On the Potential and Limitations of Proxy Voting: Delegation with Incomplete Votes

TL;DR

This paper investigates proxy voting when voters must express preferences over a vast number of issues but hold incomplete information for many of them, a setting common in blockchain governance and participatory budgeting. It develops a best-case, fully informed-dRep model where delegation occurs if a voter's revealed preferences sufficiently align with a dRep's advertised ballot, and formalizes the proxy_selection problem with a cap on the number of dReps. Theoretical results reveal a sharp impossibility: for agreement thresholds above $0.5$, the best possible approximation can be linear in the number of voters $n$ when using a single dRep; however, under coherence assumptions or with enough dReps, constant-factor or even optimal outcomes are achievable. Empirical validation on the MovieLens dataset supports the existence of meaningful delegation benefits in realistic incomplete-preference settings and highlights how the number of dReps and the size of revealed sets influence performance, guiding future work toward more realistic information and rationality models for delegation.

Abstract

We study elections where voters are faced with the challenge of expressing preferences over an extreme number of issues under consideration. This is largely motivated by emerging blockchain governance systems, which include voters with different weights and a massive number of community generated proposals. In such scenarios, it is natural to expect that voters will have incomplete preferences, as they may only be able to evaluate or be confident about a very small proportion of the alternatives. As a result, the election outcome may be significantly affected, leading to suboptimal decisions. Our central inquiry revolves around whether delegation of ballots to proxies possessing greater expertise or a more comprehensive understanding of the voters' preferences can lead to outcomes with higher legitimacy and enhanced voters' satisfaction in elections where voters submit incomplete preferences. To explore its aspects, we introduce the following model: potential proxies advertise their ballots over multiple issues, and each voter either delegates to a seemingly attractive proxy or casts a ballot directly. We identify necessary and sufficient conditions that could lead to a socially better outcome by leveraging the participation of proxies. We accompany our theoretical findings with experiments on instances derived from real datasets. Overall, our results enhance the understanding of the power of delegation towards improving election outcomes.

Figures (4)

• Figure 1: The graph illustrates the voters' preferences on the set of revealed proposals in the instance created for the proof of \ref{['2prop:2inapprox-coh']}. Each boxed vertex represents the existence of a voter with the corresponding ballot, with respect to proposals $c_2, c_3, c_4$. If a dRep advertises the ballot of a vertex $v$ in this graph, they will attract all voters whose preferences are within a distance of $1$ from $v$.
• Figure 2: The instance created in the proof of \ref{['thm:delegation-np-hard']}. Light gray cells correspond to preferences that are not revealed to the voters and dark gray cells correspond to preferences that are derived from instance $I$ of mav.
• Figure 3: The fraction of voters that chose to delegate as a function of the total number of dReps.
• Figure 4: The quality of the approximation as a function of the total number of dReps.

Theorems & Definitions (47)

• Definition 1
• Proposition 0
• proof
• Example 1
• Definition 2
• Lemma 1
• proof
• Theorem 1
• proof
• Theorem 2