Topics in Contemporary Mathematics
Topics in Contemporary Mathematics MA 103
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This 3 page Class Notes was uploaded by Braeden Lind on Thursday October 15, 2015. The Class Notes belongs to MA 103 at North Carolina State University taught by Chad Mangum in Fall. Since its upload, it has received 8 views. For similar materials see /class/223699/ma-103-north-carolina-state-university in Mathematics (M) at North Carolina State University.
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Date Created: 10/15/15
Study Guide MA103 Test 1 Test 91012 I Describingapplying 4 voting methods a Plurality Method i Contains plurality candidate ii Definition 1 Determines election winner by picking the plurality candidate iii Satisfies Majority amp Monotonicity iv Violates IIA amp Condorcet V Method only looks at first place votes vi Problem with plurality method manipulation by insincere voting b Borda Count Method i Definition 1 Points are assigned to each ranking in preference schedule ii ADVANTAGE POINT takes into account ENTIRE preference schedule not just 1st place iii Satisfies Monotonicity iv Violates Condorcet Majority IIA v used in many sports votes c MPC Method of Pairwise Comparisons i Definition quotmatch up every candidate against every other candidate individually 1 Whichever candidate wins the match up gets 1 point 2 Whoever has most points in the end wins ii Satisfies Condorcet Majority Monotonicity iii Violates IIA iv can lead to ties 1 tiebreakers situation dependent a 1st way run 2 101 method on preference schedule winner of that method wins tiebreaker b 2 1 way use Extended andor Recursive Method to eliminate last place then run method again c 3ml way many other options 2 Total comparisons in an election ofN candidate N1lNl P Plurality with Elimination Method i Definition 1 Continue to do plurality method several times in a row until PLURALITY CANDIDATE is the MAJORITY CANDIDATE 2 In each round candidate with fewest 1st place votes is eliminated The remaining are retallied ii Satisfies Majority iii Violates Condorcet IIA Monotonicity II Stating 4 fairness criteria a Majority Criterion i If candidate X has majority gt5 0 ofvotes of 1St place votes then candidate X should win b Condorcet Criterion i If candidate X is preferred by votes over each of other candidates headtohead then candidate X should win c IIA Criterion i If candidate X wins an election and in a recount one of the nonwinning candidates is removed then candidate X should win in recount d Monotonicity Criterion i If candidate X wins an election and a reelection has changes that favor candidate X and only candidate X then candidate X should win III Describingapplying extended and recursive methods for ranking rank in 155 2nd 3rd 4th nAth a Extended method i Definition rank candidates after ONE application ofwhichever voting method used ii 1 v Nquotth b Recursive method i Definition applying SAME method OVER AND OVER with different inputs each time In particular the outcome of one application of the method depends on the previous one ii Process 1 Apply chosen method MPC PWE Plurality Borda Count 2 Use it to determine a WINNER REMOVE WINNER and obtain new preference schedule with one fewer candidate Apply same method again to the NEW schedule 539quot 1 5 Pick a quotnew winner 9 aka 2 1 place 6 Continue process IV Key terms a Plurality candidate i The candidate with the most first place votes b Majority candidate i The candidate with a majority of 1st place votes c Preference schedule i Tally ofvotes d Insincere voting i When people vote differently than the way they actually feel usually occurs when people have some knowledge beforehand of the possible outcomes of an election V Knowingstating Arrow s Impossibility Theorem a There does not eXist a voting method that satisfies all fairness criteria VI Knowing the HW a OK VII Knowing the following table 9Criterion Majority Condorcet Monotonicity satisfies violates satisfies Borda Count How to figure out problems for Borda Count Method 0 maximum number ofpoints if voters gave candidate 1st place 4 of voters o 4 being an example 0 minimum number ofpoints 1 ofvoters 0 total points of voters5pts 4pts 3pts 2pts 1pt
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