Citation#

Candellone, Elena. “Disentangling conviction and conformity: a Bayesian ideal point model of voting behaviour in online debates.” arXiv preprint arXiv:2606.03786 (2026).

Disentangling Conviction and Conformity (Candellone, 2026)#

This note was prepared with assistance from OpenAI Codex.

One-Sentence Summary#

This paper analyzes voting behavior on Debate.org and asks whether users vote primarily based on:

1. Their prior beliefs (Conviction), or
2. The votes previously cast by people with similar beliefs (Conformity).

The author proposes an interpretable Bayesian logistic model to quantify the relative contribution of both mechanisms.

Research Question#

When a user votes PRO or CON in an online debate:

• Are they expressing an existing belief?
• Or are they aligning with people who think like them?

The paper attempts to disentangle these two mechanisms.

Dataset#

• 78,376 debates
• ~340k votes
• 46k+ voters

Users can explicitly report their positions on 48 political and social issues.

Core Idea#

Map both users and debates into a common 48-dimensional belief space.

User Vector#

Each user i is represented as

$$ u_i \in {-1,0,+1}^{48} $$

where each dimension corresponds to one issue.

Example:

giving

$$ u_i=(+1,-1,+1,0,\cdots) $$

Representation Choice#

This is not a learned embedding, semantic representation, or latent ideological space.

Instead, it uses a transparent 48-dimensional issue profile that stays closely tied to users’ self-reported positions.

Debate Vector#

GPT-4o-mini is used to infer:

1. Which of the 48 topics the debate belongs to.
2. Whether the debate stance is PRO or CON.

Example:

Topic = Drug Legalization

Stance = PRO

$$ d_j=(0,0,\cdots,+1,\cdots,0) $$

The debate vector is always one-hot.

Debates Outside the 48 Topics#

If GPT cannot map a debate to one of the predefined topics, it is classified as Other.

Approximately 50% of debates fall into this category.

These debates are set aside from the topic-based analysis.

Conviction Score (tau)#

Definition:

$$ \tau_{ij} = \frac{u_{i,t_j}d_{j,t_j}} {|u_i|} $$

Interpretation:

Measures how strongly a user’s prior belief aligns with the debate position.

Practical meaning:

What was this user’s prior position on this specific issue?

Conformity Score (phi)#

Definition:

$$ \phi_{ij} = \frac1{|V_{j,i}|} \sum_{k\in V_{j,i}} \cos(u_i,u_k)\,y_{kj} $$

where:

$$ V_{j,i} $$

is the set of users who voted before user i in the same debate.

Similarity:

$$ \cos(u_i,u_k) $$

Vote encoding:

• PRO = +1
• CON = -1

Interpretation:

Which side was preferred by people with belief profiles similar to mine?

Interpretive Note#

The paper interprets phi as conformity.

At the same time, the model does not directly observe:

• whether users actually saw previous votes
• whether users paid attention to them
• whether users were influenced by them

So phi can also be read as capturing:

• peer agreement
• local consensus
• belief-space exposure
• social alignment

In that sense, conformity is a plausible interpretation, though not the only one.

Statistical Model#

$$ P(y_{ij}=PRO) = \sigma( \alpha_i + \delta_j + \beta_\tau\tau_{ij} + \beta_\phi\phi_{ij} ) $$

User Effect (alpha)#

$$ \alpha_i $$

captures a user’s general voting tendency.

Examples:

• habitually voting PRO
• habitually voting CON

Debate Effect (delta)#

$$ \delta_j $$

captures baseline characteristics of a debate.

Examples:

• debates almost everyone supports
• debates almost everyone rejects

Overall Interpretation#

The model effectively decomposes voting behavior into:

Vote

= User tendency

• Debate tendency

• My prior belief

• Belief-neighborhood behavior

Main Findings#

Conviction-Only Topics#

• Drug Legalization
• Legalized Prostitution
• Affirmative Action

Voting is primarily explained by prior beliefs.

Conformity-Driven Topics#

• Abortion
• Gun Rights
• Capitalism

Votes of similar prior voters are more predictive than individual prior beliefs.

Conformity-Only Topics#

• Barack Obama
• Global Warming Exists
• Welfare
• Civil Unions

Peer agreement dominates.

Jointly-Driven Topics#

• Gay Marriage
• Euthanasia
• Minimum Wage
• National Health Care
• Socialism

Both prior beliefs and peer agreement are strong predictors.

Strengths#

1. Incorporates Temporal Ordering#

Only previous votes are used.

No information leakage from future votes.

2. Places Users and Debates in the Same Space#

User beliefs and debate content become directly comparable.

3. Defines Peers Through Belief Similarity#

The model uses belief similarity rather than friendship networks.

This can be interpreted as a belief-space social exposure model.

Interpretive Considerations#

1. The belief dimensions are treated separately#

The 48 dimensions are treated as independent.

Examples:

• Abortion ↔ Gay Marriage
• Gun Rights ↔ Death Penalty

This keeps the model simple and interpretable, though it does not explicitly model relationships between topics.

2. Many debates fall outside the predefined topic set#

Approximately 50% of debates cannot be mapped to the predefined topic space.

Those cases therefore remain outside the main analysis.

3. tau and phi may partially overlap#

Both variables are derived from the same belief vectors.

So some correlation between them is possible.

The paper explicitly interprets results as conditional associations rather than causal effects.

4. Conformity is inferred rather than directly observed#

Phi measures:

How did similar people vote?

rather than

Did I observe and imitate those people?

It may therefore be safest to read phi as a proxy for belief-neighborhood voting patterns.

Perspective from Belief Embeddings#

Compared with more recent belief embedding approaches, this paper uses a discrete 48-dimensional belief profile rather than a continuous semantic space.

The model can therefore be interpreted as:

$$ P(vote) = f( my\ position, neighborhood\ position ) $$

inside a manually constructed belief space.

One useful way to frame the model is:

Individual Position + Neighborhood Position