Editing 2193: Well-Ordering Principle
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In the final panel, the genie questions why she would wish for something so mundane, when he has the power to grant wishes beyond her wildest dreams. Megan, being savvy of tropes, used in fiction since biblical times, points out that encounters with wish-granting entities often turn out to be traps. Genies in fiction will often interpret wishes in ways the wisher did not intend, and particularly mean-spirited ones will {{tvtropes|JackassGenie|twist a mortal's desire into their own personal hell}}. Even when the wish-granting entity isn't malicious, they're often portrayed as carrying unintended consequences, such that extremely consequential wishes become extremely dangerous. So Megan tries to play it safe by wishing for something innocuous and with little room for harmful side-effects. Unfortunately, Megan appears to have forgotten the overarching trope: all wishes can be twisted against the wisher. | In the final panel, the genie questions why she would wish for something so mundane, when he has the power to grant wishes beyond her wildest dreams. Megan, being savvy of tropes, used in fiction since biblical times, points out that encounters with wish-granting entities often turn out to be traps. Genies in fiction will often interpret wishes in ways the wisher did not intend, and particularly mean-spirited ones will {{tvtropes|JackassGenie|twist a mortal's desire into their own personal hell}}. Even when the wish-granting entity isn't malicious, they're often portrayed as carrying unintended consequences, such that extremely consequential wishes become extremely dangerous. So Megan tries to play it safe by wishing for something innocuous and with little room for harmful side-effects. Unfortunately, Megan appears to have forgotten the overarching trope: all wishes can be twisted against the wisher. | ||
| − | The genie may also be reluctant to fulfill the wish due to the insurmountable practical difficulties of fulfilling such subjective, ill-defined request. The {{w|well-ordering principle}} is a mathematical fact stating that every non-empty set of positive integers contains a least element | + | The genie may also be reluctant to fulfill the wish due to the insurmountable practical difficulties of fulfilling such subjective, ill-defined request. The {{w|well-ordering principle}} is a mathematical fact stating that every non-empty set of positive integers contains a least element. This principle would apply to Megan's request if there was guaranteed to be an absolute worst costume of Marty McFly. However, subjective {{w|preference}}, while {{w|Reflexive relation|reflexive}} and {{w|Transitive relation|transitive}}, is not {{w|Well-founded relation|well-founded}} (or {{w|Symmetric relation|symmetric}} or necessarily {{w|Antisymmetric relation|antisymmetric}} or {{w|Connex relation|(semi-)connex}} for that matter) and is therefore considered to be a {{w|preorder}}, also called a quasiorder. This means that the genie may not be able to fulfill Megan's wish if the selection is based on the preferences of any one person. For example, the genie may have no opinion on the quality of any McFly costume, or might judge them on criteria completely different from Megan's. Her own criteria might apply to some pairs of costumes but not others, leading to ambiguity as to which is the worst, and no way to say whether any of the candidate possibilities are as bad as the others. |
While Megan isn't explicitly wishing for a {{w|Public opinion|common or widely-shared opinion}}, the title text contemplates organizing a "nationwide" search. People's preferences can be combined, such as with a {{w|mean opinion score}} which, while not strictly well-ordered, is usually able to identify a single worst costume, or at least a set of costumes tied for worst place according to aggregate subjective preferences. There are [https://www.docdroid.net/bcKvZmM/preference-aggregation.pdf many other ways to combine preferences] (e.g. voting) but none of them meet all of the criteria considered desirable, as demonstrated by {{w|Arrow's impossibility theorem}}. There is no way to exclude the possibility that even an omniscient and omnipotent genie might be {{w|Omnipotence paradox|technically unable}} to fulfill the wish, at least without, for example, changing one or more persons' preferences or modifying the space-time continuum to retroactively change the quality of some costumes of the past. The genie could fulfill the wish by showing Megan every McFly costume ever worn, which would necessarily show her the worst by any possible definition, but could be the trap she was hoping to avoid because viewing all the "hundreds of thousands" would take an inordinately long time. | While Megan isn't explicitly wishing for a {{w|Public opinion|common or widely-shared opinion}}, the title text contemplates organizing a "nationwide" search. People's preferences can be combined, such as with a {{w|mean opinion score}} which, while not strictly well-ordered, is usually able to identify a single worst costume, or at least a set of costumes tied for worst place according to aggregate subjective preferences. There are [https://www.docdroid.net/bcKvZmM/preference-aggregation.pdf many other ways to combine preferences] (e.g. voting) but none of them meet all of the criteria considered desirable, as demonstrated by {{w|Arrow's impossibility theorem}}. There is no way to exclude the possibility that even an omniscient and omnipotent genie might be {{w|Omnipotence paradox|technically unable}} to fulfill the wish, at least without, for example, changing one or more persons' preferences or modifying the space-time continuum to retroactively change the quality of some costumes of the past. The genie could fulfill the wish by showing Megan every McFly costume ever worn, which would necessarily show her the worst by any possible definition, but could be the trap she was hoping to avoid because viewing all the "hundreds of thousands" would take an inordinately long time. | ||
