A Gaussian landscape
Each smooth component marks a useful region. A proposal’s performance is the strongest component at that location, not their sum.
Where good solutions lie
An interactive research companion
Tomorrow’s standard. Today’s authority.
Whose proposal do we follow: the person with the strongest record, or the person closest to what we expect will count as success? Explore how those two grounds for deference work together.
A constructed example: 3 actors, 2 choices. The main study uses 10 actors and 5 dimensions.
Figure 1 · A constructed landscape
A proposal is a place. Height is performance.
Each point combines two choices in a proposal. Higher ground means better task performance. The anticipated standard is a separate location: being close to it does not necessarily mean being close to the best solution.
Time symmetry concerns whether past performance and anticipated evaluation both inform influence. Access symmetry concerns whether actors have equal say in setting that evaluation. A group can combine time-symmetric authority with unequal standard-setting access.
Preparing the landscape…
ABCAnticipated standardInfluence centerPreferred standards
What to notice
A is nearer the tallest region. C is nearest the standard. A proposal’s current performance, its best past performance, and its fit to the standard are different quantities.
See the actors’ valuesCurrent proposals, past records, and distance to the standard
| Actor | Current proposal | Current performance | Best past performance | Squared distance to standard | Influence |
|---|
Past records refer to earlier discoveries. They need not equal performance at the actor’s current position.
Go one step further
Watch the actors search.
The figures above reweight fixed proposals. This optional animation moves them: each actor combines momentum, its own best discovery, the group’s best discovery, and the influence center.
A seeded teaching run on this 2D landscape. It does not reproduce the manuscript’s reported experiments.
0roundsBest performance found0.900
Same seed, same starting controls, same run.
Ready · seed 20261013
Optional: repeat the teaching comparison
Compare past-only and time-symmetric authority for 100 paired runs of 50 rounds, using your current β, k, and standard. Across these teaching runs, only the random movement draws change; the landscape, cue, initial proposals, and retained records stay fixed. This differs from the manuscript’s experiments across independently generated landscapes.
Outcome: best discovered performance after 50 rounds. Difference: past + future fit minus past record. The approximate 95% Student-t interval describes Monte Carlo uncertainty in this fixed teaching setup. It is not a finding about organizations. Export the current state to retain all paired results.
A guide to the model
Four parts. Different jobs.
“Gaussian,” “agent-based,” and “particle swarm” describe different parts of the same model.
An agent-based model
Distinct actors hold proposals and performance records. The authority rule determines how much each actor’s proposal counts.
Whose knowledge is followed
Particle-swarm search
Actors move using their own experience, shared discoveries, and influence. These pulls guide exploration of the landscape.
How proposals change
Monte Carlo repetition
The study repeats conditions across independently generated landscapes, pairing the same starting conditions and random draws within each comparison.
How outcomes are compared
How is this different from an NK model?
An NK model represents combinations of discrete choices and controls how their contributions depend on each other. TSA’s landscape is continuous and built from Gaussian components. Both can contain multiple useful regions, but they are different constructions. More Gaussian components need not mean the same number of distinct peaks.
What does the authority rule calculate?
Each actor receives a score for its best past performance. Time-symmetric authority also subtracts a penalty for squared distance between its current proposal and the anticipated standard. A softmax converts these scores into positive influence shares that sum to one.
influence ∝ exp(β × best past performance − k × distance²)
Past-only authority sets the second term to zero. The word “symmetric” means both past and anticipated evaluation can ground present deference; their weights need not be equal. This does not imply physical time reversibility.
What this companion can—and cannot—show
The three presets reproduce the manuscript’s constructed explanatory examples. Moving a slider shows a consequence of the specified rule, not evidence that people behave this way. The optional animation keeps all three actors active, uses a fixed cue and landscape, and omits credibility updating, participation, and strategic lobbying. In the research, those mechanisms have separate specifications and comparisons.
The research
Time-Symmetric Authority
Anticipated evaluation, power, and collective search
Magnus van Haaren and Daan A. Stam