DanRoM;n3546107 said:
So
MXM, how did you calculate the percentage values per pair? I can't get my head around that.
Read the fine print
This is how I implemented it, say I'm comparing your vote with Matt2000's vote:
1. Make a list of all car pairs. Car a vs car b. Like:
Lexus vs Disco,
Lexus vs 156,
Lexus vs Tesla... then
Disco vs 156, Disco vs Tesla... etc. That's what "14 choose 2" operator does. You get 91 combinations of car pairs.
2. For each car pair, check whether you prefer a or b. So get a list like: a a a b a b b, except it's 91 letters long.
3. Do the same for Matt's vote, say the list for him is b a a b b b b.
4. If you both have the same letter for a pair of cars, you get a score +1 (concordant pair), if you have a different letter you get -1 (discordant pair). For the 7 pair example above the score is 5-2=3. The percentage is score/amount of pairs, so 3/7 = 43%.
5. Repeat steps 2-4 for every voter pair to fill the table above.
Why do it like this? Because it simulates the decision-making when ordering a list of items. It shows similarity between two people's decisions. It does not care about absolute position of the car in the list. Say you have Disco and Lexus placed 5 and 11, but Matt has them 1 and 3. That's still a positive correlation.
Could be done better? Yes, I could've assigned weights to the distance between pairs, or make it "top heavy".
https://en.wikipedia.org/wiki/Kendal...on_coefficient
My "modifications" to the algorithm are about dealing with incomplete lists, where I assume that every missing car has lower placement than cars in the list. Except if both cars in a pair are missing, then I can't make a decision and the score remains the same.
The score in the last column is just a sum of all scores on one line, but it's not very representative, as it favours people who sent a more complete list.