How can we measure the extent to which academics change their research (either whole projects, or specifics about their research projects) in order to better appeal to grantmakers / future tenure track positions / journal reviewers / etc?

Here I'm referencing the Keynesian Beauty Contest as an allegory mostly.  Researchers aren't incentivized to do the work they think as best -- the incentive is slightly different, and is for "what will the people who will judge your research in the future think is best".

My assumption in asking the question is that this difference in incentives leads to biasing in what science gets done.

I think this is implicitly measured against the alternative of which research direction they would pick if they had full reign to choose their research direction.  (Assuming this motivation differs between researchers, I'm assuming there's at least some components of impact, long term value, or altruism.)

It seems like it would be good to control for, e.g., access to resources (so neither option unlocks vastly more funding), but maybe this would be an important part of it.

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Survey question for researchers who apply for and use grant funding in their research:

If your existing funding could be spent in an unconstrained fashion, what fraction of grant dollars would you spend significantly differently?

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The Fast Grants granters surveyed their grantees on an analogous query:

In our survey of the scientists who received Fast Grants, 78% said that they would change their research program “a lot” if their existing funding could be spent in an unconstrained fashion.

Thanks!  I like this answer a lot since it suggests a nice/easy quantitative version of the question:

If your existing funding could be spent in an unconstrained fashion, what fraction of grant dollars would you spend significantly differently?

I think this scales between 0% (== fully aligned) and 100% (==totally different) research in a pretty straightforward way.

It only captures the "grant dollars" part of the original question (and not, e.g., deciding on a specialization in order to get a better chance at a tenure track position, or changing research in order to get a higher chance of getting past journal reviewers), but that's still pretty valuable.