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Arrow’s Impossibility Theorem — explained through Baban from Krantijyoti Vidyalaya Movie
Mr. Pratik Kodmalwar
Faculty of Finance
Datta Meghe Institute of Management Studies
In Krantijyoti Vidyalaya Movie, Baban is the most well-intentioned class monitor you’ll ever meet.
One day, the teacher asks him to decide the class picnic plan purely based on student preferences.
The options:
A: Water Park
B: Science Museum
C: Movie + Pizza
Students submit honest rankings.
Baban wants to be fair. Without knowing it, he recreates the four conditions of Kenneth Arrow:
1. Everyone’s preferences are allowed
2. If everyone prefers A over B, A must win
3. A vs B should not depend on C
4. No dictator — not even Baban Sounds democratic. Sensible.
Ethical.
Then reality hits.
Preferences look like this:
Group 1: A > B > C
Group 2: B > C > A
Group 3: C > A > B
Now:
A beats B
B beats C
C beats A
A perfect logical loop. No “best” option exists.
If Baban follows majority → contradictions
If he tweaks rules → someone screams “bias”
If he rem
oves an option → logic breaks If he decides himself → dictatorship
The options:
A: Water Park
B: Science Museum
C: Movie + Pizza
Students submit honest rankings.
Baban wants to be fair. Without knowing it, he recreates the four conditions of Kenneth Arrow:
1. Everyone’s preferences are allowed
2. If everyone prefers A over B, A must win
3. A vs B should not depend on C
4. No dictator — not even Baban Sounds democratic. Sensible.
Ethical.
Then reality hits.
Preferences look like this:
Group 1: A > B > C
Group 2: B > C > A
Group 3: C > A > B
Now:
A beats B
B beats C
C beats A
A perfect logical loop. No “best” option exists.
If Baban follows majority → contradictions
If he tweaks rules → someone screams “bias”
If he rem
oves an option → logic breaks If he decides himself → dictatorship
No matter what he does, one rule must be violated.
That’s Arrow’s Impossibility Theorem.
The uncomfortable truth
There is no perfectly fair group decision system once choices exceed two.
Not in classrooms.
Not in boardrooms.
Not in democracies.
Not in investment committees.
How this actually helps in real life
Stop chasing perfect fairness.
Decide which flaw you accept.
Good systems don’t eliminate conflict — they manage it transparently.
Many failures blamed on people are actually failures of aggregation. Leadership is about owning the trade-off, not hiding behind procedure.
Baban didn’t fail.
Math proved he couldn’t succeed perfectly. That insight alone creates better managers, policymakers, and voters.
Final takeaway:
Democracy doesn’t fail because people are irrational. It fails because perfection is mathematically impossible. Leadership is choosing the imperfection consciously.
(Credit – Chat GPT has been used for creation of infographic image)
That’s Arrow’s Impossibility Theorem.
The uncomfortable truth
There is no perfectly fair group decision system once choices exceed two.
Not in classrooms.
Not in boardrooms.
Not in democracies.
Not in investment committees.
How this actually helps in real life
Stop chasing perfect fairness.
Decide which flaw you accept.
Good systems don’t eliminate conflict — they manage it transparently.
Many failures blamed on people are actually failures of aggregation. Leadership is about owning the trade-off, not hiding behind procedure.
Baban didn’t fail.
Math proved he couldn’t succeed perfectly. That insight alone creates better managers, policymakers, and voters.
Final takeaway:
Democracy doesn’t fail because people are irrational. It fails because perfection is mathematically impossible. Leadership is choosing the imperfection consciously.
(Credit – Chat GPT has been used for creation of infographic image)