  The second type of debate concerns the method used to calculate  the group grade for each candidate (i.e., whether to use the mean as in Score Voting or the median as in Majority Judgement).   One important issue is whether voters have an incentive to misrepresent their evaluations of the candidates.    Consider the voter in  the middle column  that assigns the grade of 2 to  \(A\), 0 to \(B\), and 3 to \(C\).   Suppose that these grades represents the voter’s true evaluations of the candidates.  If  this  voter increases the grade for \(C\) to 4 and decreases the grade for \(A\) to  1 (and the other voters do not change their grades), then the average grade for \(A\) becomes 2.4 and the average grade for \(C\) becomes 2.6, which better reflects the voter’s true evaluations of the candidates (and results in \(C\) being elected according to Score Voting). Thus, this voter has an incentive to misrepresent her grades.   Note that the median grades for the candidates do not change after this voter changes her grades.   Indeed, Balinski and Laraki 2010, chapter 10, argue that using the median to assign group grades to candidates encourages voters to submit grades that reflect their true evaluations of the candidates. The key  idea of their argument is as follows: If a voter’s true grade matches  the median grade for a candidate, then the voter does not have an incentive to assign a different grade.  If a voter’s true grade is greater than the median grade for a candidate, then raising the grade will not change the candidate’s grade and lowering the voter’s grade may result in the candidate receiving a grade that is lowering than the voter’s true evaluation. Similarly, if a voter’s true grade is lower than the median grade for a candidate, then lowering the grade will not change the candidate’s grade and raising the voter’s grade may result in the candidate receiving a grade that is higher than the voter’s true evaluation.  Thus, if voters are focused on ensuring that the group grades for the candidates best reflects their true evaluations of the candidates, then voters do not have an incentive to misrepresent their grades. However, as pointed out in Felsenthal and Machover 2008 (Example 3.3), voters can manipulate the outcome of an election using Majority Judgement to ensure  a preferred candidate is elected  (cf. the discussion of strategic voting in Section 4.1 and Section 3.3 of List 2013).   Suppose that the voter in the middle column  assigns the grade of  4 to candidate \(A\), 0 to candidate \(B\) and 3 to candidate \(C\).  Assuming the other voters do not change their grades, the majority judgement winner is now  \(A\), which the voter ranks higher than the original majority judgement winner  \(B.\)   Consult Balinski and Laraki 2010, 2014 and Edelman 2012b  for  arguments in favor of electing candidates with the greatest median grade;  and Felsenthal and Machover 2008, Gehrlein and Lepelley 2003, and Laslier 2011 for arguments against electing candidates with the greatest median grade.      