since desires are not transitive. therefore, democracy is not transitive. evaluate
ChatGPT said:
Your statement makes a provocative leap:
“Desires are not transitive. Therefore, democracy is not transitive.”
Let’s unpack and evaluate this carefully.
1. Are desires transitive?
In general, desires are not necessarily transitive.
Example:
A person may desire:
- AAA (ice cream) over BBB (cake),
- BBB (cake) over CCC (fruit),
- but still desire CCC (fruit) over AAA (ice cream), maybe due to health reasons or mood — this violates transitivity.
This kind of intransitivity is well-documented in behavioral economics and decision theory, especially in preference cycles and irrational choice behavior.
2. Is democracy transitive?
Now, here’s the key issue: what do you mean by “democracy is transitive”?
In democratic theory, you’re likely referring to social choice — how individual preferences are aggregated into a collective decision (e.g., voting).
Arrow’s Impossibility Theorem comes into play:
It shows that when aggregating individual preferences, it’s impossible to design a voting system that always produces a transitive (i.e., rational) collective preference if:
- there are 3 or more options,
- all individual preferences are considered,
- and certain fairness conditions are met.
So, in this sense:
Even if each individual has transitive desires, the collective democratic outcome can be intransitive.
Example of intransitive majority preference (Condorcet paradox):
- 33% prefer A > B > C
- 33% prefer B > C > A
- 34% prefer C > A > B
Here:
- A is preferred to B (67%),
- B is preferred to C (66%),
- but C is preferred to A (34% + 33% = 67%) → a cycle!
✅ Conclusion:
- Desires can indeed be intransitive.
- Democratic preference aggregation can also be intransitive, not because democracy “inherits” this from individual desires directly, but due to the mathematical properties of group decision-making.
- So, the logic “desires are not transitive → democracy is not transitive” is philosophically suggestive but not logically rigorous. It skips over the formal mechanism (social choice theory) that explains why democracy may produce intransitive outcomes.
Let me know if you want a visual or game-theoretic example.Attach
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