Find the results of the poll with the Borda count method
Perl 5, 131 bytes

for(split/, /,$ARGV[0]){($n,@v)=split/:? /;$s{$v[@v-$_]}+=$n*$_ for 1..@v}$,=": ";map{say++$i,"$_ ",$s{$_}}sort{$s{$b}&lt;=&gt;$s{$a}}@v


Use as perl -E'the string above' 'the input string'