Relevant rating: Difference between revisions

Line 22:

In Relevant rating, when comparing the total number of ballots approving a candidate X at and above a rating R to a contrasting number, instead of using the ''total number of ballots'' rating X below R as that contrasting number (as in MJ), we use the maximum approval for ''any candidate'' on those complementary ballots. As in [[IBIFA]], this is what renders the method independent of irrelevant ballots, because ballots that don't change the complementary approval winner won't change the relevant rating.

Using a similar process, we could also find the Relevant Rating winner without having to create a full Relevant Ratings ranking of candidates.

Using a similar and much simpler process, we could also find the Relevant Rating winner without having to create a full Relevant Ratings ranking of candidates.

# Initialize the rating level R to MAXRATING

# Initialize candidate totals, '''T(X)''', to zero

# Find all qualifying candidates Q whose total approval at and above rating R ('''TA(Q,R)''') is greater than the maximum approval for any candidate C on ballots that rate Q below R ('''TCA(Q,C,R)'''). If there are no qualifying candidates, then decrement R and repeat.

# Initialize '''TCA(X,C)''' to the highest approval for any candidate on ballots that rate X below R

# If there is more than one qualifying candidate Q, then additionally check whether each Q's total approval ''above'' rating R (that is, Q's total approval for the previous round's rating, TA(Q,R+1)) also exceeds their corresponding current round TCA(Q,C,R). The additionally qualifying candidate with the highest TA(Q,R+1) is the winner. Otherwise [that is, the additional qualification is not met], the candidate with the highest TA(Q,R) is the winner.

# Repeat until a winner is found:

⚫

# If ~~all~~ ~~approval~~ ~~ratings~~ ~~above~~ ~~zero~~ ~~have~~ ~~been~~ ~~exhausted~~, the candidate with the highest ~~total approval~~ is the winner.

## For each candidate X, add ballots rating X at level R to T(X)

## Is '''T(X) > TCA(X,C)'''? If so X is a member of the current qualifying set

⚫

## If the current qualifying set has at least one member Q, the candidate with the highest T(Q) is the winner

## Otherwise, decrement R by one

## Set TCA(X,C) to the highest approval for any candidate on ballots that rate X below the new R

## For each candidate X, is '''T(X) > TCA(X,C)''' (using new TCA(X,C))? If so, then X is a member of a new qualifying set.

## If the new qualifying set has at least one member Q', then the candidate with the highest T(Q') is the winner.

Note that after R is decremented to zero, the new TCA(X,C) will be zero. So the final step after R is zero will always find an approval winner.

[[Category:Monotonic electoral systems]]