Следующее похоже на работу; могут быть лучшие способы
> df <- data.frame(ID = c(9, 5, 2, 4, 3),
+ group = c("Odd", "Odd", "Even", "Even", "Odd"),
+ nominated_ID = c(9, 8, 4, 9, 2) )
> df
ID group nominated_ID
1 9 Odd 9
2 5 Odd 8
3 2 Even 4
4 4 Even 9
5 3 Odd 2
> nominated_Group <- df[match(df$nominated_ID, df$ID), ]$group
> newDF <- cbind(df, nominated_Group)
> newDF
ID group nominated_ID nominated_Group
1 9 Odd 9 Odd
2 5 Odd 8 <NA>
3 2 Even 4 Even
4 4 Even 9 Odd
5 3 Odd 2 Even