Safe Voting: Resilience to Abstention and Sybils

TL;DR

This work develops a Reality-aware Social Choice framework that anchors decisions to a verifiable status quo and introduces the status-quo Enforcing (SQE) mechanism to resist sybil votes and abstention. By coupling SQE with a base rule (e.g., Majority or Median) and a tunable parameter $\tau$, the authors derive explicit safety and liveness conditions across binary, multiple-alternative, and single-peaked domains, including lower bounds showing limits of what can be achieved. They generalize the notions of safety to approximate safety via a betweenness-based safety set, quantify robustness to small perturbations (outcome range), and study random participation and delegation models that improve guarantees. The results yield practical guidelines for designing sybil- and abstention-resilient governance mechanisms in online communities, with extensions to multiple referenda and other domains, and discuss estimation of the sybil fraction for real-world deployment.

Abstract

Voting rules may implement the will of the society when all eligible voters vote, and only them. However, they may fail to do so when sybil (fake or duplicate) votes are present and when only some honest (non sybil) voters actively participate. As, unfortunately, sometimes this is the case, our aim here is to address social choice in the presence of sybils and voter abstention. % To do so, we build upon the framework of Reality-aware Social Choice: we assume the status quo as an ever-present distinguished alternative, and study \emph{status quo Enforcing (QUE) voting rules}, which add virtual votes in support of the status quo. We characterize the tradeoff between \emph{safety} and \emph{liveness} (the ability of active honest voters to maintain/change the status quo, respectively) in several domains, and show that the voting rules are often optimal. \revision{Our characterization identifies the exact conditions under which mechanisms remain both resilient to sybils and responsive to verified participation, offering a quantitative tool for designers to measure the benefit of increased participation and verified identities.

Figures (12)

• Figure 1: Example of a voting setting with two alternatives $A=\{r,p\}$. There are $|V|=9$ voters overall, of which $|S|=2$ are sybils, and $|H^-|=4$ are inactive. Therefore $s=\frac{2}{9}$ and $h=\frac{7}{9}$. Similarly, $h_p = \frac{|H_p|}{|V|}=\frac{4}{9}$ as there are 4 honest voters for $p$. We keep using full/hollow blue circles for active / inactive voters and red squares for sybils throughout the paper.
• Figure 2: Two instances from the previous examples, where Majority is unsafe with respect to itself but adding virtual voters (gray diamonds) restores safety with respect to Majority.
• Figure 3: In this figure (solid lines) the fraction of sybils is fixed at $\sigma=0.1$, i.e. 10% sybils. For every value of abstention $\mu$, we color in blue the range of $\tau-\textit{SQ-MJ}$ mechanisms that are safe. The range of live mechanisms is in red. The dotted lines mark the ranges when there are 20% sybils rather than 10%. Recall that $\tau$ denotes the fraction of virtual votes added for the status quo $r$, $\sigma$ is the fraction of sybils, and $\mu$ is the fraction of inactive honest voters.
• Figure 4: We consider two instances with five active votes. On the left there is an instance where any $\tau-\textit{SQ-PL}$ mechanism with less than $3=0.6\cdot|V^+|$ virtual votes violates safety, since $p'$ is selected. On the right there is another instance where at least $3$ virtual voters mean violation of liveness since $r$ is selected regardless of how honest voters vote.
• Figure 5: An example of seven voters on a tree. $x$ is the tree median, so by definition it is preferred by a majority of voters to any other point. In particular, the four voters to the top-left prefer $x$ over $z$, and therefore must also prefer $y$ over $z$.

Theorems & Definitions (61)

• Example 1: Sybils
• Definition 1: Safety, two alternatives, full participation
• Definition 2: Liveness, full participation
• Example 2: Abstention
• Definition 3: Safety and Liveness under Partial Participation
• Definition 4: Supermajority rule
• Definition 5: status quo–Enforcing mechanism
• proof
• Example 3: status quo Enforcing Majority
• Theorem 2