Last Monday morning, the most widely followed and recognized U.S. index looked different from when it closed the Friday before. The Dow Jones Industrial Average (DJINDICES:^DJI) had swapped out three of its former components for a trio of new ones. That may not seem like breaking news, or anything that investors will ponder for years to come, but let me explain why it may be.

The Dow's weighting methodology
The Dow is a price-weighted index. That means each of its 30 stocks has a greater or lesser influence on the index depending on its stock price. Other indexes, such as the S&P 500, also use a weighting system, but they base their weighting on market capitalization, not share price.

What this means in practice is that the weight of each stock within the index changes with every move higher or lower during the trading day. For example, back on June 19, IBM (NYSE:IBM) traded for $203.99 per share and accounted for 10.24% of the index. The following day, IBM traded at $199.54 and accounted for just 10% of the Dow's value. At the time, IBM was the most heavily weighted Dow component, and it had been for quite a while.

As my colleague Anders Bylund explained on those two days, when IBM would gain or lose 1%, it was adding or subtracting 16 points from the Dow. Meanwhile, Coca-Cola's 0.5% move on June 19 added just 1.5 points to the Dow, since Coke represented only 2.08% of the index that day. Given the stark contrast between the influence of those two stocks, it's easy to see why some investors don't agree with the way the Dow works.

The new Dow and the future
With the removal of Alcoa, Bank of America, and Hewlett-Packard, the Dow cut its three most lightly weighted components. Based on their Sept. 20 closing prices -- Alcoa at $8.29, Bank of America at $14.44, and Hewlett-Packard at $21.22 -- they represented around a combined 2% of the Dow's value.

Their replacements were Visa (NYSE:V), Goldman Sachs (NYSE:GS), and Nike (NYSE:NKE). As of Friday's closing price, Visa is the new top dog on the index with an 8.11% weighting, while Goldman comes in third at 6.8%, and Nike places 18th at 2.95%. That's a combined 17.89% of the index -- quite a contrast from the 2% they replaced.

The changes were necessary. IBM's outsized weight made it control too much of the Dow's moves. The addition of two new higher-priced stocks, combined with the removal of the three stocks at the bottom, rebalanced the Dow and helped tone down the influence of the heaviest components.

I agree with most of the Dow's critics that the price-weighting method has some flaws, and I understand that adding a few higher-priced stocks doesn't really change the underlying problem. But I do think this move will make the Dow a better gauge of the overall economy and a more accurate representation of the stock market -- which, after all, is the real purpose of an index.

Fool contributor Matt Thalman owns shares of Bank of America and Berkshire Hathaway. Check back Monday through Friday as Matt explains what caused the Dow's winners and losers of the day, and every Saturday for a weekly recap. Follow Matt on Twitter: @mthalman5513

The Motley Fool recommends Bank of America, Berkshire Hathaway, Coca-Cola, Goldman Sachs, Nike, and Visa and owns shares of Bank of America, Berkshire Hathaway, IBM, Nike, and Visa. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.