Many thanks to the early contributors to this discussion. It is exciting to see a diversity of approaches to impact ratings math in these first responses – investors pursue diverse impact strategies, and a primary aim of this discussion board is to help investors think about how to craft an impact ratings math approach that best reflects their particular impact goals and theories of change.
Two of the approaches mentioned in the piece that accompanies this discussion board have been cited thus far: the weighted average approach and the multiplication approach.
Neither of these, as currently formulated (pun oh so intended), manages to simultaneously capture three elements of impact logic that we’ve heard various investors espouse:
1. Some investors ascribe differential weight to different dimensions of impact based on their impact goals and theories of change.
In the 5 Dimensions parlance, some investors’ goals may place a greater emphasis on HOW MUCH impact is associated with an investment rather than WHAT kind of impact its associated with. An investor whose goal is to help realize the SDGs, for example, may want to prioritize investments that advance an SDG for the greatest number of people over those that advance any one particular SDG. Others may want to prioritize those investments that impact underserved stakeholders over those that achieve maximum scale; an education investor, for instance, may choose an investment that improves math scores for a smaller number of students in lowincome communities over an investment that improves math scores for a greater number of students in middle and upper income communities.
The weighted average approach allows for the assignment of weights.
A pure multiplication approach does not allow for the assignment of weights in the traditional manner (i.e. score*weight), though the group & multiply approach allows for the assignment of weights in this way within a group.

Weights

Weighted Average

Yes

Pure Multiplication

No

Group & Multiply

Partial

2. Some investors believe some investments have exponentially greater impact than others.
It makes intuitive sense to many investors (see Jonathan Harris’ comment) that a company that reaches 100x more endstakeholders than a peer working to deliver similar kinds of impact to similar kinds of stakeholders has ~100x the impact.
The weighted average approach often causes a ‘reversion to the mean’ among scores and limits their dispersion, and therefore does not allow for some investments to have exponentially higher scores than others (see Jonathan Harris and Meeta Misra’s comments). While many acknowledge that weighted averages produce an ordinal rather than cardinal ranking, others have pointed out that the weighted average method systematically undervalues the HOW MUCH dimension, and in so doing produces a distorted ordinal ranking of investment impact.
The multiplication approach allows for some investments to have exponentially greater scores than others, particularly when scores are made scalesensitive (see Jonathan Harris’ comment).

Weights

Dispersion

Weighted Average

Yes

No

Pure Multiplication

No

Yes

Group & Multiply

Partial

Yes

3. Some investors believe an investment that receives a score of 0 on any dimension of impact – WHAT, WHO, HOW MUCH, Enterprise Contribution, Investor Contribution, or Impact Risk – has 0 impact.
This idea is a bit more radical, and is an extension of the investor contribution that has gained traction in recent years: if an enterprise would have gotten the same capital, on the same terms (and the same nonfinancial support) in your fund’s absence (i.e. 0 Investor Contribution), your investment won’t have caused any impact that wouldn’t have occurred otherwise. As such, some investors believe an investment with 0 investor contribution should get a 0 on their impact rating – in other words, any investment that causes some nonzero positive impact that wouldn’t have occurred otherwise should be rated higher than any investment that causes no impact to occur that wouldn’t have occurred otherwise (even if the underlying enterprise is highly impactful).
Some have extended this line of reasoning, however, to the other dimensions of impact. Imagine an investment with the following impact profile:
WHAT: 0/5
WHO: 3/5
HOW MUCH: 5/5
Investor Contribution: 5/5
Impact Risk: 4/5
This investment might be causing significant effects that wouldn’t have occurred otherwise (Investor Contribution) for a large number (HOW MUCH) of moderately underserved stakeholders (WHO), but the WHAT score suggests that that effect is not ‘impactful’ – high scores on WHO, HOW MUCH, and Investor Contribution only entail greater impact if the WHAT itself is impactful. An investment in a video game or streaming service company, for example, might have this kind of impact profile, and some investors want their impact ratings to automatically push products like these to the bottom of their prioritization lists.
The same logic can be applied to the other dimensions. If an investment receives a 0 score on WHO, for example, one might argue the total impact is necessarily 0, as in the case of an investment that increases wages (WHAT) for huge numbers (HOW MUCH) of millionaires (WHO) that wouldn’t have occurred otherwise (Investor Contribution); a 0 score on HOW MUCH would imply no one is experiencing the intended impact, even if the target stakeholder group is underserved (WHO) and has articulated a need for the product or service in question (WHAT).
*in the case of impact risk, I have found the logic of a discount factor score (points received/possible points) intuitively resonant for many of the same reasons, though that subject is probably best left for another time.
Any approach that involves addition (weighted average and group & multiply) will not reflect this logic. Pure multiplication does, at the expense of the investor’s ability to apply different weights to different dimensions of impact.

Weights

Dispersion

0 on any dimension = 0 total impact

Weighted Average

Yes

No

No

Pure Multiplication

No

Yes

Yes

Group & Multiply

Partial

Yes

No

Having been troubled initially by this puzzle, I wanted to offer a proposed solution for investors who subscribe to all three of these elements of impact logic for consideration and discussion:
Rating = (WHAT^weight)*(WHO^weight)*(HOW MUCH^weight)*(InvestorContribution^weight)
This formula allows investors to assign different weights to different dimensions of impact; can generate impact scores that are orders of magnitude greater than others; and automatically assigns a 0 score to an investment that receives a 0 on any dimension of impact.

Weights

Dispersion

0 on any dimension = 0 total impact

Weighted Average

Yes

No

No

Pure Multiplication

No

Yes

Yes

Group & Multiply

Partial

Yes

No

Weighted Multiplication

Yes

Yes

Yes

Some investors don’t subscribe to all three of these logics – values alignment investors, for example, do not always hold an explicit aim of causing impact that wouldn’t have occurred otherwise, and as such may want their impact ratings math to allow for investor contribution to affect an investment’s rating, but not rule out those investments with 0 investor contribution.
For those that do subscribe to all three, however:
1. Are there other formulas that reflect all three of these elements of impact logic?
2. Are there other elements of impact logic that an investor may want their impact ratings math to reflect?
3. If not, should all investors use this formula in their impact ratings?