Because Sunk Costs can encode information, should Sunk Costs really be ignored? Source: p 286, Principles of Economics (7 ed, 2014) by N Gregory Mankiw


  [1.] Economists say that a cost is a sunk cost when it has already been committed
  and cannot be recovered. Because nothing can be done about sunk costs,
  you should ignore them when making decisions about various aspects of life,
  including
  business strategy.


Source: Is the Sunk Cost Fallacy Actually Smart Business? (2013 May 5), based on the research of Sandeep Baliga and Jeffrey Ely. I have not read the paper itself as it appears to need graduate-level Microeconomics and Real Analysis.


  [...] [2.] “We call it the ‘theory of the second best,’” he says. “The more you can remember, the better it is, and you don't have to commit this fallacy at all. But if it's a common feature of human beings that they do forget stuff, then the sunk cost fallacy is an optimal response to that forgetfulness. Sunk costs can encode information about decisions you made in the past, and if that's the case you should take them into account, because if you didn't, you'd make even worse decisions.” [...]


I know that Mankiw's book is for first-timers to microeconomics, but 1 appears to oversimplify the subject of Sunk Costs. Is 2 correct? And does 2 refute 1?

I do understand 2's subtlety: 2 means that Sunk Costs should motivate you to try to determine  the reasons for the past decision, which may or may NOT justify resuming a past action; 2 does not mean that high Sunk Costs oblige you to resume a past action thoughtlessly and always.
It's all about the precise idea these authors are trying to communicate:

A) Mankiew is explaining that we are sometimes too stuborn: we sometimes make a bad investment and then feel some vindication in making another bad investment that might rescue the first one, even though we know it's a bad investment on its own. In abstract terms that can be stated by saying that sunk costs should not be taken into account when evaluating whether to increase an investment in a project. Say you put in 100 dollars in a project (A) and got nothing back but you think if you only put in another 100 you will at least get you original 100 back. However, there is another project (B) that pays you 101 if you put in 100. We have the tendency to try to rescue our bad investment and put our money in project A again, but project B pays us a higher return, and we should go for project B.

B) Baliga and Eli are explaining that although, as Mankiew says, you should not use sunk costs in your calculation of whether a new investment is good or bad, it makes sense to keep track of sunk costs from an informational perspective. If you tend to forget what you did or how well it turned out, then recording your sunk costs in a notebook might help you figure out which were good investments previously and might be good in the future too, or not.