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DESCRIPTION: In the apportionment problem\, a fixed number of seats must be
  distributed among parties in proportion to the number of voters supporting
  each party. We study a generalization of this setting\, in which voters ca
 st approval ballots over parties\, such that each voter can support multipl
 e parties. This approval-based apportionment setting generalizes traditiona
 l apportionment and is a natural restriction of approval-based multiwinner 
 elections\, where approval ballots range over individual candidates. Using 
 techniques from both apportionment and multiwinner elections\, we identify 
 rules that generalize the D'Hondt apportionment method and that satisfy str
 ong axioms which are generalizations of properties commonly studied in the 
 apportionment literature. In fact\, the rules we discuss provide representa
 tion guarantees that are currently out of reach in the general setting of m
 ultiwinner elections: First\, we demonstrate that extended justified repres
 entation is compatible with committee monotonicity (also known as house mon
 otonicity). Second\, we show that core-stable committees are guaranteed to 
 exist and can be found in polynomial time.   Joint work with Paul Gölz\, Do
 minik Peters\, Ulrike Schmidt-Kraepelin\, and Kai Wilker. 
DTSTAMP:20211117T132000
DTSTART:20211122T141500
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
 es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)\n 
SEQUENCE:0
SUMMARY:Markus Brill (Technische Universität Berlin): Approval-Based Apport
 ionment
UID:107919487@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20211122-L-Brill.html
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