Question

In a corporation, the shareholders receive 1 vote for each share of stock they hold, which is usually based on the amount of money the invested in the company. Suppose a small corporation has two people who invested $30,000 each, two people who invested $20,000 each, and one person who invested $10,000. If they receive one share of stock for each $1000 invested, and any decisions require a majority vote, set up a weighted voting system to represent this corporation’s shareholder votes.

Answer 1

shareholders A and B will each have 30 votes (each invested $30,000)

shareholders C and D will each have 20 votes (each invested $20,000)

shareholder E will have 10 votes (only invested $10,000)

total number of possible votes = (30 x 2) + (20 x 2) + 10 = 110 votes

any decision must be approved by more than 50% of the votes, but since the votes are bundled in tens, 60 votes are needed.

Stockholders number of

A B C D E positive votes win

yes no no no no 30 no

yes yes no no no 60 yes

yes no yes no no 50 no

yes no no yes no 50 no

yes no no no yes 40 no

yes yes yes no no 80 yes

yes yes no yes no 80 yes

yes yes no no yes 70 yes

yes yes yes yes no 100 yes

yes yes yes no yes 90 yes

yes yes yes yes yes 110 yes

no yes no no no 30 no

no yes yes no no 50 no

no yes no yes no 50 no

no yes no no yes 40 no

no yes yes yes no 70 yes

no yes yes no yes 60 yes

no yes no yes yes 60 yes

no yes yes yes yes 80 yes

all other combinations result in negative outcome (less than 60)