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The current karma system of EA Forum, which is described here[1], is based on the assumption that karma is positively correlated with impact (of the post/comment). I think this is pretty reasonable, but how strong is the correlation?

I am also curious about the shape of the relationship between karma and impact. For example, if post Y has twice as much karma as post X, is Y roughly 2 times as valuable as X (linear function), less than than (e.g. logarithmic), or more than that (e.g. quadratic)?

Moreover, what is the impact caused by a post with a given amount of karma? Ideally, one would want an answer in terms of the effect on the expected value of the future, but I understand this is hardly feasible. So, in practice, using heuristics may be better. Examples include donations to the Long-Term Future Fund (or other), and the metric quality adjusted research papers (QARPs) used by Nuño Sempere here.

Example answers

I tried to get a very preliminary sense of the answers to the questions above based on Nuño Sempere’s analysis of the first 10 winners of the EA Forum Prize. I estimated the mean impact in QARPs of each of the posts from the mean between the lower and upper limit of the 80 % confidence intervals provided by Nuño. The calculations are in tab “Posts” of this Sheet.

The table below contains the slope and correlation coefficient for the linear regression of the mean impact on various functions of the karma. It also has the p-value for the null hypothesis that there is no correlation. The calculations are in tab “Statistics”.

Null intercept linear regression between mean impact (QARP) and...

Slope

Intercept

Correlation coefficient (R)

P-value

Logarithm of the karma

0.244

-1.04

0.445

0.269

Square root of the karma

0.0492

-0.407

0.440

0.276

Karma

2.45 m

-0.164

0.433

0.284

Square of the karma

11.8 µ

-0.0427

0.416

0.305

For the logarithm, square root and square of the karma, and karma alone, the correlation coefficient is 0.4, and the p-value 0.3. The differences are quite small given the sample size of 8[2]. Interestingly, the above estimates for the correlation coefficient are similar to the 0.47 obtained by Nathan Young here for the relationship between the inflation-adjusted karma and ranking of the posts of the Decade Review.

The table below shows the correspondence between the scale described here by Nuño and the karma predicted by the linear regression of the mean impact on logarithm of karma, which has the best fit among the 4 presented above. The calculations are in tab “Predictions”.

Mean impact (QARP)

Description

Example

Predicted karma

0.1 m

“A thoughtful comment”A thoughtful comment about the details of setting up a charity

67.0

1 m

“A good blog post, a particularly good comment”What considerations influence whether I have more influence over short or long timelines?

67.3

10 m

“An excellent blog post”Humans Who Are Not Concentrating Are Not General Intelligences

71.0

100 m

“A fairly valuable paper”Categorizing Variants of Goodhart's Law

108

1

“A particularly valuable paper”The Vulnerable World Hypothesis

475

10 to 100

“A research agenda”The Global Priorities Institute's Research Agenda

4.15 k to 40.9 k

100 to > 1000

“A foundational popular book on a valuable topic”Superintelligence, Thinking Fast and Slow

40.9 k to > 408 k

> 1000

“A foundational research work”Shannon’s "A Mathematical Theory of Communication"

> 408 k

The predictions above are quite poor. For instance, they imply:

  • An unreasonably small difference of:
    • 0.367 karma between the impact of “a good blog post, a particularly good comment” and “a thoughtful comment”.
    • 3.67 karma between the impact of “an excellent blog post” and “a good blog post, a particularly good comment”.
  • “A particularly valuable paper” is worth 475 karma, whereas I think the right value is of the order of magnitude of 10 kkarma (with huge variation), i.e. 21.1 times as large.

In any case, one should certainly be mindful of Goodhart's Law, and do not start optimising posts just for karma!

  1. ^

    For interesting discussions of the system, see this post from Arepo, and this one from Nathan Young.

  2. ^

     Nuño evaluated 10 posts, but only scored 8 in terms of QARPs.

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I would not be surprised if there was not a very strong relationship between Karma and impact because people tend to be more likely to browse and upvote topics that are easily legible to them. Thus topics related to AI Safety or charities which people are largely familiar tend to attract readership and favorable voting.

On the other hand, novel ideas tend to not get as much attention because of the higher cognitive load on prospective readers and the feeling that a post is not "for them." I imagine posts with low to medium amount of karma, reflecting approval by a smaller audience that read it carefully, may have much higher impact. When I see posts with hundreds in karma, I often think it's a well known EA figure or someone coming up with a variation of a favorite EA tune.

Even if someone considers the impact of a post to be high, regardless of how much karma it has, it doesn't necessarily mean much because that doesn't discern the worth of the post.

"Impact" needs to be operationalized and it remains infeasible to achieve a consensus on how it should be operationalized. It might be possible in theory to achieve agreement on what counts as an objectively valuable post, though in practice the criteria anyone applies for judging the value of any posts might as well be completely arbitrary.

For example, if my preferred cause is shared as a top priority only by a small minority of the effective altruism community, like invertebrate suffering, every post about that cause will receive way less karma than most other posts. That doesn't change the facts that:

  1. I'll consider the most valuable posts to be ones that have a below-average karma score among all posts.

  2. the posts most effective altruists consider the most impactful may not matter to me much at all.

Once someone becomes a more independent-minded effective altruist, how much post a karma receives matters way less.

Thanks for engaging, Evan!

Even if someone considers the impact of a post to be high, regardless of how much karma it has, it doesn't necessarily mean much because that doesn't discern the worth of the post.

I would say there is a positive correlation between my subjective impression of how impactful the post is, and its worth from an impartial point of view.

"Impact" needs to be operationalized and it remains infeasible to achieve a consensus on how it should be operationalized

Impact has implicitly been operationalised as karma in the EA Forum, to the extent... (read more)