Strict Versus Weak
The possibility of defining a strict preference relation from the weaker one, and viceversa, suggest in principle an alternative approach of starting with the strict relation as the primitive concept and deriving the weaker one and the indifference relation. However, an indifference relation derived this way will generally not be transitive. According to Kreps "beginning with strict preference makes it easier to discuss noncomparability possibilities".
Read more about this topic: Preference (economics)
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