tag:blogger.com,1999:blog-544041532485510036.post5144099052921287610..comments2018-01-01T12:33:27.214-08:00Comments on too little, too late: multiple choiceWolfganghttp://www.blogger.com/profile/07086991199438418163noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-544041532485510036.post-38219745488916891652017-03-12T12:53:55.604-07:002017-03-12T12:53:55.604-07:00>> On the other hand 20%, 40%, 60%, 0%, 100%...>> On the other hand 20%, 40%, 60%, 0%, 100% seem to be much more appropriate <br /><br />You have a random process so it seems kind of natural to me that multiples of 1/N would be more appropriate.<br /><br />I think you can probably find a way to get a paradox using your question for any N > 2 using multiples of 1/N. If N = 2 though it is a little tricky. Then you have "none of the above" and 1/2. If you say "none of the above" you end up in an infinite loop. If you say 1/2, you don't end up in a loop, but as far as I can tell there is no particularly logical reason to say 1/2 to start with.Leenoreply@blogger.comtag:blogger.com,1999:blog-544041532485510036.post-47480342983588809912017-03-12T09:11:55.156-07:002017-03-12T09:11:55.156-07:00Lee,
>> If E is correct, then A and D beco...Lee,<br /><br />>> If E is correct, then A and D become correct too<br />If A and D are correct, then E (none of the above) cannot be correct,<br />because A and D are above E ... 8-)wolfgangnoreply@blogger.comtag:blogger.com,1999:blog-544041532485510036.post-72048937592950889722017-03-12T09:09:56.367-07:002017-03-12T09:09:56.367-07:00>> a question that doesn't make sense
C...>> a question that doesn't make sense<br /><br />CIP, Lee,<br /><br />I think it is interesting to consider different options:<br />replacing D e.g. with 33% instead of 20% etc.<br />It seems to me that an option 33% or 67% etc. would be clearly irrelevant.<br />On the other hand 20%, 40%, 60%, 0%, 100% seem to be much more appropriate ...<br />So if the question and the whole setup is nonsensical, then why is there this difference?<br />And it would seem that A to E includes all possible answers (because of "none of the above").wolfgangnoreply@blogger.comtag:blogger.com,1999:blog-544041532485510036.post-56666023664433128402017-03-12T08:05:25.378-07:002017-03-12T08:05:25.378-07:00>> but just calling a sentence a question do...>> but just calling a sentence a question doesn't make it one - or does it?<br /><br />The sentence is definitely a question, but it's a question that doesn't make sense because it is self referential as you point out. According to Wolfgang's rules then the answer is E "none of the above." I disagree with Wolfgang that you can get to a 40% answer from there. If E is correct, then A and D become correct too and the answer is 60% and not 40%. Anyway, regardless of whether I am correct about that or not, since a contradiction of sorts obviously arises I think you could say the probability is undefined. I think you could also use a kind of theory of types though and say that if E is correct then A and D cannot occur so the only correct answer is E and the probability remains at 20%.Leenoreply@blogger.comtag:blogger.com,1999:blog-544041532485510036.post-22018498566961734432017-03-12T07:03:26.313-07:002017-03-12T07:03:26.313-07:00I don't think the question is the problem. Ima...I don't think the question is the problem. Imagine that we leave the question the same, but change option A and D from 20% to 30% or something else.<br />Then answer E: none of the above (which includes "this question makes no sense") would be the correct choice and there would be no problem.<br />wolfgangnoreply@blogger.comtag:blogger.com,1999:blog-544041532485510036.post-11668788965004713242017-03-12T04:52:57.819-07:002017-03-12T04:52:57.819-07:00The "paradox" hangs on the self-referent...The "paradox" hangs on the self-referentiality of "this question," but just calling a sentence a question doesn't make it one - or does it?CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-544041532485510036.post-63306628196525769692017-03-11T16:43:45.256-08:002017-03-11T16:43:45.256-08:00>> So this leaves us with C , if no answer c...>> So this leaves us with C , if no answer can be chosen correctly, but ...<br /><br />I assume since that again leads to a contradiction that you like my first answer of the probability being undefined. It's a good brain teaser!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-544041532485510036.post-49113041483777606212017-03-11T16:20:57.544-08:002017-03-11T16:20:57.544-08:00If "none of the above" is correct it has...If "none of the above" is correct it has 20% of being chosen, which means it is incorrect, because A and D would be correct.<br />But A and D would be chosen with 2:5 = 40% probability, so B would be correct, but if B is correct it would only be chosen with 20% probability, so it is false.<br />So this leaves us with C , if no answer can be chosen correctly, but ...<br />wolfgangnoreply@blogger.comtag:blogger.com,1999:blog-544041532485510036.post-40490623199390592572017-03-11T15:45:55.712-08:002017-03-11T15:45:55.712-08:00The answer is "none of the above" so the...The answer is "none of the above" so there is a 20% probability of it being chosen. So I think there are two ways to think about it. I can think the two 20% answers are also both correct and so the probability becomes 60% leading to a contradiction and therefore the probability as being undefined. Or, I could think that the only correct answer is "none of the above" which only has a 20% probability of occurring and if one of the 20% answers are chosen they are incorrect answers and don't affect anything so the answer is 20%.Leenoreply@blogger.com