Most equity indices are based on market capitalization. This means that the weights of the companies in the index increase with their (free-float) market capitalizations. Investing in such an index is suboptimal due to index arbitrage.

Therefore it is better to invest in indices based on fundamentals such as Price/Earnings, Price/Sales, etc. So far few asset management companies provide ETF's or index funds that use fundamental weighting of their assets.

One of the exceptions is WisdomTree Investments. This company provides mostly indices that are weighted by dividends. For such an index first the total amount of dividends paid on one or more stock markets is calculated. Then the weights of the companies in the index are their dividends divided by the total dividend amount. Often the number of companies is limited by only including companies that have a market capitalization within a certain range, for instance only the small-caps or only the large caps. Other ways for limiting the number of companies in the index are geographic region, P/E and sector of the economy.

I wonder what the correlation is between this kind of weighting and weightings based on market cap. Obviously there is some correlation, since large companies pay more total dividend that small companies. So this type of index is probably better than an index based on market capitalization but still sub-optimal. Indices based on relative measures such as Price/Earnings, Price/Sales may have less correlation with market-capitalization.

Up to now I have not seen any broad index that uses weights based on a fundamental characteristic that is not correlated with market capitalization. Probably such a strategy is difficult to implement. Consider for instance computing the weights based on P/E. For an individual investor this might be possible. A fund however might end up with large amounts of money in small stocks, making its investments less tradable. WisdomTree has a low P/E ETF (EZY), that  is weighted by earnings.  The low P/E characteristic is in the company selection being is the 30% companies with the lowest P/E. I would imagine that this approach is just as good as using weights based on P/E.

Here is an example on how a weighting based on market can be different from a weighting based on earnings. Recently, on November 5, 2007, PetroChina has IPO-ed. After the IPO PetroChina became the largest company in the world with a market cap of about 1 trillion dollar. Consider now Exxon Mobil, another company in the energy business, with a market cap of roughly half the market cap of PetroChina. So an index weighted by market capitalization would invest twice as much in PetroChina as in Exxon Mobile. However the earnings of Exxon Mobile are about twice as high as the earnings of PetroChina. So an index weighted by earnings would invest twice as much in Exxon Mobile as in PetroChina. In practice most indices use the free-float market cap rather that the full market and PetroChina's free-float market cap is about a third of Exxon's market cap.

Indices using weights based on characteristics such as dividends or earnings tend to shift their assets to the value side. The example above illustrates this. Probably this is a good long term strategy. But some people may want something different than just value stocks. A challenge for asset management companies is to develop indices that select the better growth stocks as well. See also this article.