Population paradox
Vote-ratio, weight-ratio, or population-ratio monotonicity is a property of some apportionment methods. It says that if the entitlement for A {\\displaystyle A} grows at a faster rate than B {\\displaystyle B} (i.e.
Metadata
- Slug: 00358-population-paradox
- Type: PARADOX
- Tags: paradox
- Sources: 1
Axioms
- Assume the rules of the domain apply uniformly.
- Assume the observer’s criteria remain fixed.
- Assume classification boundaries stay consistent.
- Assume the model describes the real case.
- Assume repeated steps do not change the outcome.
- Assume no hidden variables are introduced midstream.
Contradictions
- Two reasonable lines of inference yield opposite conclusions
- A global rule conflicts with a local judgment
- A stable resolution appears to violate a starting premise
- Changing the framing reverses the outcome
- Intuition and formalism diverge at the same step
Prompts
- Which assumption is doing the most hidden work?
- What changes if you relax the smallest constraint?
- Does the paradox dissolve or relocate when reframed?
- What is conserved, and what is sacrificed?
Notes
Sources
Overview
Vote-ratio, weight-ratio, or population-ratio monotonicity is a property of some apportionment methods. It says that if the entitlement for A {\displaystyle A} grows at a faster rate than B {\displaystyle B} (i.e.
Tension
- Two reasonable lines of inference yield opposite conclusions.
- A global rule conflicts with a local judgment.
- A stable resolution appears to violate a starting premise.
- Changing the framing reverses the outcome.
- Intuition and formalism diverge at the same step.
Why It Matters
This entry tests how a stable rule-set can yield unstable conclusions under certain assumptions.
Prompts
- Which assumption is doing the most hidden work?
- What changes if you relax the smallest constraint?
- Does the paradox dissolve or relocate when reframed?
- What is conserved, and what is sacrificed?