Percentage of Votes Cast

Date: 06/03/2003 at 12:20:40
From: Mary Pugh
Subject: Using percentage changes on percents

If you have two percentages, say 25% and 50%, can you do a percent 
change between the two?  I don't think it is valid.

It is mathematically possible to do the math, but the outcome seems 
bogus to me.

Date: 06/03/2003 at 14:38:31
From: Doctor Ian
Subject: Re: Using percentage changes on percents

Hi Mary,

Suppose that in 1980, the Revisionist Party received 1% of all votes
cast, while in 2000 it received 2% of all the votes cast.  In which
election did it receive more votes?  

It's not possible to say, without knowing the total number of votes. 
Suppose 60 million votes were cast in 1980, while only 20 million were
cast in 2000. Of course, 1% of 60 million is larger than 2% of 20
million, so the party actually got more votes when it captured a lower
percentage of the total vote. 

In fact, the percentage change in votes received would be 

    (2% of 20 million) - (1% of 60 million)
    --------------------------------------- * 100
             (1% of 60 million)


    4/10 - 6/10
  = ----------- * 100
       6/10

  = -33.3%

However, if you're writing press releases for the party, you'd want to
present things in the best possible light, so you'd focus on the 
change in percentage of the vote, and say that there was a 100%
increase in the percentage of the votes captured by the party (i.e.,
our share of the vote was twice as high in 2000 as it was in 1980). 

Both ways of looking at it are pefectly valid. Even though the second
interpretation seems kind of sneaky and underhanded, in a sense it's
the more interesting one, since the in order to win an election, you
don't have to attain a minimum number of votes. You just have to get a
majority of the votes cast. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/