[Paper Review] Proxy Voting for Better Outcomes

Gal Cohensius, Shie Manor+3 more|arXiv (Cornell University)|Nov 24, 2016

Game Theory and Voting Systems20 references20 citations

TL;DR

This paper proposes proxy voting as a mechanism to improve democratic outcomes in large populations with low voter turnout. By allowing inactive voters to delegate their votes to proxied voters based on preference proximity, the system enhances accuracy of median, mean, and majority outcomes—especially when active voter samples are small or biased.

ABSTRACT

We consider a social choice problem where only a small number of people out of a large population are sufficiently available or motivated to vote. A common solution to increase participation is to allow voters use a proxy, that is, transfer their voting rights to another voter. Considering social choice problems on metric spaces, we compare voting with and without the use of proxies to see which mechanism better approximates the optimal outcome, and characterize the regimes in which proxy voting is beneficial. When voters' opinions are located on an interval, both the median mechanism and the mean mechanism are substantially improved by proxy voting. When voters vote on many binary issues, proxy voting is better when the sample of active voters is too small to provide a good outcome. Our theoretical results extend to situations where available voters choose strategically whether to participate. We support our theoretical findings with empirical results showing substantial benefits of proxy voting on simulated and real preference data.

Motivation & Objective

• To analyze whether proxy voting improves social choice outcomes when only a small subset of voters actively participates.
• To evaluate the impact of proxy voting on median, mean, and majority mechanisms in metric spaces.
• To examine how strategic participation and preference proximity affect outcome accuracy under proxy systems.
• To validate theoretical findings using simulated and real-world preference data.
• To explore the conditions under which proxy voting leads to better welfare and representation than direct voting with small samples.

Proposed method

• Model voters' preferences as points in a metric space (interval or {0,1}^k), using ℓρ distance.
• Assume inactive voters delegate to the nearest active voter (proxied by preference similarity), increasing the latter’s effective weight.
• Apply standard social choice mechanisms: median, mean, and majority rules on the weighted set of active voters.
• Use random sampling of active voters to evaluate expected accuracy improvements under proxy voting.
• Conduct empirical validation on synthetic and real preference datasets to measure outcome fidelity to the optimal aggregate.
• Analyze strategic equilibria where voters choose whether to become active, and assess robustness of results.

Experimental results

Research questions

• RQ1 Under what conditions does proxy voting improve the accuracy of median outcomes in one-dimensional preference spaces?
• RQ2 How does proxy voting affect the expected accuracy of mean-based aggregation when active voters are randomly sampled?
• RQ3 In multi-issue binary voting, does proxy voting lead to better outcomes when the active sample is small or when voter disagreement is high?
• RQ4 How do strategic incentives to become an active voter affect the stability and accuracy of proxy-based outcomes?
• RQ5 To what extent do real-world preference patterns support the theoretical benefits of proxy voting?

Key findings

• Proxy voting substantially improves median outcomes on a line, often eliminating distortion from small or unrepresentative active samples.
• For mean-based aggregation on an interval, proxy voting improves expected accuracy when active voters are randomly sampled from the population.
• In multi-issue binary voting, proxy voting leads to a 'dictatorship of the best expert' effect, significantly improving accuracy when the active sample is small or voter disagreement is high.
• Empirical results on real and simulated data confirm strong improvements in outcome accuracy, with benefits persisting even when voter preferences are correlated.
• Theoretical results on proxy voting accuracy extend to settings where voters strategically choose whether to become active or act as proxies.
• Proxy voting reduces expressive loss and improves representation without requiring voters to report their true positions, making it robust to preference misreporting under median and majority rules.