What properties are used to quantify the odds of a star harboring earth-like life? Say you start with a list of stars. What properties do we believe to be critical in the present existence or future formation of earth-like life in those star systems? How can one reasonably pare down such a list?
To be clear, I'm specifically interested in life as we understand it, on a planet, orbiting a star. Intelligence or complexity isn't necessary to the question. If a star could have planets resembling a young earth, with very simple life, that's fine.
 A: Historically, this was discussed in terms of the Drake equation. The question corresponds to finding the product $f_p n_e f_l$, where $f_p$ is the fraction of stars having planets, $n_e$ the average number of planets that could potentially support life, and $f_l$ is the fraction that actually develop life. Current research seems to show that $f_p$ is of order unity. It's hard to estimate $n_e$ because current technology is best suited for detecting hot jupiters, and we also don't know whether earthlike conditions are necessary in order to support life -- although they are certainly necessary in order to support earthlike life as in the question. I don't think we have any hard evidence about $f_l$; if microbial life is proved to exist or to have existed on Mars, that would suggest that $f_l$ is rather large. Ward 2009 gives a pessimistic estimate for $n_e$, based on factors that they think make our planet special, such as a large moon and the right concentration of heavy elements in the primordial cloud from which our solar system formed. One possible interpretation of the Fermi paradox is that the product given by the full Drake equation is small, i.e., we're the only technological civilization in our galaxy.
Ward and Brownlee, Rare Earth: Why Complex Life is Uncommon in the Universe
