I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30).
However, as the choice $x(p',w')$ is only feasible under the price-income level $(p',w')$ and $x(p'',w'')$ is only feasible under $(p'',w'')$ in Figure 2.F.1(b), why does it still satisfy the WARP definition which requires that a choice (say, $x(p',w')$) should be feasible under two different price-income levels (say, $(p',w')$ and $(p'',w'')$)?
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Intuitively, this just says that if the bundle you choose was possible under wealth $w$ and price $p$ but it is not $x(p, w)$, then it must be that you cannot obtain it when price is $p'$ and wealth is $w'$.
It simply does not say anything about case (b) in which $p' \cdot x(p'', w'') > w$ and $p'' \cdot x(p', w') > w''$. Since the first part of the if ... then statement in the definition is false, everything evaluates to true.
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$\begingroup$ Thanks for the answer, and I can get the intuition of what WARP says. Just to clarify, by "Since the first part of the if ... then statement in the definition is false, everything evaluates to true.", do you mean Definition 2.F.1 of MWG is incorrect? $\endgroup$– YunNov 7, 2019 at 13:22
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$\begingroup$ The definition is correct. Let's say the definition is "a demand function satisfies WARP if ($x$ and $y$ then $z$)". I was just saying that figure (b) also fits into the definition since $x$ (in figure (b)) is false, so the hole thing evaluates to true. $\endgroup$– ArtNov 8, 2019 at 1:36