How to adjust result to equal mode values in R - r

Question

The code below is generating the mode value considering the columns Method1, Method2, Method3 and Method4. However, notice that for alternative 10 and 12 it has the same mode value, that is, it has a value of 2. However, I would like my Mode column to have different values, as if it were a rank. Therefore, the alternative that had Mode=1 is the best, but I have no way of knowing the second best alternative, because it has two numbers 2 in the Mode column. Do you have suggestions on what approach I can take?
database<-structure(list(Alternatives = c(3, 4, 5, 6, 7, 8, 9, 10, 11, 12),
Method1 = c(1L, 10L, 7L, 8L, 9L, 6L, 5L, 3L, 4L, 2L), Method2 = c(1L,
8L, 6L, 7L, 10L, 9L, 4L, 2L, 3L, 5L), Method3 = c(1L,
10L, 7L, 8L, 9L, 6L, 4L, 2L, 3L, 5L), Method4 = c(1L,
9L, 6L, 7L, 10L, 8L, 5L, 3L, 4L, 2L)), class = "data.frame", row.names = c(NA,
10L))
ModeFunc <- function(Vec) {
tmp <- sort(table(Vec),decreasing = TRUE)
Nms <- names(tmp)
if(max(tmp) > 1) {
as.numeric(Nms[1])
} else NA}
output <- database |> rowwise() |>
mutate(Mode = ModeFunc(c_across(Method1:Method4))) %>%
data.frame()
> output
Alternatives Method1 Method2 Method3 Method4 Mode
1 3 1 1 1 1 1
2 4 10 8 10 9 10
3 5 7 6 7 6 6
4 6 8 7 8 7 7
5 7 9 10 9 10 9
6 8 6 9 6 8 6
7 9 5 4 4 5 4
8 10 3 2 2 3 2
9 11 4 3 3 4 3
10 12 2 5 5 2 2
CHECK
output$Rank <- (nrow(output) + 1) - rank(-output$Mode, ties.method = "last")
output|>
arrange(Mode)
Alternatives Method1 Method2 Method3 Method4 Mode Rank
1 3 1 1 1 1 1 1
2 10 3 2 2 3 2 2
3 12 2 5 5 2 2 3
4 11 4 3 3 4 3 4
5 9 5 4 4 5 4 5
6 5 7 6 7 6 6 6
7 8 6 9 6 8 6 7
8 6 8 7 8 7 7 8
9 7 9 10 9 10 9 9
10 4 10 8 10 9 10 10

Answer 1

OK. Based on OP's comment above, Here's a solution that picks the row with the lowest value of Alternatives in case of ties. You can generalise to any other tie break with an appropriate modification of the second mutate.
output |>
arrange(Mode) |> # Sort by mode
group_by(Mode) |> # Assign intial ranks
mutate(Rank=cur_group_id()) |>
arrange(Rank, Alternatives) |> # Sort and assign tie break
mutate(TieBreak=row_number()) |>
ungroup()
# A tibble: 10 × 8
Alternatives Method1 Method2 Method3 Method4 Mode Rank TieBreak
<dbl> <int> <int> <int> <int> <dbl> <int> <int>
1 3 1 1 1 1 1 1 1
2 10 3 2 2 3 2 2 1
3 12 2 5 5 2 2 2 2
4 11 4 3 3 4 3 3 1
5 9 5 4 4 5 4 4 1
6 5 7 6 7 6 6 5 1
7 8 6 9 6 8 6 5 2
8 6 8 7 8 7 7 6 1
9 7 9 10 9 10 9 7 1
10 4 10 8 10 9 10 8 1
Note that cur_group_id() required dplyr v1.0.0 or later and that row_number() takes account of groups when a data frame is grouped.