Selected topics in finite mathematics/Weighted voting

Weighted voting is a means of voting or pass (or fail to pass) a motion when the voters may have differing power.

Objectives
Understand weighted voting and critical voters.

Details
A weight is the number of votes that each participant is given and in order for a motion to pass, the number of in votes in favor of a decision must reach a quota. With weighted voting systems there are two important types of voters, one who has veto power and a dummy voter. If one has veto power, their vote is required to pass or gail any motion, and a dummy voter has not influence in any part of the election.

Unreasonable: when it can't pass due to the fact that they pass and fail at the same time

Reasonable: when the motion either fails or passes

Examples
Three entrepreneurs found a company together. But they all invest different amounts. One invests $20,000, another invests $30,000, and the third invests $40,000. Accordingly they own 20, 30, and 40 shares of stock in the company. In case of dispute, a decision is made based on stock, using the weighted voting system [45:20,30,40]. While each founder owns a different amount of stock, it turns out that their voting system is nothing more than a simple two-out-of-three majority.