On Sat, 22 Dec 2001, Ralph Noble asked:
> How would you have done this?
>
> A local newspaper asked its readers to rank the year's Top 10 news stories
> by completing a ballot form. There were 10 choices on all but one ballot
> (i.e. local news, sports news, business news, etc.), and you had to rank
> those from 1 to 10 without duplicating any of your choices. One was their
> top pick, 10 their lowest. Only one ballot had more than 10 choices,
> because of the large number of local news stories you could choose from.
>
> I would have thought if you only had 10 choices and had to rank from 1 to
> 10, then you'd count up all the stories that got the readers' Number One
> vote and which ever story got the most Number One votes would have been
> declared the winner.
That is certainly one way of determining a "winner". But if one were
going to do this in the end, there is not much point to asking for ranks
other than 1, because that information is not going to be used at all.
(Unless, of course, one uses a variant of this method for the breaking of
ties, or for obtaining a majority of votes cast for the "winner".)
> Not so in the case of this newspaper. So maybe I do not understand
> statistics.
Non sequitur. You are not discussing statistics, you are discussing the
choice of methods of counting votes.
> The newspaper told the readers there were several ways it could have
> tallied the rankings.
This is true. "Several" may be an understatement.
> The newspaper decided to weight everybody's responses and gave each
> first place vote a value of 10, each second place nine, each third place
> eight, and so on. They then added together the values for each story and
> then ranked the stories by point totals.
>
> So is this an accurate way to have tallied the votes?
Why not, assuming they didn't err in their arithmetic? In what sense do
you want to mean "accurate"? I would use the word to describe the care
with which the chosen method was carried out, not the choice of method,
as you appear to mean. "Accurate" ordinarily refers, at least by
implication, to how closely some standard or other is being met: what
standard did you have in mind?
> And why weight them since the pool in all but one category only had 10
> items to choose from?
One answer is, precisely because all categories (but the one, and you
haven't quite described what happened to the one, but I'll assume that
only the ranks 1 to 10 were used in that case) had 10 items. If you add
up all the 1st, 2nd, 3rd, etc. votes _without_ weighting them (that is to
say, weighting them equally instead of unequally), you get the same total
for each item, and have no way of declaring a "winner". (This may not be
true for the one category, since there are more than 10 items but only 10
ranks to be apportioned among them.)
One could, of course, have weighted them according to their ranks
(1st = 1, 2nd = 2, etc.) and chosen the one with the _lowest_ point
total. (This of course is equivalent to what the newspaper actually
did: this point total equals 11 minus the newspaper's point total, and
you get the same "winners" this way.) Or according to the reciprocal of
their ranks (1st = 1, 2nd = 1/2, 3rd = 1/3, etc.) and added those up,
and taken the highest score. This is not equivalent to the method
actually used, although sometimes the results are not different. Etc.
If you conclude from all this that the choice of "counting" method for
tallying votes is an arbitrary one, you are quite right. It is.
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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