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Social Choice_Lecture 6_Yes-No Voting

Social Choice_Lecture 6_Yes-No Voting - Yes-No Voting1 Matt...

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Yes-No Voting 1 Matt Van Essen University of Alabama 1 These slides are based on Chapter 2 of Taylor and Pacelli (2008). Van Essen (U of A) Y/N 1 / 30
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Yes-No Voting Consider the following scenario: The company °Orange LLC± owned by the Van Essen family with three share holders whose ²rst names are: Van, Vanessa, and Essen. After a very unsuccessful travel app introduction, the three shareholders of have called an emergency shareholders meeting to decide the fate of their current vice president of app development, Rhode Tonowhere. The number of shares of stock held by each shareholder is Shareholder Shares Van 101 Vanessa 97 Essen 2 Van Essen (U of A) Y/N 2 / 30
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Yes-No Voting At the start of the meeting, Van makes a proposal to ²re Rhode and search for a replacement. A vote is called, and each shareholder is to vote °yes± or °no.± on Van³s proposal. Question: What voting system should be used in this situation? Is majority rule appropriate? Van Essen (U of A) Y/N 3 / 30
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Yes-No Voting At the start of the meeting, Van makes a proposal to ²re Rhode and search for a replacement. A vote is called, and each shareholder is to vote °yes± or °no.± on Van³s proposal. Question: What voting system should be used in this situation? Is majority rule appropriate? Probably not. Van and Vanessa own most of the company. They should probably have more to say about operations than Essen. A natural suggestion is that each person should have the same number of votes as shares and then establish some critical number of votes for passage. Van Essen (U of A) Y/N 4 / 30
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Yes-No Voting Yes-no voting systems are ones where there is a single alternative pitted against the status quo and each voter must decide whether to respond °yea± or °nay.± The voting system suggested in the example is a special case of a yes-no voting system called a weighted voting systems. Weighted voting systems are an important class of yes-no voting systems. They are appear frequently in application, are often easier to analyze than non-weighted systems (for instance, it is easier to ²gure out which voters posses °voting power± ), and many results concerning them are known. In this set of notes: We will de²ne a yes-no voting system. Examine several real life examples of yes-no voting systems. De²ne a weighted voting system. Look at two ways of determining whether a given yes-no voting system is weighted. Van Essen (U of A) Y/N 5 / 30
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Example 1: The European Economic Community In 1958, the Treaty of Rome established the existence of a yes-no voting system called the European Economic Community. The voters in this system were the following six countries: France, Germany, Italy, Belgium, the Netherlands, and Luxembourg. 2 France, Germany, and Italy were given four votes each.
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