Puzzle Quality Gate Concept

The puzzle process is the moving quality target against which elected orderings are judged. The shorthand used in the project is puzzle.

1. Why the Puzzle Quality Gate Exists

The simulation requires a mechanism that adds decision-quality pressure: decisions should be rewardable or punishable based on alignment with the current puzzle.

Originally, this quality reference was coupled to current grid state. However, this created lock-in states by favoring alignment with start conditions and current majorities, which are not very interesting to study. Now it is separated into its own stochastic process.

The split is meant to avoid fixed directional lock-in in quality pressure, keep quality pressure symmetric over the simplex in expectation, and allow the realized grid state and the quality-pressure mechanism to diverge.

2. Implemented Process

In puzzle mode (quality_target_mode=puzzle), each area has a puzzle distribution over colors.

Update logic per step:

1. If no previous puzzle exists: sample fresh Dirichlet distribution.
2. Otherwise:
3. with probability puzzle_shock_prob, redraw fresh Dirichlet sample
4. else sample local Dirichlet step around previous puzzle with concentration puzzle_local_kappa

Process properties:

• color-symmetric priors (no label favoritism)
• local persistence controlled by puzzle_local_kappa
• occasional jumps controlled by puzzle_shock_prob

3. Quality Gate Mechanics

After election, the elected ordering is compared to:

• puzzle ordering in puzzle mode (puzzle_distance)
• grid ordering in reality mode (dist_to_reality)

Decision sign is binary via threshold break_even_distance_common:

• if distance <= threshold: "good" mode (positive reward sign)
• else: "bad" mode (negative reward sign)

So the puzzle controls the sign regime, not just a descriptive metric.

4. Conceptual Interpretation

Puzzle Quality Gate represents changing external viability pressure that collective decisions need to track to avoid systemic penalties.

This does not make the process an ontological "true reality". It is a modeled quality constraint with controlled stochastic dynamics.

5. Why It Is Useful for This Thesis

The split enables analysis of three distinct forces:

• path-dependent collective self-shaping (grid)
• external quality pressure (Puzzle Quality Gate)
• aggregation structure (voting rule)

That makes it possible to study whether some voting rules better balance self-regarding pressure and quality alignment.

6. Limits and Non-Claims

The Puzzle Quality Gate is a stylized process and not an empirical exogenous data process. It supports internal comparative validity, not external causal claims about real societies.