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Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?

$\succsim$ is a weak order over $\mathbb R^L$. For a closed budget set $B\subset\mathbb R^L$, define demand correspondence: $$D(B)=\{x\in B|x\succsim y\forall y\in B\}$$. We know that $D$ is always ...
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0answers
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Does Pascal's Wager fail archimedean property?

I assume most people have heard of Pascal's Wager, in case you have not: https://en.wikipedia.org/wiki/Pascal%27s_Wager By the Stanford encyclopedia of philosphy: "We have a decision under risk,...
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5answers
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Violation of completeness axiom (simple everyday examples)

Simple everyday examples of violations of transitivity are not difficult to come up with, but I'm having trouble thinking of some for the completeness axiom. One possible formulation of the ...