[math-fun] a voting/stats puzzle
That arose the other day with some aid+confusion provided by Jameson Quinn, is this. V voters each provide a score for each of C candidates (V*C scores in all) from some fixed set of allowed scores, e.g. the integer interval [0,1,2,...,9999]. Now plain "range voting" would be, the candidate with greatest average score, wins. We here instead consider this voting system, which might be called "(N,V) maxprob winner": If N voters were selected as a random subset of the V (0<N<=V) then the candidate with the greatest probability that his sample mean is maximal, wins. Note that if N=1, this is plain plurality voting. If N=V it is plain range voting. If done using pairs of candidates and N=1 then it is "Condorcet voting." So this is an interesting way to "hybridize" several proposed voting systems as one. Anyhow, QUESTION: is there any efficient algorithm to compute the (N,V) maxprob winner, or is this task #P-hard or NP-hard? (I have a pseudopolynomial time algorithm, i.e. if C and the score-set-cardinality are bounded, then it runs in polynomial time.) -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Yesterday there was an episode of the TV show "Elementary" (as you probably guessed, yet another Sherlock Holmes show), in which the mystery to solve was the murder of an eminent mathematician. And the whole show revolved around the putative solution to the P = NP question. There wasn't much actual math on the show, of course, but at least when one character explained what P = NP meant to another character, it was fairly close to accurate. There were plenty of blackboards filled with what was supposed to be actual math, but they never resembled actual blackboards filled with actual math. I wonder why they can never get that right. --Dan
Hmmm, I thought it was far enough off to qualify as "wrong". "Numbers" used to do a pretty good job on blackboard math, I thought. But I think that there is a difference between absolute accuracy and conveying an effective impression. What drives me nuts is actors playing string instruments (that is, instruments with vibrating strings, not instruments constructed from strings, not even in theory). You cannot fake bowing or fingering.
Yesterday there was an episode of the TV show "Elementary" (as you probably guessed, yet another Sherlock Holmes show), in which the mystery to solve was the murder of an eminent mathematician. And the whole show revolved around the putative solution to the P = NP question.
There wasn't much actual math on the show, of course, but at least when one character explained what P = NP meant to another character, it was fairly close to accurate.
There were plenty of blackboards filled with what was supposed to be actual math, but they never resembled actual blackboards filled with actual math. I wonder why they can never get that right.
Okay, maybe it was "wrong". (But only with quotation marks.) I wanted so much to like "Numbers", but was put off by the large amount of gunplay. But as long as we're on the subject, are there any books or short stories involving math that math-fungi have liked? (Let's exclude the wonderful but well-known Mathematica Fantasia and Mathematical Magpie collections.) --Dan On 2013-10-04, at 5:07 PM, Hilarie Orman wrote:
Hmmm, I thought it was far enough off to qualify as "wrong".
"Numbers" used to do a pretty good job on blackboard math, I thought. But I think that there is a difference between absolute accuracy and conveying an effective impression. What drives me nuts is actors playing string instruments (that is, instruments with vibrating strings, not instruments constructed from strings, not even in theory). You cannot fake bowing or fingering.
Yesterday there was an episode of the TV show "Elementary" (as you probably guessed, yet another Sherlock Holmes show), in which the mystery to solve was the murder of an eminent mathematician. And the whole show revolved around the putative solution to the P = NP question.
There wasn't much actual math on the show, of course, but at least when one character explained what P = NP meant to another character, it was fairly close to accurate.
There were plenty of blackboards filled with what was supposed to be actual math, but they never resembled actual blackboards filled with actual math. I wonder why they can never get that right.
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Dan, I remember reading "Uncle Petros and Goldbach's conjecture" quite a while ago, and found it enjoyable. But, quite honestly, after all this time I don't remember any details. Here's a review by Allyn Jackson: http://www.ams.org/notices/200010/rev-jackson.pdf Victor On Fri, Oct 4, 2013 at 8:39 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Okay, maybe it was "wrong". (But only with quotation marks.)
I wanted so much to like "Numbers", but was put off by the large amount of gunplay.
But as long as we're on the subject, are there any books or short stories involving math that math-fungi have liked?
(Let's exclude the wonderful but well-known Mathematica Fantasia and Mathematical Magpie collections.)
--Dan
On 2013-10-04, at 5:07 PM, Hilarie Orman wrote:
Hmmm, I thought it was far enough off to qualify as "wrong".
"Numbers" used to do a pretty good job on blackboard math, I thought. But I think that there is a difference between absolute accuracy and conveying an effective impression. What drives me nuts is actors playing string instruments (that is, instruments with vibrating strings, not instruments constructed from strings, not even in theory). You cannot fake bowing or fingering.
Yesterday there was an episode of the TV show "Elementary" (as you probably guessed, yet another Sherlock Holmes show), in which the mystery to solve was the murder of an eminent mathematician. And the whole show revolved around the putative solution to the P = NP question.
There wasn't much actual math on the show, of course, but at least when one character explained what P = NP meant to another character, it was fairly close to accurate.
There were plenty of blackboards filled with what was supposed to be actual math, but they never resembled actual blackboards filled with actual math. I wonder why they can never get that right.
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I enjoyed Stansilaw Lem's "His Master's Voice" and remember thinking that it was narrated from a genuinely mathematical point of view, so to speak. Not that I'd want to pass a quiz on its content now, 30 years later. https://en.wikipedia.org/wiki/His_Master's_Voice_(novel) On Fri, Oct 4, 2013 at 5:50 PM, Victor Miller <victorsmiller@gmail.com>wrote:
Dan, I remember reading "Uncle Petros and Goldbach's conjecture" quite a while ago, and found it enjoyable. But, quite honestly, after all this time I don't remember any details. Here's a review by Allyn Jackson: http://www.ams.org/notices/200010/rev-jackson.pdf
Victor
On Fri, Oct 4, 2013 at 8:39 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Okay, maybe it was "wrong". (But only with quotation marks.)
I wanted so much to like "Numbers", but was put off by the large amount of gunplay.
But as long as we're on the subject, are there any books or short stories involving math that math-fungi have liked?
(Let's exclude the wonderful but well-known Mathematica Fantasia and Mathematical Magpie collections.)
--Dan
On 2013-10-04, at 5:07 PM, Hilarie Orman wrote:
Hmmm, I thought it was far enough off to qualify as "wrong".
"Numbers" used to do a pretty good job on blackboard math, I thought. But I think that there is a difference between absolute accuracy and conveying an effective impression. What drives me nuts is actors playing string instruments (that is, instruments with vibrating strings, not instruments constructed from strings, not even in theory). You cannot fake bowing or fingering.
Yesterday there was an episode of the TV show "Elementary" (as you probably guessed, yet another Sherlock Holmes show), in which the mystery to solve was the murder of an eminent mathematician. And the whole show revolved around the putative solution to the P = NP question.
There wasn't much actual math on the show, of course, but at least when one character explained what P = NP meant to another character, it was fairly close to accurate.
There were plenty of blackboards filled with what was supposed to be actual math, but they never resembled actual blackboards filled with actual math. I wonder why they can never get that right.
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
Correction: I would want to *pass* the quiz. Just not *take* it. On Fri, Oct 4, 2013 at 5:59 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
I enjoyed Stansilaw Lem's "His Master's Voice" and remember thinking that it was narrated from a genuinely mathematical point of view, so to speak.
Not that I'd want to pass a quiz on its content now, 30 years later.
https://en.wikipedia.org/wiki/His_Master's_Voice_(novel)
On Fri, Oct 4, 2013 at 5:50 PM, Victor Miller <victorsmiller@gmail.com>wrote:
Dan, I remember reading "Uncle Petros and Goldbach's conjecture" quite a while ago, and found it enjoyable. But, quite honestly, after all this time I don't remember any details. Here's a review by Allyn Jackson: http://www.ams.org/notices/200010/rev-jackson.pdf
Victor
On Fri, Oct 4, 2013 at 8:39 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Okay, maybe it was "wrong". (But only with quotation marks.)
I wanted so much to like "Numbers", but was put off by the large amount of gunplay.
But as long as we're on the subject, are there any books or short stories involving math that math-fungi have liked?
(Let's exclude the wonderful but well-known Mathematica Fantasia and Mathematical Magpie collections.)
--Dan
On 2013-10-04, at 5:07 PM, Hilarie Orman wrote:
Hmmm, I thought it was far enough off to qualify as "wrong".
"Numbers" used to do a pretty good job on blackboard math, I thought. But I think that there is a difference between absolute accuracy and conveying an effective impression. What drives me nuts is actors playing string instruments (that is, instruments with vibrating strings, not instruments constructed from strings, not even in theory). You cannot fake bowing or fingering.
Yesterday there was an episode of the TV show "Elementary" (as you probably guessed, yet another Sherlock Holmes show), in which the mystery to solve was the murder of an eminent mathematician. And the whole show revolved around the putative solution to the P = NP question.
There wasn't much actual math on the show, of course, but at least when one character explained what P = NP meant to another character, it was fairly close to accurate.
There were plenty of blackboards filled with what was supposed to be actual math, but they never resembled actual blackboards filled with actual math. I wonder why they can never get that right.
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_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
participants (5)
-
Dan Asimov -
Hilarie Orman -
Thane Plambeck -
Victor Miller -
Warren D Smith