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Posted 16 Apr 2004

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Is CodeProject's Voting system really smart?

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3.49/5 (45 votes)
25 Apr 2004CPOL3 min read
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)

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About the Author

Dr. Ivan S Zapreev
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

 
QuestionIt is time for the next chalange Pin
Lutosław6-Jan-12 2:16
MemberLutosław6-Jan-12 2:16 
GeneralTrue in a perfect world Pin
Chris Maunder30-Apr-07 5:22
cofounderChris Maunder30-Apr-07 5:22 
GeneralRe: True in a perfect world Pin
Dr. Ivan S Zapreev7-Aug-07 2:05
professionalDr. Ivan S Zapreev7-Aug-07 2:05 
GeneralRe: True in a perfect world Pin
Lutosław6-Jan-12 2:07
MemberLutosław6-Jan-12 2:07 
GeneralOpen voting system! [modified] Pin
Mathieu Jacques16-Jan-07 7:43
MemberMathieu Jacques16-Jan-07 7:43 
GeneralRe: Open voting system! Pin
Dr. Ivan S Zapreev7-Aug-07 2:02
professionalDr. Ivan S Zapreev7-Aug-07 2:02 
GeneralMandatory message for each vote Pin
Mathieu Jacques16-Jan-07 7:35
MemberMathieu Jacques16-Jan-07 7:35 
GeneralDifferent Distributions Pin
Sam NG20-Mar-06 19:06
MemberSam NG20-Mar-06 19:06 
GeneralRe: Different Distributions Pin
Dr. Ivan S Zapreev21-Mar-06 5:49
professionalDr. Ivan S Zapreev21-Mar-06 5:49 
GeneralI'd like to see the rating distribution Pin
Rei Miyasaka7-Sep-05 17:37
MemberRei Miyasaka7-Sep-05 17:37 
GeneralRe: I'd like to see the rating distribution Pin
Dr. Ivan S Zapreev7-Sep-05 22:25
professionalDr. Ivan S Zapreev7-Sep-05 22:25 
GeneralRe: I'd like to see the rating distribution Pin
Mathieu Jacques16-Jan-07 7:22
MemberMathieu Jacques16-Jan-07 7:22 
GeneralThe Yea/Nea/Meh Model PinPopular
Christopher Lord26-Apr-04 8:37
MemberChristopher Lord26-Apr-04 8:37 
GeneralRookie/Guru Pin
Wackatronic26-Apr-04 8:06
MemberWackatronic26-Apr-04 8:06 
GeneralRe: Rookie/Guru Pin
Jeff Varszegi26-Apr-04 8:25
professionalJeff Varszegi26-Apr-04 8:25 
GeneralRe: Rookie/Guru Pin
Wackatronic26-Apr-04 9:01
MemberWackatronic26-Apr-04 9:01 
GeneralRe: Rookie/Guru Pin
Jeff Varszegi26-Apr-04 9:27
professionalJeff Varszegi26-Apr-04 9:27 
GeneralRe: Rookie/Guru Pin
Wackatronic26-Apr-04 9:34
MemberWackatronic26-Apr-04 9:34 
GeneralRe: Rookie/Guru Pin
Jeff Varszegi26-Apr-04 9:40
professionalJeff Varszegi26-Apr-04 9:40 
GeneralRe: Rookie/Guru Pin
Wackatronic26-Apr-04 11:46
MemberWackatronic26-Apr-04 11:46 
Generalетить. What an article. Pin
Gevorg26-Apr-04 7:25
MemberGevorg26-Apr-04 7:25 
GeneralRe: етить. What an article. Pin
Dr. Ivan S Zapreev26-Apr-04 22:47
professionalDr. Ivan S Zapreev26-Apr-04 22:47 
QuestionWhat a waste of time... Pin
ToneEngel26-Apr-04 1:39
MemberToneEngel26-Apr-04 1:39 
AnswerRe: What a waste of time... PinPopular
Dr. Ivan S Zapreev26-Apr-04 1:47
professionalDr. Ivan S Zapreev26-Apr-04 1:47 
QuestionStatistics? Pin
Luca Piccarreta26-Apr-04 1:24
MemberLuca Piccarreta26-Apr-04 1:24 

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