On the 4th Saturday of the month the Philadelphia Math Counts meetup meets at the greatest coffee shop in Philly, Capriccio Cafe & Espresso Bar, to spread Math culture in the city of Philly by discussing videos and books. This month, the meeting is on August 23It's that time of the month, the time for people in Philadelphia to get together and discuss an idea in mathematics. This is later then it should be since I got the book late and have been putting off writing something until I was done with it. Now it's the Monday before and I need something.^{rd}and the discussion is on George G. Szpiro's Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present. As per the usual order of the group, you don't need to see the video to join in the discussion, just come with an interest in the material and two dollars to help make sure we get to continue doing this. Everybody from novices with questions to experts with answers are welcomed, because the regulars fall under both categories. It's fun, informative, and there is a ton of coffee involved. Or tea or bagels, if that's your thing.

This book is not just for math fans. Again, this book is not just for math fans. This is good for everyone who has a problem with "the system". It's a summary of voting systems developed from Plato to modern times, and it outlines the pros and cons of each system.

There is a long history of voting systems, because early on philosophers and thinkers had with problems with the simple "majority wins" system of voting. Namely, Plato thought the majority couldn't be trusted with making decisions. As time went on, others simply saw problems in the system. They felt that the system didn't actually represent the majority.

With 3 possible candidates, the voters cast their votes, and an exit poll is given. The results of the hypothetical election:

8 voters: Candidate A; Candidate B; Candidate C

7 voters: B; C; A

6 voters: C; B; AThe setup is that the first candidate listed is the preferred candidate, and the last candidate is the least preferred by the voters. According to "majority wins", candidate A wins, since he has 8 votes to others 7 and 6 votes. Right here we can see that A is only the preferred candidate of 8 voters, 13 voters wish he would rot in hell. And the problem arises that the majority didn't win.

Throughout the years, mathematicians came up with their own ways of solving this dilemma. More than a few built point systems. The earlist was a system called m-units. The preferred candidate would get

*n*amount of m-units, with

*n*being the number of candidates. In the hypothetical example, Candidate A would get 3 m-units for every first place, 2 for second and 1 for third. In this case, Candidate A would receive 8 * 3 + 13 * 1, or 24 + 13 = 37 m-units. B would get 7 *3 + 14 * 2 = 49 m-units, and C would get 6 * 3 + 7 * 2 + 8 * 1 = 40. Candidate B is the winner in this outcome.

This book is fond of point out that politicians can't not be trusted. And any untrustworthy politician can really mess with a majority vote. With 2 candidates, the majortiy wins is quiet simple.

3 voters: A; B

2 voters B; ASimple, right? The winner is A, no muss, no fuss, and by way of m-units A gets 6 to B's 4. But lets add C back in there:

3 voters: A; B; C

2 voters B; C; AA now gets 11 m-units, B gets 12, and C gets 7. By adding the one candidate who had no chance of winning, the winner changed. Funny enough, this is why Democrats tell me to not vote for third party candidates.

And there are other paradoxes and problems that befall voting systems. An important one to mention here is what congress has to go through in order to gain enough representatives. The American readers are (hopefully) familiar with how the Senate and House of Representatives work. In the Senate, every state gets two senators to represent their states, so that each state gets an equal say for the matters at hand. The House of Representatives assigns 1 congressman to every 30,000 people the country, so that the people get represented in political matters. This ended causing problems every 10 years when the census comes out. Szpiro spends like 3 chapters going through every problem that arose through the history of the United States, there is no way I can do justice to the problems in a paragraph. Quick run-down of an example given in the book:

Three states in the union, Louisibama, Calyoming, and Tennemont. Louisibama has 506, Calyoming has 307, and Tennemont has 187. Total, there's 1000 people. 1 representative per 10 people, so 100 seats are available. Each state gets its number based on its population in the total. So Louisibama would have 50.6 seats, Calyoming would have 30.7 and Tennemont would have 18.7 seats. This is a problem since 0.X of a person isn't possible without an axe murder present. Rounding all the numbers up (51, 31, and 19) would give us 101 seats. So somebody is going to lose a seat.This caused problems for a couple hundred years. Many ideas were tried then scrapped because they either didn't work or somebody with power would risk losing some power. Simply put, politics is not simple and mathematics is left in the hands of people with agendas. It's a good book, and if you're interested, come on down to the Philadelphia Math Counts this Saturday at 110 N. 16th Street , Philadelphia, PA, 19102 to give your two cents, or buy the book here at Amazon or here at abebooks if you're a poor broke writer.

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