Indecisive effect on weighted voting systems
Creators: name: Zhang, Hainan
Publisher: name: No Publisher Supplied
Year: 2022

description: This dissertation studies the impact of indecision on weighted voting systems. A weighted voting system is a decision-making model of voters with unequal powers. To quantify the system performance, system reliability defined as the probability of the system making the correct decision is introduced, which is based on assumptions that the system operates as 2 types of input values (0,1) and 3 types of output values (0,1,x) with 3 types of errors, and voters are unequally weighted and subject to 3 failure-modes (stuck-at-0, stuck-at-1, stuck-at-x). For any weighted voting system, a decision rule is a criterion of how to process the information to generate the final decision. Indecision effect results from one of output values x, where any voter may have no decision on given input values, and it is first considered into the decision rule. To investigate how indecision affects the system performance, this dissertation demonstrates the research in three parts including (1) a threshold weighted voting indecisive system is built, (2) dynamic process on the built system is studied, and (3) a controlled weighted voting indecisive system is generated given unknown inputs. In the first part, a new system is built by considering indecisive effects in the process of decision-making. A generalized threshold weighted voting n-unit indecisive system using a new decision rule consisting of a threshold parameter and a new indecisive parameter is created. The main results imply the high dependence of the system performance from indecisive effect via static parameter initialization, which suggests more research on the indecisive parameter. In the second part, a dynamic process on the indecisive parameter is applied to study system characterization under various situations such as weights change and input types. The results provide a full picture of system performance under the probability distribution of indecisive parameters given different values of threshold and lead the further investigation on prior information of inputs. In the third part, a threshold weighted voting indecisive system with embedded control systems on unknown inputs is designed, where three sub-systems including unknown input observers (UIO), feedforward-feedback controllers (FFC), and the weighted voting system (WVS). To informatize unknown inputs, UIO does the translation of unknown inputs which is used to produce reference inputs in the feedforward controller for disturbances elimination before generating intermediate outputs in WVS, in which, intermediate outputs are monitored in the feedback controller to identify the consistency from reference inputs based on independent final decision criterion. Two major contributions are made from this dissertation including (1) developing a threshold weighted voting system for decision-making when indecision is considered, and (2) developing a fundamental framework on the controlled threshold weighted voting indecisive system when inputs are unknown. Numerical examples are presented to illustrate the generated systems, voting methods, and criteria.