Exercise $5$: Block Voting Systems Part $2-$ The Deciding Vote $(5$ points$)$

More important than determining how and when ties can occur in a block voting system, we can also determine how many situations arise in which a given block can cast the deciding vote.

E$.$g$.,$ given voting blocks $[1,2,3,4],$ to determine the number of times the last block casts the deciding vote, we observe that:

there are a total of eight ways in which blocks $1,2,$ and $3$ can vote:

$1+2+3($for$)$ vs$.0($against$)1+2($for$)$ vs$.3($against$)1+3($for$)$ vs$.2($against$)1($for$)$ vs$.2+3($against$)2+3($for$)$ vs$.1($against$)2($for$)$ vs$.1+3($against$)3($for$)$ vs$.1+2($against$)0($for$)$ vs$.1+2+3($against$)$

in cases $2-7,$ the last voter $($with a block of $4$ votes$)$ can cause the result to swing one way or the other $($or end in a tie$)$; we therefore say that the last block has the deciding vote in $6$ cases

If you repeat the analysis for blocks $1,2,$ and $3,$ you'll find that they are the deciding voters in $2,4,$ and $4$ cases, respectively $($meaning that the blocks with $2$ and $3$ votes are equally important!$).$

Complete the function deciding$\_$votes$\_$per$\_$block, which will take a list of voting blocks and return a list of times that each block is the deciding vote. You may wish to define a separate helper function that computes the number of deciding votes for a given block.