Recreate lists (ballots) from counted results - r

Question

I am at a loss, I feel as if I am finding the answer... but I have been unable to do so. I really don't know where to start
I have the results from ranked voting:
It shows how many votes (100 voters) each candidate (5 candidates) got for each place (reproducible data is at the bottom):
Name 1st 2nd 3rd 4th 5th
Can1 50 0 15 25 10
Can2 15 25 0 10 50
Can3 25 50 10 0 15
Can4 0 10 50 15 25
Can5 10 15 0 0 0
I am trying to recreate ballots from the results, 100 ballots like this (also, some ballots have not been filled completely):
Ballot1: Can1, Can3, Can4, Can5, Can2
Ballot2: Can1, Can3, Can5
Ballot3: Can3, Can5, Can2, Can1, Can4
...
Ballot100: Can2, Can5, Can1, Can4
I need to do this with 60 candidates and more than 1000 votes.
voting.results <- structure(list(X1 = c("Can1", "Can2", "Can3", "Can4", "Can5"),
`1place` = c(50L, 15L, 25L, 0L, 10L), `2place` = c(0L, 25L,
50L, 10L, 15L), `3place` = c(15L, 0L, 10L, 50L, 0L), `4place` = c(25L,
10L, 0L, 15L, 0L), `5place` = c(10L, 50L, 15L, 25L, 0L)), .Names = c("X1",
"1place", "2place", "3place", "4place", "5place"), class = "data.frame", row.names = c(NA,
-5L), spec = structure(list(cols = structure(list(X1 = structure(list(), class = c("collector_character",
"collector")), `1place` = structure(list(), class = c("collector_integer",
"collector")), `2place` = structure(list(), class = c("collector_integer",
"collector")), `3place` = structure(list(), class = c("collector_integer",
"collector")), `4place` = structure(list(), class = c("collector_integer",
"collector")), `5place` = structure(list(), class = c("collector_integer",
"collector"))), .Names = c("X1", "1place", "2place", "3place",
"4place", "5place")), default = structure(list(), class = c("collector_guess",
"collector"))), .Names = c("cols", "default"), class = "col_spec"))

Answer 1

at the beginning would be nice to have this dataset with each candidates and his/her all performances. What was done below it's just repeating each row (candidate, place) by the time it's occurred in voting.results.
df1 is a number of specific places by candidate.
library(magrittr);library(dplyr)
df1 <-
voting.results %>%
reshape2::melt() %>%
mutate( variable = as.integer(gsub("place","",variable) )) %>%
rename(place=variable,can=X1)
head(df1)
# can place value
# 1 Can1 1 50
# 2 Can2 1 15
# 3 Can3 1 25
# 4 Can4 1 0
# 5 Can5 1 10
# 6 Can1 2 0
And df2 is a dataset with row per each performance.
df2 <-
df1[ rep(row.names(df1), df1$value) , ] %>%
mutate(id = 1:n()) %>%
select(-value) %>%
arrange(place)
head(df2)
# can place id
# 1 Can1 1 1
# 2 Can1 1 2
# 3 Can1 1 3
# 4 Can1 1 4
# 5 Can1 1 5
# 6 Can1 1 6
We know that all events have it's winners, so we can initiate each separate event with first candidate (Assuming there is no ex-qequo). And then in every for( e in 1:length(events) ) add candidates at other places. Added candidates are substracted from initial dataset.
If some individuals from initial dataset are not assigned (nrow(temp)>1), then process is repeated until it's finish with success.
i <- 0
temp <- data.frame(1)
while(nrow(temp)>0){
i <- i + 1
temp <- df2[ sample(1:nrow(df2)),]
events <- temp %>% filter(place==1) %>% split(1:nrow(.))
for( e in 1:length(events) ){
for( p in sort( unique(temp$place) ) ){
inAlready <- events[[e]]
toInput <-
temp %>%
filter( !can %in% inAlready$can & place == p) %>%
.[1,]
events[[e]] <- rbind( inAlready , toInput )
}
events[[e]]$event <- e
idToExclude <- lapply( events , function(x) x$id) %>% unlist
temp %<>% filter(!id %in% idToExclude)
}
}
all <-
bind_rows(events) %>%
arrange(event, place) %>%
filter(!is.na(id))
I don't know if it's perfect solution, and how many iterations are necessary, but I hope this will help you find perfect solution. Anyway, probably there is more than one final solutions, so the perfect reproducibility could be impossible. I'm curious if there is some operational-research-like method to solve this problem.
Enjoy and good luck!