Unrepresentative Voting

Leslie Green explains how our voting systems can be unrepresentative.

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Five different parties are standing in an election for one representative. The voting  methods:  First past the post (FPTP): the party with the highest vote-count wins.

Is the voting system representative?

The no-pets party has 30% of the total, whereas parties that want pets are the remaining 70%.  As it stands the FPTP system would vote-in the no-pets party, which does not represent the view of the electorate.  What has happened is that the pro-pet movement has splintered, dividing the vote. In order to overcome this, one can use a transferable vote scheme so people can vote for their preferred option safely, preventing the hated no-pets party from winning.

A more detailed analysis can be found in an example.

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First Woman to Win the Abel Prize

Karen Uhlenbeck to win the most prestigious award in mathematics – the Abel Prize.

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The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck of the University of Texas at Austin, USA.

Her theories have revolutionized our understanding of minimal surfaces, such as those formed by soap bubbles.

Niels Henrik Abel (1802–1829) was a Norwegian mathematician. In spite of his short life, he made significant contributions to a variety of mathematical fields.

Markov Chain in Every Day Life

The picture shows a subway map.  A team of inspectors verifies passengers’ tickets at a station on a line, or all lines through it if there are many lines.  Then they randomly choose the next neighboring station and move there to make their inspection.

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Subway map

How many times higher is the probability of being inspected at station C than at station A?

Are you eager to know the answer? Try yourself before reading how Markov Chain helps to solve the problem. The answer is here.

 

 

The perfect explanation is given in the PBS Infinite Series video:

Interesting Maths Facts

 

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  • Notches (cuts or indentation) on animal bones prove that humans have been doing mathematics since around 30,000 BC.
  • Ancient Greeks used little rocks to represent numbers. The name of Calculus means pebbles in Greek.
  • The = sign (“equals sign”) was invented by 16th Century Welsh mathematician Robert Recorde, who was fed up with writing “is equal to” in his equations.
  • The word hundred is derived from the word “hundrath”, which actually means 120 and not 100.
  • Zero (0) is the only number which cannot be represented by Roman numerals.
  • Many Chinese hospitals do not have a 4th floor  because the words four in Japanese, Cantonese, Mandarin and Korean (shi, sei, si, sa) sound the same as the words in those languages for death.
  • Forty is the only number with letters in alphabetical order, while one is the only one with letters in reverse order.
  • The number 5 is pronounced as ‘Ha‘ in Thai language. 555 is also used by some as slang for ‘HaHaHa’.
  • Zero is an even number. Mathematicians remember it. Many people take longer to decide whether it is even or odd.