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Algebra/Two candidates having same number of votes.

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Question
Dear Prof Scott

Is the following question valid?
In a election out of n number of candidates standing, find out the probability of two candidates having the same number of votes?

Is further information required for this probability question?

Thanks
Prashant

Answer
Yes, it is possible.  However, it is not very likely.
I'll assume that the election has a 50-50 chance of voting for two choices.

Let's suppose that only 20 people voted on something.

To get the election to come out with 10 people voting yes and 10 people voting no would be
[20!/(10!10!)][0.5^20], and that is exactly 1/184576.

Now that possibility is quite small, and that only deals with 20 people voting.
Here, in the USA, there are 50 states in this nation and 20 or more counties in each state.

Note that here in the USA, most cities are in one county unless they are really large.
Then the city takes up a few counties.  That means there are usually thousands voting in a county election (millions if the county is a section of New York, Chicago, San Francisco, Seattle, etc.) millions of people voting in a state election (and tens of millions in New York, California), and 100's of millions voting in the country election (it can get up over 300,000,000 if every voter voted - now perhaps over in your country that's written as 300.000.000??).

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Scott A Wilson

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I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

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