#### Corrigendum
#### by the Editors, Berlin, July 27, 2018


In the first issue (Issue #1) of “The Liquid Democracy Journal on electronic participation, collective moderation, and voting systems”, in the article “The Evolution of Proportional Representation” [Evolution] it was wrongly claimed that the Harmonic Weighting algorithm would allow

»any group of size P · M / (1+N) to place M initiatives of a set S amongst the first N positions, if all members of the group support all initiatives in that set (S), and no member of the group supports an initiative outside the set which gains a display position amongst the first N positions.«

[Evolution, p.35]

For the proof, the article references to the book “The Principles of LiquidFeedback” [PLF]. In this book, a proof is given in the footnote on page 78. This proof, however, only proves a weaker statement covering

»those cases where parts of the minority support initiatives that are not supported by all members of the minority (i.e. initiatives that are not in S), as long as those other initiatives which are supported by parts of the minority do not gain a better display position than [any of] the best-ranked M initiatives of S.«

[PLF, p.78] [Errata]

Furthermore, [Aziz, Example 2] shows that the stronger statement wrongly used in our article “The Evolution of Proportional Representation” is indeed violated by Harmonic Weighting. We therefore must correct the statement in that article. Instead of

»no member of the group supports an initiative outside the set which gains a display position amongst the first N positions«

read

»no member of the group supports an initiative outside the set which gains a better display position than any of the best-ranked M initiatives of S«

and skip the rest of the paragraph.


The claim in our book “The Principles of LiquidFeedback” (with the existing [Errata]) is correct.


We would like to thank Markus Brill from the Technische Universität Berlin for his help and for kindly referring us to the counter-example (Example 2 in [Aziz]).


References:
[Aziz] Haris Azis: “A Note on Justified Representation Under the Reverse Sequential PAV rule”, working paper, 2017. Retrieved on 2018-02-18 from: http://www.cse.unsw.edu.au/~haziz/invseqpav.pdf
[Errata] “Errata as of 2016-12-22” for ‘The Principles of LiquidFeedback’. Available at: http://principles.liquidfeedback.org/errata/
[Evolution] Jan Behrens: “The Evolution of Proportional Representation in LiquidFeedback”. In “The Liquid Democracy Journal on electronic participation, collective moderation, and voting systems”, Issue 1, March 20, 2014, pp. 32-41. ISSN 2198-9532. Published by Interaktive Demokratie e. V., available at http://www.liquid-democracy-journal.org/issue/1/The_Liquid_Democracy_Journal-Issue001-04-The_evolution_of_proportional_representation_in_LiquidFeedback.html
[PLF] Behrens, Kistner, Nitsche, Swierczek: “The Principles of LiquidFeedback”. ISBN 978-3-00-044795-2. Published January 2014 by Interaktive Demokratie e. V., available at http://principles.liquidfeedback.org/


=============================================================================
This file is part of:

The Liquid Democracy Journal
on electronic participation, collective moderation, and voting systems
Issue 6, Berlin 2018-07-27 (electronic version 2019-02-23, rev2 2019-02-24)

The full issue is available at: http://www.liquid-democracy-journal.org/issue/6/

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Copyright © 2018, 2019 Interaktive Demokratie e. V., Berlin, Germany
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Published by: Interaktive Demokratie e. V., Berlin, Germany
Edited by: Jan Behrens, Axel Kistner, Andreas Nitsche, Björn Swierczek

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ISSN-L: 2198-9532
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