Ralph Noble wrote:
> 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.
If you only count the #1 votes, then the other positions do not count for
anything, and do not matter. You loose the opportunity to discover that lots
of people felt a single item was #2. You might, in fact, elect Spiro Agnew as
Gov. of Maryland. Depending on your politics, this may be a good thing or not.
> Not so in the case of this newspaper . so maybe I do not understand
> statistics. The newspaper told the readers there were several ways it could
> have tallied the rankings. 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.
this ranking system assumes that 2 second place votes are worth 1.8 times as
much as 1 first place vote. And two 5th place votes are worth as much as one
first place vote. My gut suspicion is that this puts more emphasis on the 3rd
& 4th place finishers than most people would use, if they could award the
points of the scale as they choose. Maybe not.
But this does give credit for the rank of a vote in the list. Even a last
place finisher gets some credit.
> So is this an accurate way to have tallied the votes?
I think 'accurate' as a term here, does not compute. there are many ways to
consider preference for items in a list of more than 2 items. the complexity
increases with the length of the list. the newspaper made up the rules; so
long as they followed them, it was 'accurate.'
> And why weight them
> since the pool in all but one category only had 10 items to choose from?
If they simply added the rank positions, 1, 2, 3... 10, then the 'winner' would
be the one with the lowest score. Unless you play a lot of golf, this does not
make much intuitive sense to many people. A simple first reaction is to
reverse the rank 'position' number, as they did. Another way might be to
weight the ranks by an exponential decay model, so that the difference in
weight between a #1 and #2 would be greater than the difference between a #8
and #9. Like I said, the newspaper can make up whatever rules they like.
> Thanks!
>
> Ralph Noble
>
> [EMAIL PROTECTED]
Cheers & lots of diverse Holidays,
Jay
--
Jay Warner
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