I love examples like this. My interpretation of this generally depends on an idea of "Expected Impact", where ex. the difference between $10^6 and $10^9 in terms of lifestyle impact can be smaller than the difference between $10^3 and $10^6. You could assume a logarithmic value function, for example, but each person might have a different function depending on what you would do with the money.

Not that people actually think that way, but you can construct a model where the guaranteed million is the rational choice.

I believe the definition they are using is something like: given a random process X for your percent return, if you invest in n nths of your money into iid copies of X, you will get the same expectation, but with smaller variance compared to putting it all into one copy of X. That's diversification.

You're using a different definition than the one I learned in school. The purpose of diversification, as opposed to simply picking the best asset, is to decrease variance.

Given a choice between two assets, or portfolios, one first maximizes expected value. Between two portfolios of equal expected value, you pick lower variance. That's the rational thing to do if you are managing a fund. The whole risk ratio thing arises only because so many investors are trying to build a well-diversified portfolio and bid up or down the price of assets accordingly. Price in turn affects expected return -- the expected value of the asset.