<ul>
<li><a href="/en/Definition%20of%20efficiency">Definition of efficiency</a></li>
<li>How can the consequence $x \in X] be efficient under the preference pair [$ \succsim \in \mathscr{D}_I$?<ul>
<li>$y \succsim_i x \quad \forall i \in I$</li>
<li>$y \succ_j x \quad \exists j \in I$</li>
</ul>
</li>
<li>is that there is no consequence $y$ that satisfies<ul>
<li>In other words, if any one person can improve without making anyone worse off, that is not efficient.</li>
<li><a href="/en/social%20choice%20function">social choice function</a> $f: \mathscr{D}_i \to X$, if the consequence $f(\succsim)] is efficient under the preference [$ \succsim] for all preference pairs [$ \in \mathscr{D}_I$ $f$ is said to be efficient.</li>
</ul>
</li>
</ul>
<hr>
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Gibbard-Satterthwaite theorem