(In)efficient markets, indices and investors - Martellini explains - brilliant!

Highly recommended: Lionel Martellini's Inefficient Benchmarks in Efficient Markets at the EDHEC Research Institute. Martellini is precise and brief in his explanation of a couple of the slipperiest and most important ideas in finance and investing. Quotes: 

• " ... cap-weighted indices are inefficient benchmarks, regardless of whether or not markets are efficient (keeping in mind that they probably are efficient, at least to a first-order approximation)... " i.e. the implication is that indices like the S&P 500 and the S&P/TSX 60 aren't very good
• " ... When the word “efficient” is used in reference to a market, as in the efficient market hypothesis (EMH) formulated by Eugene Fama in 1970, it suggests that at any given time, prices in the market fully reflect all available information on all stocks in the market. ... " and "... there is a consensus regarding the fact that markets can still be regarded as somewhat efficient ... " i.e. it's not impossible but it's hard to outperform the market, considering fees and costs
• " ... even if markets are efficient, at least up to a first order approximation, investors can still be holding highly inefficient portfolios. The word “efficient”, now applied to a portfolio as opposed to a market, means that the portfolio performance can be improved without any increase in risk through an improvement in the portfolio diversification ..." i.e. it isn't a great idea to invest only in Royal Bank shares even if the price is correct
• " ... empirical evidence also suggests that the average investor holds a severely inefficient portfolio. In other words, the finding here is that the portfolio held by the average investor, which by definition is a cap-weighted index, tends to be poorly diversified. This result is hardly a new finding, ..." i.e. buying SPY (S&P 500 tracker ETF) or even VTI (Vanguard Total US Market ETF) or XIC (S&P/TSX Total Market ETF) is NOT the ideal thing to do.
• "... various alternative weighting schemes have been proposed to improve upon cap-weighting (see Amenc et al. (2011), Arnott, Hsu and Moore (2005), Choueifaty and Coignard (2008), Maillard, Roncalli and Teiletche (2008) to name but a few), and it is now commonly accepted that moving away from cap-weighting tends to enhance diversification and increase risk-adjusted performance over long horizons. ..." i.e. consider dumping SPY and XIC. I think the best practical answer is an empirical matter - if another non-cap-weighted (like equal-weighted, or fundamental weighted) index ETF exists for the asset class with reasonable costs that do not eat up the performance gain (e.g. perhaps PRF, EWI, RSP, PXC, CRQ;