Comparison And Non-manipulability Analysis On The Ordinary Voting Rules

Voting is a representative problem on social choice theory study. At present, voting has applied in true-life and acquired a great deal of effect, but there are some problems. This thesis studies and discussess rational choice of ordinary voting rules and strategy-proof of voting. Firstly, the importance of voting rules study and the necessity of strategy-proofness study are described. The theoretical foundation of voting is introduced. To domestically and internationally ordinary three types of voting rules: plurality voting system,proportional voting system,mixed voting system, analysing their merits,shortcomings and usage scopes. It introduces two famous social choice functions: Condorcet's function and Borda's function. Then, G-S Strategy-proofness Impossibility Theorem —the theoretical foundation of Strategy-proof voting is introduced. On the basis of this analysis, in strict preferences condition , studying and analyzing the property of Multi-valued strategy-proof social choice function, proving the theorem —if a Multi-valued social choice function is strategy-proofness, then it is constant and satisfied with Unanimity. The strategic votings of plurality rule,run-off rule and Borda rule are mainly discussed. The three voting rules can be manipulated are proved. It analyze the three voting rules what situation produces strategic voting and what situation doesn't produce strategic voting. Finally, the problems of village's election and community's election are focused on study. To do research for "the double-simple majority voting", which village's election and community's election use. It studies and discussess ordinary village's voting rules, analysing their merits and shortcomings. All in all, combined the existent problems of actual election, merits,shortcomings and strategic votings of the ordinary voting rules are discussed and studied.