Weighted voting systems: The decision making time aspect

摘要

The weighted voting system (WVS) consists of n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction x of the cumulative weight of all non-abstaining units (threshold). Otherwise, system output is 0. The system input is either 0 or 1. Every unit is characterized by probability of making decisions 0 and 1 and by probability of abstaining for each input. The system fails if its output is not equal to its input. The decision time of the entire WVS composed from voting units with different constant decision times can vary. In some cases the decisions of the slow voting units do not affect the decision of the entire system since this decision becomes evident after the fast units have voted. This happens when the total weight of units voting for the proposition acceptance or rejection is enough to guarantee the system decision independently of the decisions of the units that have not voted yet. In such situations the voting process can be terminated without waiting for slow units' decisions and the WVS decision can be made in a shorter time.