Calculations of votes (Behind the Scenes):
Before starting what is this ELO ranking and why is it required. Lets first try to understand the problem at hand with a simple example.
Lets say we have four colleges , College A , College B , College C and College D which we need to rank based on voting : To vote those colleges we will need at least 4C2 questions (read as votes) to be answered . Below will be possible voting results and points accumulated by each colleges.
Rating and Point Methodology
*For simplicity of understanding following assumptions are made in above example:
1. There are no skip options.
2. For each winning vote for college there is 1 point given to college voted over other . There is no penalty if a college is voted below any college ie : for losing there is 0 points allotted.
3. There are no bogus and fake votes.
So total of 6 votes are allocated to 4 colleges(3+2+1) By capturing the more number of people answer for the above survey and keep updating the scores of each college, it can be extended further. The more the number of people answers the survey, the more representative the rankings will become of a large population. Arrange the college in the decreasing number of scores and you have the ranking according to this particular respondent..Bingo!!!
Now let go back to the each vote individually
Though there are drastic differences of score between colleges under observation in two question wining college always gets the same points. So it similar to saying India winning over Bangladesh carries same point of India winning over Australia. College A will have same impact if it is voted over College B (Just next to it) or College D (very far away from it) At the same time if College D has to move up the ladder it will require lot many more votes. Also there are no negative points associated to losing so , we don’t capture the information where one of the college is voted down over other Seems unfair isn’t it ?
Remember how many colleges we started with (4), these flaws will be more prominent if we increase the number of colleges by 20 fold times, So we have to revisit our approach. We went back and tried to find the best method to capture and calculate the voting information in such scenarios. We were able to relate our case with sports, a similar ranking problem happens there as well, we did a bit of research and we found the perfect match of ranking method for our case “Elo Rating System”. The Elo Rating System is actually used for rankings in Chess, Cricket, Football and other sports.
What is ELO ranking ?
Elo Rating System Explained. (Source Wikipedia)
Each player has a rating, which is a number. A higher number indicates a better player, based on their results against other rated players. The winner of a contest between two players gains a certain number of points in his rating and the losing player loses the same amount. The number of points won or lost in a contest depends on the difference in the ratings of the players, so a player will gain more points by beating a higher-rated player than by beating a lower-rated player. In chess, for instance, if one player is rated 100 points higher than the other player, he is expected to win about five games out of eight, and the rating changes reflect that. Over a series of games, if a player does better than expected, based on the ratings (his compared to his opponents), his rating will go up.
So what happens when someone votes?
Lets try to explain this with an example. Lets consider we compared College A to College B, lets assume that College A is ranked better than College B at the moment the vote was being cast and the probabilites of College A winning over College B was Ea and College B winning over College A was Eb where Ea + Eb = 1 and Ea and Eb are calculated by the formula presented in Elo Rating system. Now in case the person voting votes for College A, its final points are calculated by forumla's presented in the Elo Rating System.
With each vote the points for each college increases or decreases based on the opponent that it was voted against thereby giving the Voting a more meaningful result. We will also keep track of the total number of wins per college to give the data a more realistic output.
Most preferred Engineering College as per everyone who voted is out. Click to view the results!