Over the past three decades, index-style investing has moved from the fringes to the mainstream, with an estimated $3 trillion now committed to this simple strategy — to match broad market returns and give up as little as possible to fees and taxes.

Clearly, indexing has served investors well and is here to stay. But can it be made even better? Wharton finance professor Jeremy Siegel thinks so. The standard index, which gives more weight to stocks of bigger companies, should be replaced by “fundamental indexing” that assigns each stock a role based on factors like corporate sales or dividend payments, Siegel says. “Capitalization-weighted indices are no longer the best ones for investors. Fundamentally weighted indices will give you superior risk and return characteristics.”

But many index-investing experts are unconvinced. “I don’t believe in new paradigms,” says John C. Bogle, founder of the Vanguard Group mutual fund company, which specializes in traditional index investing.

Traditional indexing allows investors to easily match the overall market’s performance, and new schemes are destined to run afoul of the law of averages, which says it’s near impossible for any investing strategy to beat the broad market’s performance over long periods, according to Bogle. Any short-term advantage offered by fundamental indexing would be negated by higher operating costs that come out of investors’ pockets, he argues.

Debate about tweaking indexing investing strategies simmers most of the time. But it heated up recently as Siegel and Bogle squared off in dueling op-ed pieces in The Wall Street Journal.

In a June 14 piece, Siegel argued that traditional indexes such as the Standard & Poor’s 500 suffered from too much market “noise” — price distortions caused by speculation, momentum investing and other factors. Investors could get higher returns, with less risk, using indexes built upon stocks’ fundamental values, such as dividend payments, he said. “With the advent of fundamental indexes, we’re at the brink of a huge paradigm shift,” wrote Siegel, author of Stocks for the Long Run and The Future for Investors. He is also senior investment strategy adviser to WisdomTree Asset Management, Inc., which in June began marketing a family of exchange-traded funds based on its own dividend-based indexes.

Siegel’s piece drew a June 27 response from Bogle and Burton G. Malkiel, author of the legendary investing book A Random Walk Down Wall Street. Beware anyone pushing an investing strategy based on supposed paradigm shifts, they said, recalling how such a belief — that old-fashioned measures like corporate profits no longer mattered — spurred the disastrous tech-stock bubble of the late 1990s. “While we have witnessed many ‘new paradigms’ over the years, none have persisted,” they wrote. “The ‘concept’ stocks of the Go-Go years in the 1960s came and went. So did the ‘Nifty Fifty’ era that soon followed… .”

The debate centers on the way various indexes are constructed. Most of the major indexes, such as the Standard & Poor’s 500, are based on member companies’ size, or capitalization — each stock’s share price times the number of shares in circulation. Although there are 500 stocks in the S&P 500, “capitalization weighting” gives big companies larger roles.

Exxon Mobil Corp and General Electric, the two largest, each make up just over 3% of the index: Every $100 an investor had in a fund tracking the index would include a little over $3 in each of those stocks. Many smaller companies represent only a fraction of 1% of the index’s weight. That means, for example, that a 10% move in Exxon’s share price will have a much bigger effect on the S&P 500’s value than a 10% move in a smaller company’s share price.

To Bogle and Malkiel, “capitalization-weighted” or “market-weighted” indexes such as the S&P 500 make sense because they accurately reflect the way all investors’ holdings, taken together, are distributed in the market. Investors have more money tied up in Exxon and GE, so an index meant to reflect the market’s changing values should place greater weight on those stocks.

The rise and fall of a market-weighted index will therefore accurately reflect the rise and fall of investors’ fortunes. “I know I will capture my fair share of the total market’s return if I own a market index fund,” Bogle says in an interview. “I don’t know whether these new paradigms will be better or whether they will be worse.”

But Siegel sees problems. Capitalization-weighted indexes, he notes, are based on the “efficient market hypothesis,” which says a stock’s price reflects the market’s best estimate of the firm’s underlying value at any given time. A growing body of research, however, shows that the market’s best estimate is often wrong. “I think it was the tech bubble that alerted people, and particularly me, to the flaws of these cap-weighted indices,” he says in an interview.

According to Siegel, efficient market theory cannot explain why stocks of small companies, as well as those with low share prices relative to their annual earnings, have persistently provided better returns than the market as a whole. If efficient market theory were correct, investors would spot the special values offered by these stocks and rush to buy them. That demand would drive their prices up until those stocks were bargains no longer. Their returns would therefore settle back to the market average.

To explain these stocks’ behavior, he says, efficient-market theorists have resorted to a kind of fudge factor — an assumed role of unseen risks — similar to that once used by astronomers to shrug off unexplained planetary movements when they thought the solar system revolved around Earth.

Often, says Siegel, share prices are driven up or down by temporary factors that have nothing to do with a stock’s true value. Momentum investors, for example, pour money into certain stocks simply because those issues have been rising, not because those investors are impressed by the firms’ fundamental values. The demand causes prices to rise even more.

Similarly, institutions and inside investors with huge blocks of shares may sell simply because they want to diversify their holdings, not because they think those stocks are poor investments. Big sales drive prices down. This “market noise” is behind bubbles and other price changes that cannot otherwise be explained, Siegel says.

Investors suffer as a result, he argues. If market noise drives a stock’s price up to unjustified levels, as in the tech-stock bubble, its market capitalization will rise and that stock will have greater weight in a capitalization-weighted index: It might go from 2% of the index to 3% or 4%, for example. Investors with mutual funds tracking that index will therefore have a larger portion of their money tied up in that stock, even though the smart move would be to reduce that holding as the rising price made it riskier.

Investors would be better served by index funds that are less susceptible to market noise, Siegel contends, echoing arguments made in recent years by several academics. Speculators, momentum players, insiders and institutions have the power to influence share prices — and, hence, market capitalization. But they have little influence on fundamentals like corporate sales figures or dividend payments.

Siegel favors indexes based on dividends. In such an index, all the stocks’ dividends are added together and each stock’s dividends are divided by the total to determine that issue’s desired weight in the index. If dividends of all the fund’s stocks totaled $100 a year, a stock with $2 in annual dividends should have 2% of the fund’s weight. Every $100 invested in a mutual fund tracking this index should therefore include $2 in that stock.

If that stock’s dividend remained the same but its price rose so that it represented more than 2% of the fund, shares would be sold to restore the 2% weighting. And if the share price sank so the weight fell below 2%, shares would be bought.

Using the relatively steady dividend payment figures to determine weightings, the fund would minimize the effects of market noise and reduce volatility. Investors therefore would not automatically see a greater percentage of their money committed to overpriced stocks in a bubble, as they do with capitalization-weighted indexes, Siegel says.

Bogle says, however, that such a fund would end up with weightings that could be quite different from those in the market overall. The market, for example, includes billions held in stocks of companies that pay little or no dividends, but investors using dividend-based fundamental indexing would have little or nothing in those stocks.

Fundamental indexes therefore do not mirror the entire market, only a slice of it, Bogle argues, noting that simple math says that all investors, taken as a group, will enjoy returns matching the broad market, since their holdings make up the broad market. Any individual or group of investors who beat the market must therefore be counterbalanced by others who trail it. While some investing strategies beat the broad market over certain periods, they are usually brought back to earth by the law of averages, Bogle states.

He also doubts that fundamental indexers can match traditional indexers’ low-fee benefits.

Traditional indexers keep costs down by avoiding the need to employ market analysts and stock pickers, and by minimizing the amount of trading they have to do. Because individual stocks’ weightings are allowed to fluctuate as share prices rise and fall, traditional indexers do not have to buy and sell to maintain desired weightings, as a fundamental indexer would, Bogle says. The greater trading costs incurred by fundamental indexers would undermine their performance over time, he argues. In addition, sales to maintain a fund’s desired weightings could trigger year-end capital gains distributions that would be taxable for many investors, further undercutting compounding. “Gross return minus costs equals net return,” he says. “Costs matter.”

Siegel’s firm, WisdomTree, has just begun marketing its 20 fundamentally indexed exchange-traded funds, so they have no track record. But the firm says it has done extensive back-testing to see how its indexes would have performed over various periods through the end of 2005. WisdomTree’s U.S.-stock indexes cover the broad market and smaller slices, such as large, medium and small companies. The firm’s data shows that all six of those indexes beat comparable capitalization-weighted indexes for periods of 1964-2005, 1980-2005 and 1996-2005.

But Bogle counters that such studies are misleading because they all include the most recent six years, when the fundamental indexing strategy would have done exceptionally well in the wake of the burst tech-stock bubble. Indeed, WisdomTree’s back-testing shows all its fundamental indexes produced their best results in the 1996-2005 period.

Since WisdomTree’s funds use an automatic system for weighting each stock, the firm does not need to pay expensive analysts and stock pickers, allowing it to offer some of the same cost advantages traditional indexers have over actively managed funds. But the fund’s costs are not rock bottom. Its expense ratios range from 0.28% of an investor’s assets per year to 0.58%, while some of the cheapest traditional indexers charge only 0.1% to 0.2%.

The firm’s back-testing did not account for management fees, trading costs and other expenses that will be incurred by its funds; Bogle believes the cumulative effect of such costs could be higher than those for traditional indexers, and quite damaging over time. Siegel, however, is confident that when all costs are taken into account fundamental indexers will beat traditional ones.

New investing strategies take time to take root — even Bogle’s ideas about the benefits of indexing did not catch on overnight when he introduced them in the 1970s, although they are widely accepted today. So it will be years before anyone knows for sure whether fundamental indexing will change the investing landscape for the better — or end up on the trash heap of new paradigms.