I found this interesting problem on the internet. Can someone help?
When a proposal has to be approved, there must be at least 5 more yes votes than no votes. If not, the proposal is rejected.
There are a 26 representatives, but the weights of the vote per representative are divided according to the number of preferential votes in their election. (We assume that there are no abstentions and that no two representatives have exactly the same number of preferential votes.)
The person with the least number of preferential votes receives only one vote with weight 1. The member with the second smallest number of preferential votes gets a vote with weight 2. That with the third smallest number gets weight 4. The member with the fourth smallest number of preferential votes is vote counts for 6. Thus, multiples of 2 continue until the member is elected with the most number of preferential votes in total entitled to a vote with weight 50.
Proof that that the municipal councilor with the least number of preferential votes actually no longer has the right to vote.
There are 651 total weighted votes. A motion requires 328 to pass (vs. 323 against).
For a measure to pass requires an even number of affirmative votes.
All members, excepting the junior member cast an even number of votes.
Suppose we have a really close vote, and the junior member is on the fence, and he hasn't cast his vote yet. Every other vote has already been submitted.
There must be an even number of votes submitted. That means.
Either there are 328 or more votes in the ballot box. And the junior members vote is irrelevant.
Or there are 326 votes or fewer in the ballot box, and the junior member's vote is irrelevant.
The Junior member's one vote is only relevant in the case that there have been 327 votes received and he has the vote to push it over the top. But that is an impossibility.