Friday, July 3, 2015

Friday: And now I'm hungry again.

I probably should have had more than this today.

Clicking on this item from my RSS (side note, the correct answer is yaki-gyoza, obviously) started me thinking about the following problem.  Given a poll, what's the best way to estimate the minimum number of poll responses necessary to create the observed result distribution?  My initial thought is that you take the minimum response separation.  When I clicked, this poll had yaki: 70.79%; omnomnom: 14.85%; wrong: 14.36%.  The minimum separation is 0.49%.  Assume this is one person.  Then the results have [144.469    30.306    29.306].  Hrm.  Big fractional residuals.  Two people? [288.939    60.612    58.612].  Still pretty bad.  Three?  [433.408    90.918    87.918].  And then I wrote a perl script, and it looks like dN = 20 is the lowest solution, although the residual is still pretty large (0.63).  dN=7 has lower residual, but doesn't round to the right solution.  This seems to suggest that the residual isn't the best metric here.  There's a periodicity in the residual, so that should limit the number of points that need to be checked, but it still seems like there's no great algorithm other than "check a bunch of possibilities."


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