They have a policy, as noted in the public document that clarifies how OpenPhil split from Givewell. but I do not know if it the new CoI policy for either org is public. The previous version of the policy, from when OpenPhil was part of Givewell, is here (Note: Link is to a .doc file.)
Excerpt from the previous policy:
"Specifically, there may be no transaction(s) in which any board or staff members have material conflicting interests with the charity resulting from any relationship or business affiliation. Factors that will be considered when concluding whether or not a related party transaction constitutes a conflict of interest and if such a conflict is material, include, but are not limited to: any arm's length procedures established by the charity; the size of the transaction relative to like expenses of the charity; whether the interested party participated in the board vote on the transaction; if competitive bids were sought and whether the transaction is one-time, recurring or ongoing. "
This seems very important and I'm surprised it's been downvoted. Perhaps they've already done so, but it might be valuable for OpenPhil to seriously reconsider its conflict of interest policy.
To answer the question, OpenPhil has a relationship disclosure policy. Before August 2017 they disclosed relationships publicly, but since then have disclosed only internally by default. Unlike the foundations you linked, OpenPhil does not require that employees with conflicts of interest remove themselves from the decisionmaking process for relevant grants. Instead, these conflicts are considered internally before grantmaking decisions are made.
To point out the most obvious conflict of interest, CEO Holden Karnofsky is married to Daniella Amodei and brother in law to Dario Amodei. After OpenPhil donated $30M to OpenAI, the Amodei siblings were promoted to VP level positions at OpenAI. They have since left to cofound Anthropic, which received a $124M Series A from folks including Dustin Moskovitz, the primary funder of OpenPhil. OpenPhil has been fairly transparent about this, stating it in their grant report on OpenAI (and I believe I've seen it elsewhere). But with OpenAI and Anthropic both contributing to the emerging arms race in language models, some have criticized the history of decisions that led to the success of these organizations. Putting optics aside, OpenPhil might want to consider whether a stronger stance against conflicts of interest might have led to different decisions, and whether those decisions would have been better or worse.
Given that the investment didn't go through OpenPhil, saying this involves a conflict of interest is a big stretch.
Back in March 2017, in a writeup about the $30M grant recommendation to OpenAI, OpenPhil were transparent about HK (then-CEO of OpenPhil) being engaged to DA's sister, while DA was a researcher at OpenAI and also a technical advisor to OpenPhil and living in the same house as HK. (This was before the two siblings were appointed to VP positions at OpenAI, which I'm not aware was ever publicly reported by OpenPhil).
As you mentioned in your comment, OpenPhil changed their policy about publicly disclosing relationships. If today OpenPhil faces CoI situations that are similar to the ones they faced when recommending that $30M grant to OpenAI, they may not mention those CoIs publicly at all. It is also possible that the relationship disclosures about the $30M grant are publicly available on OpenPhil's website today only because they were publicly discussed prior to the change in OpenPhil's policy (I don't know whether they were). Quoting from OpenPhil's Relationship Disclosure Policy:
Thank you for sharing.
I wasn't aware that Open Philanthropy had a relationship disclosure policy. I wonder what other policies they have or had to prevent potential "favoritism" in their grantmaking.
Also I would suggest deleting the reference to the other particular relationship. Publicly discussing someone else’s relationships when they haven’t given consent seems unfair, particularly when the grant process didn’t require public disclosure. Given that several conflicts of interest have been voluntarily disclosed, I don’t think we need more examples to have a good conversation.