 However, these two definitions are not equivalent, and neither of them is plausible in all cases. For instance, let \(x\) be good and not bad in the context \(\{x,y\}\), and let \(y\) be neither good nor bad in the same context. Then \(x \succ y\) holds according to first definition but \(\neg(x \succ y)\) according to the second. To avoid such problems, Hansson and Liu (2014) proposed the following definition: 