Yesterday, I wrote that the Securities and Exchange Commission is reportedly looking into rounding of earnings per share.  The point of my post was to call attention to the fact that there is more than one way to round numbers.  Rounding is intended to make numbers less cumbersome reducing the number of digits.  Rounding necessarily results in a reduction of precision and the technique used can bias data when applied repeatedly. 

This lack of precision can have real consequences.  In Germany, for example, a political party must achieve at least 5% of the vote to be seated in Parliament.  In 1992, it was reported that the Green Party had achieved this threshold in a regional election.  Then it was discovered that the computer had been programmed to round up.  To make matters worse, this rounding software had been used for years and no one had ever noticed.  See Debora Weber-Wulff, Rounding error changes Parliament makeup, The Risks Digest (Vol. 13, Issue 37, April 9, 1992).

Truncation similarly reduces the number of digits, but with a lot less muss and fuss.  All that truncation requires is to lop off the undesired digits.  If you want to truncate 3.456 to two decimal places, you simply excise the 6 to make the number 3.45.  It should be no surprise that truncation can lead to anomalous results.   When, for example, the Vancouver Stock Exchange adopted a new index in the 1980s with an initial value of 1000.000, the index soon fell to the low 500 range.  The fall wasn't the result of low stock prices.  Rather, the drop was due to truncation.  As explained by The Wall Street Journal:

The index is based on the selling price of all 1,400 or so stocks listed on the exchange. Every time a stock price changes, which happens 2,800 times on a average day, a computer recalculates the index to three decimal places. The mistake was made in calculating the last decimal place. If the index stood at, say, 540.32567, the computer simply dropped the last two digits, making it 540.325. Instead, it should have rounded off the last digit, making the index 540.326.

Kevin Quinn, Ever Had Problems Rounding Off Figures? This Stock Exchange Has, The Wall Street Journal (Nov. 8, 1983).