A simple characterization of single-peaked domains
Mihir Bhattacharya, Anup Pramanik
TLDR
A simple characterization of single-peaked domains on a tree is achieved through the strategy-proofness of extreme rules.
Key contributions
- Characterizes single-peaked domains on a tree structure.
- Utilizes the strategy-proofness of extreme rules for this characterization.
- Demonstrates extreme rules are unanimous and anonymous across any preference domain.
- Proves these rules are strategy-proof exclusively on the associated single-peaked domain.
Why it matters
This work offers a fundamental characterization of single-peaked domains on trees, crucial in social choice theory. By linking them to the strategy-proofness of extreme rules, it provides new insights into mechanism design.
Original Abstract
This paper characterizes the single-peaked domain on a tree via the strategy-proofness of extreme rules defined on that tree. For any tree, these rules are unanimous and anonymous on any preference domain. In particular, we show that they are strategy-proof only on the single-peaked domain associated with that tree.
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