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Is CodeProject's Voting system really smart?

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25 Apr 2004CPOL3 min read 165.3K   21   55
In this article I continue my discussion of the CodeProject''s voting system.

Introduction

This is a sequel of the article called "CodeProject's Article voting system" in which I have discussed two voting models, one of which I thought is used on the CodeProject's website.

As far as I was corrected by Chris Maunder who provided me with the model that is really used, I have decided to analyze this model too.

In this article you will find the rating counting algorithm, the description of its model and then some analysis of it.

Rating counting algorithm

The following description was cut and pasted from the following post "Excellent analysis. Unfortunately not quite correct":

Each article on CodeProject has associated with it a Vote Total (Vt), a Weight Total (Wt), and a number of votes (N). When a member votes, the system adds the weight of their vote (dependant on membership level) to Wt, and the rating itself multiplied by their weight to Vt. The rating of an article is then R = Vt / Wt.

If everyone has a weight of 1 then Wt = N, and R = Vt / N. Having differing weights, though, means that when a gold member (weight = 4) and bronze member (weight = 1) vote, the vote is weighted towards the gold:

Assume Gold votes 5 and Bronze votes 1:
Wt = 4 + 1 = 5
Vt = 4 x 5 + 1 x 1 = 21
R = 4.2

This is quite clear and looks very reasonable as each person has its weight in the system that depends on its status. But does it really works? An answer to this question along with the probability model will be given in the following sections.

Voting probability model

In the algorithm described above we deal with two types of random variables:

  • Image 1 - the peoples' vote values
  • Image 2 - the person's weight in the system

Note that:

  1. Image 3 , Image 4, Image 5 and Image 6 are independent when Image 7 and Image 8
  2. Image 9, Image 10 have the same distribution Image 11
  3. Image 12, Image 13 have the same distribution Image 14

Now we can represent the algorithm given above by the following formula:

Image 15

In this formula index Image 16 means that Image 17 is the rating after the Image 18'th vote. It is also obvious that Image 19 is the weight of the person who put in the Image 20 vote and thus voted with the value Image 21.

Let us now assume that we have the following mean values of our random variables:

Image 22, Image 23 Image 24

It is well known from the probability theory that for two random variables Image 25 and Image 26:

Image 27

If they are independent then:

Image 28

Now we are ready to calculate the following mean value Image 29:

Image 30
Image 31

(These calculations are trivial and self descriptive)

In other words Image 32 and doesn't depend anyhow from weights of the persons who participated in the voting!

It is also interesting to note that if the rating formula would be the following:

Image 33

then the mean value of the rating would be Image 34 i.e. independent from vote values!

Conclusions

In this article I have calculated the mean value of the rating that measures the quality of any article on CodeProject's website.

It was discovered that although the weight of each person in the system is taken into account in case when the vote and the weight are independent, the mean value of rating random variable doesn't depend on the weight. Even more, the mean value is also the same as the mean value for the two other voting models described in my previous article "CodeProject's Article voting system".

Note that if the vote values depend on person's weights then the rating mean value is different and involves the weights distribution. Thus this approach may be considered to be more general than simple approaches that do not involve weights.

References

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)


Written By
Architect
Netherlands Netherlands
PhD in Numerical and Statistical Model Checking of Probabilistic systems. Bachelor and Masters degrees (with honors) in Theoretical Mathematics. Thirteen (13) international research publications, among which nine (10) are DBLP recognized. Seventeen (17) years of work experience in Research, Design and Development of Verification Algorithms for Probabilistic and Control Systems, Scientific Software, Embedded Systems and Web applications. Excellent English (TOEFL-257-PC) and Good Dutch (NT2-2) skills. Permanent Dutch residence.

Specialties:
• Theoretical and applied research in Control and Formal Verification (numerical and statistical);
• Acquiring information, sharing knowledge, lecturing, mentoring, motivating and evaluating people;
• Working on large-scale distributed, multi-threaded, event-driven, cross-disciplinary software projects;

Research experiences:
• Numerical and Statistical Model Checking of Markov Chains;
• Type-2 Computable Topological semantics for CTL* on Dynamic Systems;
• Statistical Machine Translation;
• Deterministic and Symbolic-regression based compression of Symbolic controllers;
• Multi-dimensional trajectory planning with position and derivative constraints.

Teaching and supervision:
• 5 years of teaching at Novosibirsk State University, University of Twente, Fontys Hogescholen
• Supervising 3 master students at TU Twente and RWTH Aachen
• Supervising 11+ trainee-ship/internship students at Fontys Hogescholen
• Managing a group of 7 volunteers in the Russian school foundation
• Leading leading 3 project groups at Fontys Hogescholen

Software experiences (years):
• C++ (8), UML (6), Java (5), C (5), Matlab (4), C# (2), Python (1), Mathematica (1)
• GIT (4), SVN (5), Clearcase (4), Clear Quest (4), SCCS (2)
• CMake (3), Make (2), Ant (2)
• CSS (3), HTML (3), JavaScript (2)

Comments and Discussions

 
GeneralRe: Not a critique, but Pin
Dr. Ivan S Zapreev18-Apr-04 4:20
professionalDr. Ivan S Zapreev18-Apr-04 4:20 
GeneralCircular Argument. Pin
73Zeppelin17-Apr-04 8:42
73Zeppelin17-Apr-04 8:42 
GeneralRe: Circular Argument. Pin
leppie17-Apr-04 12:08
leppie17-Apr-04 12:08 
GeneralRe: Circular Argument. Pin
Dr. Ivan S Zapreev18-Apr-04 4:14
professionalDr. Ivan S Zapreev18-Apr-04 4:14 
GeneralRe: Circular Argument. Pin
73Zeppelin18-Apr-04 7:16
73Zeppelin18-Apr-04 7:16 
GeneralRe: Circular Argument. Pin
Dr. Ivan S Zapreev18-Apr-04 21:11
professionalDr. Ivan S Zapreev18-Apr-04 21:11 
QuestionHuh???? Pin
interj17-Apr-04 7:17
interj17-Apr-04 7:17 
AnswerRe: Huh???? Pin
Dr. Ivan S Zapreev17-Apr-04 7:34
professionalDr. Ivan S Zapreev17-Apr-04 7:34 
Hello there,

>>All you showed in this article is that assuming independence of votes and
>>weights, the expected rating has the same value as the expected vote.

Yes, It seems to me that you have got it.

>>This seems quite obvious,

Good for you.

>>and in fact I wouldn't trust a rating algorithm
>>that didn't have a similar property.

To use weights is a good idea the question is how to use them to get better results.

>>Yet in your conclusion you say that
>>this algorithm is not good. Care to explain why?

I didn't say anything like that. Care to read it more carefully.

The only point is that for the given model the mean values of three approaches are the same. Why to choose the complicated one then?

>>Besides, you assumption of independence is incorrect. When a user votes, he
>>can see the current rating and his vote is influenced by it.

Very doubtfully. This concerns only people who have no personal opinion.

>>Also, it's quite possible that people with different weights have
>>different voting distributions.

Everything is possible. This is only a model and I give the solution to it.
For another model there could be another solution.

Besides, to choose a proper model you have to do statistical analysis.

Until that your assumptions are not better than mine.


Ivan S Zapreev
cerndan@mail.ru
GeneralRe: Huh???? Pin
Daniel Turini17-Apr-04 16:14
Daniel Turini17-Apr-04 16:14 
GeneralRe: Huh???? Pin
Dr. Ivan S Zapreev18-Apr-04 3:58
professionalDr. Ivan S Zapreev18-Apr-04 3:58 

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