This component contains three R functions that are used for all three applications: - **[bordaCount.R][1]** <br> Contains the R function to calculate the [Borda Count][2]. The function needs a matrix with the rankings of the items per person, the number of people who ranked, and the number of items that were ranked as input: *bordaCount(rankMatrix, nPeople, nItems)*. - **[boundsFunction.R][3]** <br> Contains the R function to calculate the bounds that are implied by the ranking. For example, if somebody ranked the items x₁ to x₅ as **x₁, x₃, x₄, x₂, x₅**, this implies the following order restrictions: **x₁ < x₃ < x₄ < x₂ < x₅**. Using these order restrictions you can define lower and upper bounds for every item in the list. So, item **x₁** would have a lower bound of **-&infin;** and an upper bound of **x₃**; **&infin; < x₁ < x₃**. The Thurstonian top-*n* model uses these bounds to infer the latent ground truth. The function needs a matrix with the rankings of the items per person, the number of people who ranked, and the number of items that were ranked as input: *bounds(rankMatrix, nPeople, nItems)*. - **[partialTau.R][4]** <br> Contains the R function to calculate the partial [tau distance][5] (Fagin, Kumar, Mahdian, Sivakumar, & Vee, 2006). The tau distance is a metric that describes the similarity between two ranked lists. The function needs two lists of ranks as input: *partialTau(A, B, penalty = 0.5)*. References <br> Fagin, R., Kumar, R., Mahdian, M., Sivakumar, D., & Vee, E. (2006). Comparing partial rankings. *SIAM Journal on Discrete Mathematics, 20,* 628-648. [1]: https://osf.io/8dbe9/ [2]: http://en.wikipedia.org/wiki/Borda_count [3]: https://osf.io/dspha/ [4]: https://osf.io/i6g7z/ [5]: http://en.wikipedia.org/wiki/Kendall_tau_distance