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FULL COMPREHENSIVE NOTEBOOK FOR MATH130: MATHEMATICS IN ACTION

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Course
MATH130

Institution
State University Of New York - Binghamton

FULL NOTEBOOK FOR MATH130: MATHEMATICS IN ACTION. COURSE OFFERED AT BINGHAMTON UNIVERSITY FOR FALL 2023. INSTRUCTOR JAGDEEP SINGH. FRESHMAN/SOPHOMORE LEVEL COURSE. "Emphasizes the real-world significance of mathematics and applications of several areas of mathematics. Topics covered include des...

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Uploaded on September 17, 2024
Number of pages 48
Written in 2023/2024
Type Class notes
Professor(s) Jagdeep singh
Contains All classes

math
math130
mathematics
mathematics in action
binghamton university
voting
systems
numbers
notebook
full notebook
class
jagdeep singh
freshman
sophomore
notes

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,Chapter 1: Voting Systems

voting: typically; candidates run, people vote, votes are counted, majority wins
two-candidate election: only 2 candidates
e.g. stockholders often get a number of votes proportional to the number of stocks
they own

voting methods, 4 categories:
- one person, one vote, two candidates
- one person, one vote, multiple candidates
- one person, multiple votes, two candidates
- one person, multiple votes, multiple candidates

* if there’s 8 votes for A, 5 votes for B, 7 votes for C, 0 votes for D, A wins but
majority voted against A/voted for someone else (12 people)
^ under the plurality method, the candidate with the largest number of votes
is declared the winner; winning candidate may or may not have a majority of votes
(majority: more than half of the votes)

drawbacks of the plurality method
• voters only get to express their first choice (e.g. maybe all 5 people who voted for
B would prefer C over A)

advantages of the plurality method
• if a candidate happens to get a majority, then that candidate will be the winner
under the plurality method
• the plurality method respects the majority criterion (if a candidate receives a
majority of first-place votes, then that candidate ought to be the winner of the
election)
* the majority criterion does not say that a candidate must have a majority in
order to win

,1.2.2: Preference ballots and intro to fairness criteria

preference ballots: the voters rank all or some of the candidates according to their
preferences

preference schedule: each distinct ballot is listed only once, with the number of
occurrences indicated on top

*there’s no simple way to pick a
winner, taking everything into
account and being fair; therefore
different methods have been designed

, What does “fair” mean?
• there are 4 basic fairness criteria that a method may or may not satisfy
• majority criterion was the first
• each voting method fails at least one of the four criteria, therefore there is no fair
voting method (Kenneth Arrow proved the General Impossibility Theorem in
1952, which says it’s impossible to have a voting method satisfying all 4 fairness
criteria)

Borda count method: each candidate gets a certain number of points, depending on
the ranking
• the points for all the ballots are added up
• candidate with the largest number of points win

the basic version of the Borda count method:
• first-choice candidate gets as many points as there are candidates
• second-choice gets one fewer point, and so on

e.g. points for A
4 x (8) + 3 x (0) + 2 x (1) + 1 x (11)
= 32 + 0 + 2 + 11
= 45

points for B, C, D: 57, 58, 40
* C is the winner.

* one of the drawbacks of the Borda count method is that it violates the majority
criterion.

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