What's more important: being in the Dow Jones industrial average, or showing the world you're too cool for conventions like splitting your shares? It's a question that many are asking as the century-old benchmark tries to stay relevant in today's tech-driven economy.

At the center of the debate are Google and Amazon, which just soared past $1,000 a share after strong earnings.

Although no one doubts the internet giants would be near the top of any list of blue-chip companies, the sky-high shares would break the Dow, which weighs companies by price rather than market value. If they went in now and replaced the smallest members, the two stocks would account for 40 percent of the index.

Part of the Dow's problem, at least among Silicon Valley acolytes, is that splitting stock is seen as downright old-fashioned, a fuddy-duddy relic of the 20th century. Driven by everything from index funds to peer pressure, only about 10 companies in the S&P 500 have split their stock annually since 2009, down from around 70 in the 1990s.

"They want to portray themselves as cutting edge, and the Dow industrial just is not that," said Jerry Braakman, chief investment officer of First American Trust in Santa Ana, Calif., where the firm oversees about $1.3 billion. "They'd rather have the cachet of high stock prices being indicative of high-flying tech stocks."

Three years ago, the Dow's overseers won a major battle when Apple Inc. carried out a 7-to-1 stock split and brought its shares in line with other members. Since then, the prejudice against splits has grown. There have been only five in the S&P 500 since January, the fewest in 25 years.

A slew of benefits come with equities trading in the three and four digits. According to a study published by Wolfe Research in August, high-priced stocks have lower volatility, less short interest and lower transaction costs.

But the reluctance to split is starving the Dow of some of the most popular companies. Among the five largest publicly traded companies by value, three are absent from the Dow. Even among existing Dow companies, a gap is quietly opening between the highest- and lowest-priced stocks.

David Blitzer, chairman of the S&P Dow Jones Indices index committee, wouldn't comment on whether the refusal to split is harming the Dow. "Whether a company splits their stock or not is a decision up to the company. It's not up to us," he said.

Wang writes for Bloomberg.