This is far from a comprehensive or fully vetted list, but here are some ideas off the top of my head on the improving institutional decision-making front:

• The Alliance for Useful Evidence
• The UK What Works Centres/Evidence Quarter, particularly the What Works Centre for Wellbeing
• Society for Judgment and Decision-Making
• Society of Decision Professionals
• Behavioural Insights Team and ideas42 (mentioned below by Mati)
• Campbell Collaboration (research syntheses of social science literature)
• Cochrane (research syntheses of medical literature)
• CEDIL (Centre of Excellence for Development Impact and Learning)
• Project Evident
• Hubbard Decision Research
• Strategic Decisions Group

Of these, most operate on a fee-for-service model and wouldn't necessarily be able to make good use of individual donations in the, say, $5k-and-under range. However, I believe that Alliance for Useful Evidence and Campbell Collaboration specifically operate on shoestring budgets and are mostly funded by contributed income, so I'd check into those first if you're considering a donation.

FYI, the improving institutional decision-making (IIDM) coordinating group within EA is working on a resource directory that will eventually be able to answer questions like these in greater detail. We'll be posting more about that on the EA Forum later this month.

Institutional decision making

Updated: 2020-12-08

• Quantified Uncertainty Research Institute
• The Good Judgment Project

Note: I document this here: https://causeprioritization.org/Mechanism_and_institution_design (I might not keep this answer up-to-date, so check out the link)

Note: I don't have the impression The Good Judgement Project has room for more funding. I like what the people behind QURI have been doing (I've been following their work). Disclaimer: I was contracted by both groups, and could be again.

Also, documented here: https://causeprioritization.org/Forecasting :

• Replication Markets
• Social Science Prediction
• Metaculus (is for-profit I think)

Note: I don't know if any of those organizations have room for more funding.

Disclaimer: I am a co-founder.

The Simon Institute for Longterm Governance. We help international civil servants understand individual and group decision-making processes to foster the metacognition and tool-use required for tackling wicked problems like global catastrophic risks and the representation of future generations.

We have a well-researched approach and direct access to senior levels in most international organizations. Given that we just launched, we have no sense of our effectiveness yet but hope to provide a guesstimate by 2023. 

You can donate to us here.

I work for the APPG for Future Generations (https://www.appgfuturegenerations.com) in this space. Or impact report is here: https://forum.effectivealtruism.org/posts/AWKk9zjA3BXGmFdQG/appg-on-future-generations-impact-report-raising-the-profile-1 If you wish to donate please get in touch.

The APPG is affiliated with the Center for the Study of Existential Risk (https://www.cser.ac.uk/) which I behind is the best research organisation with content related to longtermism and improving institutional decision making.

More generally I think Transparency Intentional (https://www.transparency.org/en/) and Global Witness (https://www.globalwitness.org/en/) are the dominant charities in the space of reducing government corruption, a key feature of improving institutional decision making. I have not seen any evaluations of them but I'd reject they'd do well.

See also some of the institutions listed in this article (https://forum.effectivealtruism.org/posts/94QtuT4ss3RzrfH8A/improving-institutional-decision-making-a-new-working-group) under the section on "IIDM within and outside of EA"

FHI's Centre for the Governance of AI

I have not seen anything remotely convincing that the EA community has any insight into how to improve human decision making in group settings, which I believe is how "improving institutional decision making" should be phrased. Institutions do not make decisions. Phrasing this wrong is part of the problem, in my opinion.  The assumption, correct me if I am wrong, being made is that making better decisions is a matter of having better information.  This assumption, ironically,  appears to lack any information about how humans make decisions in groups. For example, people tend very strongly to make decisions that align with their existing beliefs and group commitments. Humans also have the evolved skill of self-deception, which allows us to not know information that conflicts with our beliefs.  Further, there is a thing called "office politics" where the source of an idea greatly or entirely determines whether it is accepted or rejected. 

As for improving global coordination...to achieve what, exactly? If we want to improve global coordination, I believe, we need to suggest plans that benefit all the stakeholders and power holders, as well as achieve whatever benefit we hope to achieve.  I do not believe anyone in EA has an interest in developing such ideas, correct me if I am wrong.  I tried a few years ago to share such ideas, and the reaction was pretty hostile. 

someone I know posted the following names on my facebook post for this ea forum post:

• nested minds network
• Verses
• Aeos (soon)

but I am unsure which organization they are reffering to (could not quickly find websites for some of those)
and I could not find an obvious donation form for those 

RadicalXChange

What does "effective charity" mean in this context?

Global coordination

• Global Challenges Foundation
• Good Country
• Together 1st
• The Stimson Center

Note: I document this here: https://causeprioritization.org/Global_coordination (I might not keep this answer up-to-date, so check out the link)

Note: Inclusion in the list doesn't mean endorsement. I love GCF, but I don't have the impression they need more funding. I feel good about the Good Country. I don't know the other 2 well.

Hummm, seems to me like it would be better to ask a question for institutional decision making and another question for global coordination, no? if you agree, you can edit it and post another:)