Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2410.08127 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910644160167936 |
|---|---|
| author | Deng, Xiaotie Tao, Biaoshuai Wang, Ying |
| author_facet | Deng, Xiaotie Tao, Biaoshuai Wang, Ying |
| contents | We study a two-alternative voting game where voters' preferences depend on an unobservable world state and each voter receives a private signal correlated to the true world state. We consider the collective decision when voters can collaborate in a group and have antagonistic preferences -- given the revealed world state, voters will support different alternatives. We identify sharp thresholds for the fraction of the majority-type voters necessary for preference aggregation.
We specifically examine the majority vote mechanism (where each voter has one vote, and the alternative with more votes wins) and pinpoint a critical threshold, denoted as $θ_{\texttt{maj}}$, for the majority-type proportion. When the fraction of majority-type voters surpasses $θ_{\texttt{maj}}$, there is a symmetric strategy for the majority-type that leads to strategic equilibria favoring informed majority decisions. Conversely, when the majority-type proportion falls below $θ_{\texttt{maj}}$, equilibrium does not exist, rendering the aggregation of informed majority decisions impossible.
Additionally, we propose an easy-to-implement mechanism that establishes a lower threshold $θ^\ast$ (with $θ^\ast \leq θ_{\texttt{maj}}$) for both equilibria and informed majority decision aggregation. We demonstrate that $θ^\ast$ is optimal by proving a general impossibility result: if the majority-type proportion is below $θ^\ast$, with mild assumptions, no mechanism can aggregate the preferences, meaning that no equilibrium leads to the informed majority decision for any mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aggregation of Antagonistic Contingent Preferences: When Is It Possible? Deng, Xiaotie Tao, Biaoshuai Wang, Ying Computer Science and Game Theory We study a two-alternative voting game where voters' preferences depend on an unobservable world state and each voter receives a private signal correlated to the true world state. We consider the collective decision when voters can collaborate in a group and have antagonistic preferences -- given the revealed world state, voters will support different alternatives. We identify sharp thresholds for the fraction of the majority-type voters necessary for preference aggregation. We specifically examine the majority vote mechanism (where each voter has one vote, and the alternative with more votes wins) and pinpoint a critical threshold, denoted as $θ_{\texttt{maj}}$, for the majority-type proportion. When the fraction of majority-type voters surpasses $θ_{\texttt{maj}}$, there is a symmetric strategy for the majority-type that leads to strategic equilibria favoring informed majority decisions. Conversely, when the majority-type proportion falls below $θ_{\texttt{maj}}$, equilibrium does not exist, rendering the aggregation of informed majority decisions impossible. Additionally, we propose an easy-to-implement mechanism that establishes a lower threshold $θ^\ast$ (with $θ^\ast \leq θ_{\texttt{maj}}$) for both equilibria and informed majority decision aggregation. We demonstrate that $θ^\ast$ is optimal by proving a general impossibility result: if the majority-type proportion is below $θ^\ast$, with mild assumptions, no mechanism can aggregate the preferences, meaning that no equilibrium leads to the informed majority decision for any mechanism. |
| title | Aggregation of Antagonistic Contingent Preferences: When Is It Possible? |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2410.08127 |