There are 1200 students in a school. they are allowed to cast vote either omly for X or Y as their school respect. 50 of them cast vote for both X AND Y AND 24 didnot cast the vote. The candidate Y won the election with the majority of 56 votes more vote than X. 1] how many students cast the vote? 2] how many valid votes are recieved by X candidate? 3] Show the result in venn diagram.
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Answer:
Voting Methods
First published Wed Aug 3, 2011; substantive revision Mon Jun 24, 2019
A fundamental problem faced by any group of people is how to arrive at a good group decision when there is disagreement among its members. The difficulties are most evident when there is a large number of people with diverse opinions, such as, when electing leaders in a national election. But it is often not any easier with smaller groups, such as, when a committee must select a candidate to hire, or when a group of friends must decide where to go for dinner. Mathematicians, philosophers, political scientists and economists have devised various voting methods that select a winner (or winners) from a set of alternatives taking into account everyone’s opinion. It is not hard to find examples in which different voting methods select different winners given the same inputs from the members of the group. What criteria should be used to compare and contrast different voting methods? Not only is this an interesting and difficult theoretical question, but it also has important practical ramifications. Given the tumultuous 2016 election cycle, many people (both researchers and politicians) have suggested that the US should use a different voting method. However, there is little agreement about which voting method should be used.
This article introduces and critically examines a number of different voting methods. Deep and important results in the theory of social choice suggest that there is no single voting method that is best in all situations (see List 2013 for an overview). My objective in this article is to highlight and discuss the key results and issues that facilitate comparisons between voting methods.
1. The Problem: Who Should be Elected?
1.1 Notation
2. Examples of Voting Methods
2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods
2.2 Voting by Grading
2.3 Quadratic Voting and Liquid Democracy
2.4 Criteria for Comparing Voting Methods
3. Voting Paradoxes
3.1 Condorcet’s Paradox
3.1.1 Electing the Condorcet Winner
3.2 Failures of Monotonicity
3.3 Variable Population Paradoxes
3.4 The Multiple Elections Paradox
4. Topics in Voting Theory
4.1 Strategizing
4.2 Characterization Results
4.3 Voting to Track the Truth
4.4 Computational Social Choice
5. Concluding Remarks
5.1 From Theory to Practice
5.2 Further Reading
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1176 students cast the votes because out of total 1200, 24 didn't vote so, n(U)= 1200-24=1176
