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Suppose there is election such that $n$ votes are given to $m$ candidates. I would like to express the results of elections in two decimal places, like

0.13
0.15
0.03
...

Suppose further that after listing those numbers, the decimal numbers add to, say 1.03 due to rounding offs. What is the correct method to express the result? Should I divide the 0.03 to three candidates who got highest number of votes to minimize the relative error or what kind of method I should use?

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  • You're rounding, I think it's fine to have the total not add up to $1$. Otherwise you have to make arbitrary decisions that are not necessarily right or wrong. I would say that you should 1) only round up or down in the least significant digit (e.g. if Bob gets 15.657%, which you then round to 15.66%, you shouldn't "fix" Bob's value by giving him 15.67%, it should either by 15.66% or 15.65%) and 2) your rounding should preserve the correct order (e.g. if Bob gets 15.657% and Lucy gets 15.656%, your rounding scheme shouldn't give Bob 15.65 and Lucy 15.66). – Jared Nov 23 '14 at 00:47

1 Answers1

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It might be better to say "Components may not sum to $1$ (or $100\%$) due to rounding". A Google search suggests this kind of statement is common.

This was discussed in a stackoverflow question.

If you are interested, I once wrote a note on the likely distribution of rounding errors. In it I looked at the UK general elections in 2001 and 2005, where there were a total of $6873$ candidates in $1305$ constituency contests. The rounded percentages per candidate added up to 

 total    times
 99.8%      11  
 99.9%     261
100.0%     774
100.1%     249
100.2%      10
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Henry
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