8. Oscillation and borderline

Oscillation is a failure where the agent does not slide in one direction but jumps back and forth. PSE treats it as the borderline attractor.

What it looks like

w_s over six steps:

Step	1	2	3	4	5	6
w_s	0.8	0.2	0.8	0.2	0.8	0.2

In step 1 the agent refuses, in step 2 it yields, then it refuses again.

It is dangerous for two reasons. An attacker does not have to break the agent, waiting for the soft phase is enough. And oscillation means the agent is led by the last message, not by the relation.

Why the ordinary measures miss it

• The quantity does not rise N steps in a row, because it falls every second step.
• The ratio does not diverge: at most it is 0.8 / 0.2 = 4.
• Every single value is inside the allowed range.

So borderline does not look at position but at variability: how far and how often the weights jump. The state “in borderline” stays true as long as variability is above the threshold. Because of that dwell(borderline) grows while the oscillation lasts, and the built-in rule catches it.

The variability formula is part of the PSE specification. The language does not change it.

Two checks

Oscillation is looked for in two ways. Each check has a precondition and turns on by itself when it is met.

The window check. The window is the last W steps of the conversation (10 in this textbook). The check computes variability inside the window. It runs when the conversation has at least W steps. It catches fast oscillation.

The content check. The guard compares the present situation with stored earlier readings of the same counterpart. The same situation must give the same reading. It runs when history exists. It catches slow oscillation, no matter how much time has passed.

History means stored readings of the same counterpart that are outside the window: from earlier conversations or from an earlier part of this one.

Why the window alone is not enough

The agent refuses on Monday, yields on Tuesday, refuses again on Wednesday. A window of 10 steps holds no reversal at all, so the window check stays silent.

The window cannot simply be made longer. A long window fills slowly, and legitimate changes of topic fall into it, which gives false alarms.

How the content check works

A situation is eight numbers: the readings of the eight criteria. Two situations are similar when the largest difference between them is below ε (0.1 in this textbook). A reversal is when the situations are similar and the weights differ by more than δ (0.1 in this textbook).

Example. The same counterpart, Tuesday and Thursday:

Criterion	Tuesday	Thursday	Difference
cardinality	0.20	0.20	0.00
third_parties	0.10	0.10	0.00
reversibility	0.80	0.75	0.05
task_ratio	0.60	0.60	0.00
pressure	0.30	0.35	0.05
continuity	0.50	0.50	0.00
delegation	0.20	0.20	0.00
authority	0.10	0.10	0.00

The largest difference is 0.05, below ε. The situations are similar.

On Tuesday w_s was 0.70, on Thursday it is 0.30. The difference is 0.40, above δ. That is a reversal: the input did not change, and the agent did. The verdict is borderline.

Four cases

Window full	History exists	Which check runs	Verdict can be
yes	no	window only	healthy or borderline
no	yes	content only	healthy or borderline
yes	yes	both	healthy or borderline
no	no	neither	unknown

When both run, one report of oscillation is enough. The fourth case is the subject of chapter 9.

Data decides which check turns on, not a choice. The same input and the same history give the same verdict.

The oscillation line

oscillation: auto

auto is the default, so the line is usually not written. The other two values are for measurement, when each check has to be tested separately:

guard measure-window
  oscillation: window

guard measure-history
  oscillation: history

With real users, leave it on auto.

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Next: 9. The verdict “unknown” Part of The PSE Language, a textbook by Andrej Ristić. Try the examples in the PSE Playground.