Diversified Investing

In the absence of inside information, on average a diversified strategy should do better unless the person has good judgment.

Unless the investor is a risk lover

This is a no brainer. The only qualification is that the diversified portfolio may not be exactly the market portfolio.

This is the prediction of our basic "no free lunch principle". All my savings are in index tracker, so i am living this view!

I agree with the statement as "doing better" is interpreted to mean enjoying a higher average return for any given level of risk.

for a typical investor I strongly believe a passive, cheap index is better than a passive portfolio of a few stocks

The empirical evidence is overwhelming.

"Do better"understood to capture risk as well as expected return, of course.

A quant hedge fund may extract extra return by big data strategies, but an average guy, like myself, will likely fail with stock-picking.

I don't know of any convincing systematic evidence to the contrary.

Lots of evidence. Few people consistently earn risk-adj. ret > index ret. And even then, much might be compensation for time & effort.
-see background information here

A small industry exists to help naive investors beat the market. It should be subject to mandatory health warnings.

A no-brainer.

I interpret "do better" in terms of a better risk-return tradeoff. Why take unnecessary idiosyncratic risk.

Even if you get it right some of the time eventually you will get it wrong

Assuming a degree of risk aversion. However some investors might rationally want some exposure to assets not available passively.

Just look at the long-term Warren Buffett bet against managed funds -- whenever there is outperformance, fees eat them up
-see background information here