Convex preferences

In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, 'averages are better than the extremes'. The concept roughly corresponds to the concept of diminishing marginal utility without requiring utility functions. In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, 'averages are better than the extremes'. The concept roughly corresponds to the concept of diminishing marginal utility without requiring utility functions. Comparable to the greater-than-or-equal-to ordering relation ≥ {displaystyle geq } for real numbers, the notation ⪰ {displaystyle succeq } below can be translated as: 'is at least as good as' (in preference satisfaction). Similarly, ≻ {displaystyle succ } can be translated as 'is strictly better than' (in preference satisfaction), and Similarly, ∼ {displaystyle sim } can be translated as 'is equivalent to' (in preference satisfaction). Use x, y, and z to denote three consumption bundles (combinations of various quantities of various goods). Formally, a preference relation ⪰ {displaystyle succeq } on the consumption set X is called convex if for any and for every θ ∈ [ 0 , 1 ] {displaystyle heta in } :