Modeling Democratic Innovations: The Case of Transitive Delegations

Abstract:
Proposals to change ballot types, channel decisions through citizens' assemblies, or participatory budgeting are being researched and tested in the real world. Liquid democracy, a transitive proxy voting system, is making its way to the democratic innovation table as it may stand for non-active stakeholders and enhance collective intelligence using the wealth of interpersonal information embedded in social networks. Herein, we study the propensity of liquid democracy to track the truth: we model votes on a binary issue for which there is a ground truth and examine stochastic delegation behaviors that guarantee that the liquid vote finds the correct answer with a probability approaching 1. Technically, we demonstrate that transitive delegations dynamics compare to well-known random graphs processes that are sufficiently bounded for our purposes. We confront our models to practice, running twelve liquid democracy experiments with various organizations; the experimental results largely support our theoretical predictions. In all, we identify theoretically and empirically regimes of interest where liquid democracy is an effective alternative to existing voting schemes, bolstering the case for this emerging paradigm.

This is based on joint work with Adam Berinsky, Daniel Halpern, Joe Halpern, Ali Jadbabaie, Elchanan Mossel and Ariel Procaccia

Bio:

Manon Revel is a Ph.D. student at MIT in the Institute for Data, Systems, and Society and a Doctoral Fellow at the Harvard Kennedy School’s Ash Center for Democratic Governance and Innovation. She studies new voting systems to improve fairness, legitimacy, and efficiency in collective decision-making. In particular, she investigates the potential and limitations of liquid democracy, a delegative voting scheme, in transforming representation in democracy. Manon models various voting schemes to derive theoretical insights on those and further works on experimenting with the new voting paradigms, confronting and enriching mathematical results with real-world observations. Following an early passion for journalism, Manon also worked on misinformation, studying the credibility crisis of traditional media as news migrated to the web.

Summary:

Goal: fix democracy
- Focus is on the process of selecting representatives of our interests in government
- Not on how to keep them accountable once they’ve been selected
Challenges:
- Lack of confidence in our democratic institutions (e.g. Congress and Supreme Court)
- Lack of representation by various groups
US localities are exploring alternatives to the current selection model
- Rank choice voting on ballot in Nevada,
- Rank choice and approval voting on ballot in Seattle
Other ideas being evaluated:
- Sortition: draw citizens at random to be representatives
- Delegation: choose other citizens to whom to delegate decisions (FOCUS OF THIS TALK)
Focus is on quality of the outcome of decisions
Model:
- N agents vote on 0 or 1
- Ground truth is 1
- Each person i votes correctly with probability pi (their expertise level)
Algorithms:
- Enlightened dictatorship: choose person with highest pi and have them vote
- Majority vote:
  - If most of the population has pi > .5 then majority’s average vote is better than expert (votes are uncorrelated, so we’re diversifying away their wrongness)
  - Otherwise, it is worse
- How can we protect us from bad decisions when population is not well informed?
Approach: Liquid democracy
- Assume social network
- People can choose to vote or delegate to someone in their network, who can also delegate to others
- Take weighted average of votes of delegates (weighted by the number of people who delegated to them)
- Edge case: everyone delegates to the expert, which is not as good as the average of many informed voters
- Average delegation works if (sufficient, not necessary):
  - As population grows the number of root delegates increases (not constant)
  - Average expertise of delegates increases post-delegation by a constant
- Work most applicable to denser social networks, less useful right now for whole countries
Delegation models:
- Random:
  - People know the expertise of others
  - People randomly choose their social network neighbors, with probability that depends on their expertise and their neighbors expertise
- Variants:
  - Upward delegation:
    - Delegate with constant probability
    - Choose someone with higher expertise
  - Confidence based: Delegate with probability that decreases with expertise
  - General continuous:
    - Delegate with constant probability
    - Delegate more often to more competent voters (probability increases monotonically with expertise of delegation recipient)
Experiments:
- Qualtrics survey where people are asked questions and can answer and/or delegate
- This makes it possible to compare the direct vote and the delegation model
- Outcomes: Liquid democracy improves accuracy across most tasks (4% on average, upto 12%)
- Observation: the more expert someone is, the less they delegate and vice versa
Application areas:
- Democracy: improve diversity and reduce barrier to entrance for representatives
- Corporate governance: Accountability of direct links, endogenous selection of experts
- Prediction markets: Exploit information wealth