In article <firstname.lastname@example.org>, Jennifer Murphy <JenMurphy@jm.invalid> wrote:
> There are many lists containing rankings of great books. Some are > limited to a particular genre (historical novels, biographies, science > fiction). Others are more general. Some are fairly short (50-100 books). > Others are much longer (1,001 books). > > Is there a way to "average" the data from as many of these lists as > possible to get some sort of composite ranking of all of the books that > appear in any of the lists? > > I took a crack at it with a spreadsheet, but ran into problems. I will > explain it briefly here. > > If the lists are all the same length and include exactly the the same > books, the solution is relatively simple (I think). I can just average > the ranks. I can even add a weighting factor to each list to adjust the > influence on the composite ranking up or down. > > I ran into problems when the lists are of different lengths and contain > different books. I could not think of a way to calculate a composite > ranking (or rating) when the lists do not all contain the same books. > > Another complicationb is that at least one of the lists is unranked (The > Time 100). Is there any way to make use of that list? > > I created a PDF document with some tables illustrating what I have > tried. Here's the link to the DropBox folder: > > https://www.dropbox.com/sh/yrckul6tsrbp23p/zNHXxSdeOH
One way to compare rankings when there are different numbers of objects ranked in different rankings is to scale them all over the same range, such as from 0% to 100%.
Thus in all rankings a lowest rank would rank 0% and the highest 100%, and the middle one, if there were one, would rank 50%. Four items with no ties would rank 0%, 33 1/3%, 66 2/3% and 100%, and so on.
For something of rank r out of n ranks use (r-1)/(n-1) times 100%. --