I'm going to do something completely out of character and write a TOPICAL post! Yes, I may live underneath a proverbial rock (what, there was an earthquake recently?) but even I am aware that there is a General Election today in the UK. In fact, I was the first person at my polling station to vote this morning!
I've
mentioned in a previous post that I love Lewis Carroll. He combines two of my
favourite things: books and maths (Lewis Carroll is the pen name of
mathematician Charles Dodgson. Please keep up!)
Dodgson
became involved in college elections in the early 1870s at Oxford university
where he was a professor. He became interested in the theory of voting, of the
accuracy and fairness of different voting systems.
First Past The Post
Dodgson
was not a fan of this voting system. He claimed "the extraordinary
injustice of this Method may be very easily demonstrated". He then gives
an example to show how stupid it is:
Suppose
there are 11 electors and 4 candidates a, b, c and d. Each elector ranks the
four candidates in order of preference. The 11 columns here show their choices:
a
|
a
|
a
|
b
|
b
|
b
|
b
|
c
|
c
|
c
|
d
|
c
|
c
|
c
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
d
|
d
|
d
|
c
|
c
|
c
|
c
|
d
|
d
|
d
|
c
|
b
|
b
|
b
|
d
|
d
|
d
|
d
|
b
|
b
|
b
|
b
|
It's easy
to see that a is considered best by three of the electors and second best by
the rest. But in actual fact, it is b who ends up winning, even though he/she
was considered the worst by seven voters.
I don't
think Dodgson looked at "Alternative Vote", although he did write
about lots of other systems.
The Method of Elimination
In this
method, each voter chooses their favourite, and then the one who gets the
fewest votes is eliminated, and the process is repeated (a bit like Big
Brother? The TV show, not the Orwellian thing). This method at first seems
pretty flawless. However, consider the following situation:
b
|
b
|
b
|
c
|
c
|
c
|
d
|
d
|
d
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
a
|
b
|
c
|
d
|
c
|
d
|
b
|
b
|
b
|
c
|
c
|
b
|
d
|
d
|
c
|
d
|
c
|
d
|
d
|
d
|
b
|
b
|
c
|
c
|
b
|
Notice
that a is everybody's first or second choice, and hence appears to be the best
candidate. However, he/she will be eliminated first. c will be elected instead.
The Method of Marks
In this
method, each voter is given a specified number of marks that they can divide
between the candidates. Then the candidate who gets the most marks wins.
Dodgson said that this method would be perfect as long as the voters divided
their marks fairly: giving most to their favourite but some to the candidates
that they wouldn't mind electing. But Dodgson commented that "since we are
not sufficiently unselfish and would assign all our votes to our favourite
candidate, the method is liable in practice to conicide with that of the simple
majority [first past the post] which has already been shown to be
unsound".
I hope you voted today! Let's get rid of the current education-ruining idiots!
Emma x x
x
All
quotes are from Robin Wilson's "Lewis Carroll in Numberland", a book
I highly recommend.
its rigged anyways
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