case, we identify lessons learnt
that are applicable to participatory computational systems used in societal or
political contexts. Good practices are identified and presented.
