Beyond plurality: Truth-bias in binary scoring rules

Svetlana Obraztsova; Omer Lev; Evangelos Markakis; Zinovi Rabinovich; Jeffrey S. Rosenschein

doi:10.1007/978-3-319-23114-3_27

Beyond plurality: Truth-bias in binary scoring rules

Svetlana Obraztsova, Omer Lev^*, Evangelos Markakis, Zinovi Rabinovich, Jeffrey S. Rosenschein

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

It is well known that standard game-theoretic approaches to voting mechanisms lead to a multitude of Nash Equilibria (NE), many of which are counter-intuitive. We focus on truth-biased voters, a model recently proposed to avoid such issues. The model introduces an incentive for voters to be truthful when their vote is not pivotal. This is a powerful refinement, and recent simulations reveal that the surviving equilibria tend to have desirable properties. However, truth-bias has been studied only within the context of plurality, which is an extreme example of k-approval rules with k = 1. We undertake an equilibrium analysis of the complete range of k-approval. Our analysis begins with the veto rule, the other extreme point of k-approval, where each ballot approves all candidates but one. We identify several crucial properties of pure NE for truth-biased veto. These properties show a clear distinction from the setting of truth-biased plurality. We proceed by establishing that deciding on the existence of NE in truth biased veto is an NP-hard problem. We also characterise a tight (in a certain sense) subclass of instances for which the existence of a NE can be decided in poly-time. Finally, we study analogous questions for general k-approval rules.

Original language	American English
Title of host publication	Algorithmic Decision Theory - 4th International Conference, ADT 2015, Proceedings
Editors	Toby Walsh
Publisher	Springer Verlag
Pages	451-468
Number of pages	18
ISBN (Print)	9783319231136
DOIs	https://doi.org/10.1007/978-3-319-23114-3_27
State	Published - 2015
Event	4th International Conference on Algorithmic Decision Theory, ADT 2015 - Lexington, United States Duration: 27 Sep 2015 → 30 Sep 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9346
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Conference on Algorithmic Decision Theory, ADT 2015
Country/Territory	United States
City	Lexington
Period	27/09/15 → 30/09/15

Bibliographical note

Funding Information:
This research was supported in part by Israel Science Foundation grant #1227/12, Israel Ministry of Science and Technology grant #3-6797, and by Microsoft Research through its PhD Scholarship Programme. It has also been supported by the EU (European Social Fund) and Greek national funds through the Operational Program “Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES. The work of S. Obraztsova was partially supported by ERC grant #337122 under the EU FP7/2007–2013 and RFFI grant 14-01-00156-a.

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Access to Document

10.1007/978-3-319-23114-3_27

Cite this

Obraztsova, S., Lev, O., Markakis, E., Rabinovich, Z., & Rosenschein, J. S. (2015). Beyond plurality: Truth-bias in binary scoring rules. In T. Walsh (Ed.), Algorithmic Decision Theory - 4th International Conference, ADT 2015, Proceedings (pp. 451-468). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9346). Springer Verlag. https://doi.org/10.1007/978-3-319-23114-3_27

Obraztsova, Svetlana ; Lev, Omer ; Markakis, Evangelos et al. / Beyond plurality : Truth-bias in binary scoring rules. Algorithmic Decision Theory - 4th International Conference, ADT 2015, Proceedings. editor / Toby Walsh. Springer Verlag, 2015. pp. 451-468 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Beyond plurality: Truth-bias in binary scoring rules",

abstract = "It is well known that standard game-theoretic approaches to voting mechanisms lead to a multitude of Nash Equilibria (NE), many of which are counter-intuitive. We focus on truth-biased voters, a model recently proposed to avoid such issues. The model introduces an incentive for voters to be truthful when their vote is not pivotal. This is a powerful refinement, and recent simulations reveal that the surviving equilibria tend to have desirable properties. However, truth-bias has been studied only within the context of plurality, which is an extreme example of k-approval rules with k = 1. We undertake an equilibrium analysis of the complete range of k-approval. Our analysis begins with the veto rule, the other extreme point of k-approval, where each ballot approves all candidates but one. We identify several crucial properties of pure NE for truth-biased veto. These properties show a clear distinction from the setting of truth-biased plurality. We proceed by establishing that deciding on the existence of NE in truth biased veto is an NP-hard problem. We also characterise a tight (in a certain sense) subclass of instances for which the existence of a NE can be decided in poly-time. Finally, we study analogous questions for general k-approval rules.",

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note = "Funding Information: This research was supported in part by Israel Science Foundation grant #1227/12, Israel Ministry of Science and Technology grant #3-6797, and by Microsoft Research through its PhD Scholarship Programme. It has also been supported by the EU (European Social Fund) and Greek national funds through the Operational Program “Education and Lifelong Learning{"} of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES. The work of S. Obraztsova was partially supported by ERC grant #337122 under the EU FP7/2007–2013 and RFFI grant 14-01-00156-a. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 4th International Conference on Algorithmic Decision Theory, ADT 2015 ; Conference date: 27-09-2015 Through 30-09-2015",

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Obraztsova, S, Lev, O, Markakis, E, Rabinovich, Z & Rosenschein, JS 2015, Beyond plurality: Truth-bias in binary scoring rules. in T Walsh (ed.), Algorithmic Decision Theory - 4th International Conference, ADT 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9346, Springer Verlag, pp. 451-468, 4th International Conference on Algorithmic Decision Theory, ADT 2015, Lexington, United States, 27/09/15. https://doi.org/10.1007/978-3-319-23114-3_27

Beyond plurality: Truth-bias in binary scoring rules. / Obraztsova, Svetlana; Lev, Omer; Markakis, Evangelos et al.
Algorithmic Decision Theory - 4th International Conference, ADT 2015, Proceedings. ed. / Toby Walsh. Springer Verlag, 2015. p. 451-468 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9346).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Rosenschein, Jeffrey S.

N1 - Funding Information: This research was supported in part by Israel Science Foundation grant #1227/12, Israel Ministry of Science and Technology grant #3-6797, and by Microsoft Research through its PhD Scholarship Programme. It has also been supported by the EU (European Social Fund) and Greek national funds through the Operational Program “Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES. The work of S. Obraztsova was partially supported by ERC grant #337122 under the EU FP7/2007–2013 and RFFI grant 14-01-00156-a. Publisher Copyright: © Springer International Publishing Switzerland 2015.

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AB - It is well known that standard game-theoretic approaches to voting mechanisms lead to a multitude of Nash Equilibria (NE), many of which are counter-intuitive. We focus on truth-biased voters, a model recently proposed to avoid such issues. The model introduces an incentive for voters to be truthful when their vote is not pivotal. This is a powerful refinement, and recent simulations reveal that the surviving equilibria tend to have desirable properties. However, truth-bias has been studied only within the context of plurality, which is an extreme example of k-approval rules with k = 1. We undertake an equilibrium analysis of the complete range of k-approval. Our analysis begins with the veto rule, the other extreme point of k-approval, where each ballot approves all candidates but one. We identify several crucial properties of pure NE for truth-biased veto. These properties show a clear distinction from the setting of truth-biased plurality. We proceed by establishing that deciding on the existence of NE in truth biased veto is an NP-hard problem. We also characterise a tight (in a certain sense) subclass of instances for which the existence of a NE can be decided in poly-time. Finally, we study analogous questions for general k-approval rules.

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Obraztsova S, Lev O, Markakis E, Rabinovich Z, Rosenschein JS. Beyond plurality: Truth-bias in binary scoring rules. In Walsh T, editor, Algorithmic Decision Theory - 4th International Conference, ADT 2015, Proceedings. Springer Verlag. 2015. p. 451-468. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-23114-3_27

Beyond plurality: Truth-bias in binary scoring rules

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