Unformatted text preview: b are preferable to d ). Convexity is meant to capture related intuitions that rely on the existence of “geography” in the sense that we can talk about an alternative being between two other alternatives. The convexity assumption is appropriate for a situation in which the argument “if a move from d to b is an improvement then so is a move part of the way to c ” is legitimate, while the argument “if a move from b to d is harmful then so is a move part of the way to c ” is not. ±ollowing are two formalizations of these two intuitions (Fg. 4.2). We will see that they are equivalent. Convexity 1: The preference relation % satisFes convexity 1 if x % y and α ∈ ( 0, 1 ) implies that α x + ( 1 − α) y % y . This captures the intuition that if x is preferred to y , then “going a part of the way from y to x ” is also an improvement....
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- Fall '10
- 43 M, relation satisﬁes convexity