Decision Rules
A decision rule is an if-then statement: if debt ratio is above 50% and missed payments exceed one, route the application to manual review. Rules are compact enough to implement in a workflow, discuss with domain experts, or place directly into a policy document.
A decision list applies rules in order and stops at the first match. A decision set allows several rules to match the same case. Lists resolve conflicts through order; sets need an explicit conflict strategy.
Decision List vs. Decision Set
A decision list stops at the first matching rule. A decision set checks every rule and needs a conflict strategy when more than one fires. Select an applicant, then trace what each approach does.
Select applicant
Ama
Rules
Step through the list
Two numbers matter together:
- Coverage or support: the share of cases where the rule applies.
- Precision: among matched cases, the share with the predicted outcome.
A perfect rule that applies to two people may be less useful than a 90% accurate rule that covers half the population. The right balance depends on what happens after the rule fires.
Coverage Versus Precision
A lender needs a short rule for routing applications to human review. Compare a broad rule with a narrow one and watch what each rule catches and misses.
Matched cases
4 / 8
Coverage
50%
Precision
75%
#1
D 18%
M 0
paid
#2
D 48%
M 2
default
#3
D 54%
M 0
default
#4
D 31%
M 3
default
#5
D 42%
M 1
paid
#6
D 39%
M 0
paid
#7
D 62%
M 2
default
#8
D 27%
M 0
paid
Domain shapes the format
Financial services often favors ordered rules because staff can apply them consistently and document which condition triggered an action. A clinical team may prefer a small tree when the order of questions mirrors an existing diagnostic process.
Plan for overlap and silence
What happens when three rules match? What happens when none match? A deployed rule system needs conflict resolution and a default action. Leaving those cases implicit creates unpredictable policy.
Algorithms for learning rules
- OneR — builds a classifier from a single feature; maximum simplicity.
- Sequential Covering — learns rules one at a time, removing covered examples after each.
- RIPPER — Sequential Covering with aggressive pruning to reduce overfitting.
- SLIPPER — boosted variant of RIPPER; combines weak rule learners.
- CN2 — Sequential Covering using a beam search to find high-quality rules.
- Bayesian Rule Lists — selects an ordered list from pre-mined rules using a Bayesian prior over list length and rule complexity.
- RuleFit — generates rules from a tree ensemble, then fits a sparse linear model over those rules and the original features.
OneR
OneR is the simplest rule-learning algorithm: it builds a classifier from a single feature. For each feature, it generates rules by reading off the most frequent class at each value. It then picks the one feature whose rules produce the lowest total error across the training set.
The algorithm runs in five steps:
- Discretize continuous features into intervals.
- Build a cross-table counting how often each feature value coincides with each class.
- For each feature value, write a rule predicting the majority class in that cell.
- Sum the errors across all rules for that feature.
- Select the feature with the smallest total error.
The result is a decision list with one condition per rule. OneR is interpretable by construction — a single feature drives every decision — but that same constraint limits accuracy when the outcome depends on combinations of features.
OneR in a screening context
A hospital triage tool that routes patients by a single vital sign is following OneR's logic. Staff can apply it instantly without a chart, and the rule can be audited against any dataset. The cost is that patients with an unusual combination of normal vitals and high risk may be misclassified.
OneR Algorithm Walkthrough
OneR picks the single best feature and turns each of its value ranges into a rule. Step through the algorithm to see how it scores and selects that feature.
Step 1 of 5
Discretize features
Feature
Continuous features are split into discrete bins. The split points come from the data distribution and domain knowledge — finer bins allow more expressive rules but risk overfitting.
Credit score < 580
9 instances
Credit score 580–669
8 instances
Credit score 670–739
8 instances
Credit score ≥ 740
10 instances
Sequential Covering
Sequential Covering is a general procedure for building a decision list one rule at a time. Rather than learning all rules simultaneously, it peels off a layer of the data with each iteration:
- Start with an empty rule list.
- Learn the best rule on the current dataset.
- Add that rule to the list and remove all data points it covers.
- Repeat on the remaining data until no rule meets a quality threshold or all positive examples have been covered.
- Return the decision list.
Each rule is learned on a different subset, so later rules can focus on patterns that earlier rules missed. The final list is applied in order — the first matching rule fires. RIPPER and CN2 are concrete algorithms built on this procedure, differing mainly in how they measure rule quality and prune overfitting.
Order matters downstream
Because each rule is trained on whatever data the previous rules left behind, the list is order-dependent. Swapping two rules can change predictions even if both rules look correct in isolation. Document the training order alongside the rules themselves.
Sequential Covering Walkthrough
Sequential Covering learns rules one at a time. After each rule is found, the instances it covers are removed so the next rule can focus on what remains.
Start: full dataset
We have two classes mixed in feature space. Sequential Covering will learn one rule at a time, peeling off the data it explains.
Rule list so far
Rule A is 100% precise and covers 2% of cases. Rule B is 88% precise and covers 60%. Which is better?
Design a default action for a loan-review rule set when no rule matches. What risk does your default create?