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Topic: Is there a way to calculate an average ranking from uneven lists?
Replies: 12   Last Post: Nov 2, 2013 12:55 PM

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Jennifer Murphy

Posts: 24
Registered: 2/23/12
Re: Is there a way to calculate an average ranking from uneven lists?
Posted: Oct 29, 2013 1:39 AM
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On Mon, 28 Oct 2013 17:37:04 -0700 (PDT), grahamcooper7@gmail.com wrote:

>On Monday, October 28, 2013 2:36:13 PM UTC-7, David Bernier wrote:
>> On 10/27/2013 03:20 PM, Jennifer Murphy 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
>>
>> >
>>
>>
>>
>> I have a couple of ideas...
>>
>>
>>
>> (1) The different lists have different criteria for
>>
>> inclusion or exclusion. They may not be explicit,
>>
>> but let's assume they are made explicit.
>>
>> An exclusion criterion "not poetry" can in principle
>>
>> be turned into a combination of "ors" and "inclusion factors", as
>>
>>
>>
>> "not poetry" = "is novel" or "is non-fiction" or "is historical
>>
>> novel".
>>
>>
>>
>> these selectors matter because Tolstoy's "War and Peace"
>>
>> would not appear in a list "English literature" works ...
>>
>> yet, it's Russian literature, has been translated in English,
>>
>> and has received wide acclaim.
>>
>>
>>
>> The idea would be to find all lists which, according to
>>
>> their explicit selection criteria, may include say
>>
>> "War and Peace" if all books in said category were ranked.
>>
>> But different lists which may include "War and Peace" will
>>
>> probably sometimes have different criteria.
>>
>>
>>
>> (2) To consider calibrating between lists, say if
>>
>> 10 out of 20 lists all included the novel
>>
>> "Moby Dick", then to sort of use "Moby Dick" as
>>
>> a benchmark.
>>
>>
>>
>> (3) My own observation with movies and books is
>>
>> that some books and movies seem designed to
>>
>> maximize sales, or to "target" a specific segment
>>
>> of readers & tastes, e.g. Harlequin series, which
>>
>> while "good reading for entertaiment", can be
>>
>> more easily read than "Remembrance of Things Past",
>>
>> a multi-volume novel by French author Marcel Proust,
>>
>> < http://en.wikipedia.org/wiki/In_Search_of_Lost_Time > .
>>
>>
>>
>> David Bernier
>>
>>
>>

>
>
>
>Its an error minimization problem.
>
>START: LIST1=1 LIST2=1 LIST3=1
>
>
>Rank List 1 List 2 List 3
> 1 A B F
> 2 B A H
> 3 C E C
> 4 D G D
> 5 E D A
>
>
>
>CALC WEIGHTED AVERAGES
>
>A = (( 100*LIST1) + (75*LIST2) + (0*LIST3) ) / 3
>B = (( 75*LIST2) + (100*LIST1) ) / 2
>C = (( 50*LIST1) + (50*LIST3) ) / 2
>...
>
>
>CALC ERROR
> = |A-100| + |A-75| + |A-0|
> + |B-75| + |B-100|
> + |C-50| + |C-50|
> + ...
>
>
>Randomly adjust LIST1, LIST2 & LIST3
>to minimize the error.
>
>
>
>This does not take into account some lists will be best sellers
>or poor sellers, and some will have a larger spread... but that's
>a lot more complicated.


You make some interesting suggestion, but the principles are foreign to
me. I'll have to study them a bit to see if I can make sense of them.
They may be beyond my meager skills. :-(



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