MATH

• Mathematical theory and tools have become valuable in the social sciences, notably in the fields of economics, demography, psychology, and political science, among others.
• Computational methods and modern technology such as geospatial information systems are now routinely used to study and simulate social behavior and social systems.
• Mathematics helps us understand and examine many social issues.
• In the Philippine Congress, the number of seats for a given region is determined by a mathematical formula.
• In a company, power among shareholders is determined by a mathematical formula.
• The US President is elected by a mathematical formula.
• Voting systems can be fair or unfair, as determined by mathematical principles.
• Mathematics can help answer social issues in a more informed and scientific way.
• The upper quota is the standard quota rounded up.
• Hamilton Method 1 involves calculating each state's standard quota, initially assigning each state its lower quota, and then giving surplus seats, one at a time, to states with the largest absolute fractional parts until you run out of surplus seats.
• A state's apportionment should either be its upper or lower quota.
• Lowndes Method 1 starts out as in Hamilton's method, but assigns surplus seats using relative (not absolute) fractional parts.
• The lower quota is the standard quota rounded down to the nearest whole number.
• Apportionment methods that satisfy the quota rule are called quota methods.
• The mathematics related to social issues involves elementary concepts only but arriving at answers can be complicated.
• After studying this module, you should be able to apply four different methods of voting to determine the winner of a ranked election.
• In a voters' election, the Borda Count method awards the victory to candidate B, but this outcome violates the Majority Criterion as candidate A has a majority of first-place votes.
• In a student club election, the plurality with elimination method awards the victory to candidate C, but the Election Committee declared the election null and void due to some irregularity and asked the voters to cast their votes again.
• The preference schedule for a certain election shows that A is the winner using the method of pairwise comparison.
• In a second election, the voters who changed their ranking in the first election expected to be on the winner's side after the new election, but the winner was candidate B, which violates the Monotonicity Criterion.
• You should be able to discuss the concept of principles of fairness in voting and define at least 5 of these principles.
• In the 2000 US presidential elections, George W. Bush won the election despite losing the popular vote to Albert Gore due to the Electoral College system.
• Hillary Clinton won the popular vote in the 2016 US Presidential elections, but Donald Trump won the election due to the Electoral College system.
• Some big and small states have a certain number of electoral votes used for the 2016 US elections based on the 2010 US Census.
• George W. Bush won the 2000 US presidential elections due to the Electoral College system, with the governor of Florida being Jeb Bush, the candidate's brother.
• Albert Gore initially filed a protest against the 2000 US presidential election results, but later withdrew and accepted the election results.
• In the 2016 US Presidential elections, Donald Trump won the election with 290 electoral votes against Hillary Clinton's 232 electoral votes.
• The Electoral College system has been controversial due to allegations of cheating in the 2000 US presidential elections in Florida.
• The Electoral College results can produce surprising results, as evidenced by the 2000 US presidential elections where George W. Bush won despite losing the popular vote to Albert Gore.
• The Electoral College system was first proposed in 1787 and has been used by the US since 1876.
• You should be able to create a hypothetical preference schedule that produces different winners using different voting methods.
• The notion of power as it applies to weighted voting systems can be studied mathematically.
• Many problems in society and government, such as voting, power relations, and fair division and apportionment, can be more clearly understood and analyzed using mathematics.
• Apportioning seats can be affected greatly by simple operations such as rounding-up or rounding-down numbers.
• In Section 2.0, we are reminded that in any society, no matter how democratic, some individuals and groups have more power than others.
• The Banzhaf power index is one way to measure power.
• In Section 3.0, the problem of how to divide certain sets fairly was examined and applied to the process of seat allocations in congress.
• The Plurality with Elimination Method starts by eliminating the candidate with the fewest number of 1st place votes, repeating the process until a candidate with a majority of 1st place votes emerges.
• The Borda Count Method is a weighted voting method where each place on a ballot is assigned points.
• In a Borda Count Method with N candidates, N points are given for first place, N - 1 points for second, and so on, until the last place, to be given 1 point.