Full Proportional Justified Representation
In multiwinner approval voting, forming a committee that proportionally represents voters' approval ballots is an essential task. The notion of justified representation (JR) demands that any large "cohesive" group of voters should be proportionally "represented". The "c...
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Zusammenfassung: | In multiwinner approval voting, forming a committee that proportionally
represents voters' approval ballots is an essential task. The notion of
justified representation (JR) demands that any large "cohesive" group of voters
should be proportionally "represented". The "cohesiveness" is defined in
different ways; two common ways are the following: (C1) demands that the group
unanimously approves a set of candidates proportional to its size, while (C2)
requires each member to approve at least a fixed fraction of such a set.
Similarly, "representation" have been considered in different ways: (R1) the
coalition's collective utility from the winning set exceeds that of any
proportionally sized alternative, and (R2) for any proportionally sized
alternative, at least one member of the coalition derives less utility from it
than from the winning set.
Three of the four possible combinations have been extensively studied:
(C1)-(R1) defines Proportional Justified Representation (PJR), (C1)-(R2)
defines Extended Justified Representation (EJR), (C2)-(R2) defines Full
Justified Representation (FJR). All three have merits, but also drawbacks. PJR
is the weakest notion, and perhaps not sufficiently demanding; EJR may not be
compatible with perfect representation; and it is open whether a committee
satisfying FJR can be found efficiently.
We study the combination (C2)-(R1), which we call Full Proportional Justified
Representation (FPJR). We investigate FPJR's properties and find that it shares
PJR's advantages over EJR: several proportionality axioms (e.g. priceability,
perfect representation) imply FPJR and PJR but not EJR. We also find that
efficient rules like the greedy Monroe rule and the method of equal shares
satisfy FPJR, matching a key advantage of EJR over FJR. However, the
Proportional Approval Voting (PAV) rule may violate FPJR, so neither of EJR and
FPJR implies the other. |
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DOI: | 10.48550/arxiv.2501.12015 |