Parameterized Voter Relevance in Facility Location Games with Tree-Shaped Invitation Graphs

TL;DR

A series of anonymity properties applicable to the diffusion mechanism design model, as well as parameterized voter-relevance properties for guaranteeing reasonably-fair decision making are defined.

Abstract

Diffusion mechanism design, which investigate how to incentivise agents to invite as many colleagues to a multi-agent decision making as possible, is a new research paradigm at the intersection between microeconomics and computer science. In this paper we extend traditional facility location games into the model of diffusion mechanism design. Our objective is to completely understand to what extent of anonymity/voter-relevance we can achieve, along with strategy-proofness and Pareto efficiency when voters strategically invite collegues. We define a series of anonymity properties applicable to the diffusion mechanism design model, as well as parameterized voter-relevance properties for guaranteeing reasonably-fair decision making. We obtained two impossibility theorems and two existence theorems, which partially answer the question we have raised in the beginning of the paper

Figures (2)

• Figure 1: An example showing that AN-S is incompatible with combination of SP and PE, explained in the proof of Theorem \ref{['thm:imp:ANS-R0']}. The right diagram indicates the social network among three voters. The left top diagram shows the case where voter $i$ never invites any child, and the left bottom shows the case where $i$ invites both children $u$ and $v$. The outcome monotonically gets closer to $i$'s peak $p_{i}$.
• Figure 2: An example showing that SP-D holds in our proposed weighted median method, explained in the proof of Theorem \ref{['thm:p:ANSD-R2']}. The right diagram indicates the social network among the four voters. The left top diagram shows the case where voter $i$ never invites any child, the left middle shows the case where $i$ only invites a child $u$, and the left bottom shows the case where $i$ invites both children $u$ and $v$. The outcome monotonically gets closer to $i$'s peak $p_{i}$, which intuitively implies SP-D.

Theorems & Definitions (21)

• definition 1: Single-Peaked Preferences
• definition 2: Social Choice Function (SCF)
• definition 3: Strategy-Proofness
• definition 4: Ontoness
• definition 5: Anonymity
• definition 6: Generalized Median Voter Schemes (GMVS) moulin:PC:1980
• theorem 1: Moulin moulin:PC:1980
• definition 7: Strategy-Proofness over Networks (SP) li:AAAI:2017
• definition 8: Strategy-Proofness over Networks on Information Diffusion (SP-D)
• definition 9