Outline Examples of voting system -What should be an ideal voting system Arrow's Impossibility Theorem Main idea of the proof of Arrow's Impossibility Theorem Yes-no voting systems and the dimension of these systems. How to quantify political power -Examples of power indices and their applications to the LEGCO voting system
Outline Examples of voting system What should be an ideal voting system ? Arrow's Impossibility Theorem Main idea of the proof of Arrow's Impossibility Theorem Yes-no voting systems and the dimension of these systems. How to quantify political power ? Examples of power indices and their applications to the LEGCO voting system
Simple majority vote for two candidates When there are only two candidates or alternatives,we can simply use the simple majority vote. The situation is much more complicated if we have at least three candidates or alternatives
Simple majority vote for two candidates When there are only two candidates or alternatives, we can simply use the simple majority vote. The situation is much more complicated if we have at least three candidates or alternatives
Voting Paradox Suppose we have three candidates,A,B and C,and that there are three voters with preferences as follows: Voter 1:A>B>C Voter 2:B >C>A Voter 3:C >A>B For A vs B,A wins(2 to 1) For B vs C,B wins(2 to 1) For C vs A,C wins(2 to 1) ■ Therefore,the requirement of majority rule then provides no clear winner. This is paradoxical,because it means that majority wishes can be in conflict with each other
Voting Paradox Suppose we have three candidates, A, B and C, and that there are three voters with preferences as follows: Voter 1: A> B> C Voter 2: B >C> A Voter 3: C >A> B For A vs B, A wins (2 to 1) For B vs C, B wins (2 to 1) For C vs A, C wins (2 to 1) Therefore, the requirement of majority rule then provides no clear winner. This is paradoxical, because it means that majority wishes can be in conflict with each other
Social Choice Theory Vote Outcome Individual Preferences or Social B C C Voting System Choice/Social D A or Choice List C B A Social Choice A E F E Procedure C B D F Social choice theory studies a given voting system or social choice procedure and describe how individual preferences are aggregated to form a collective preference
M M M E F E … C B A D A F B C C … Individual Preferences Voting System or Social Choice Procedure Vote Outcome or Social Choice/Social Choice List A C B D F M Social Choice Theory Social choice theory studies a given voting system or social choice procedure and describe how individual preferences are aggregated to form a collective preference
Who is your favorite hero A C SUPERMAN B E D
Who is your favorite hero ? A B C E D