1

Not triple counting impact

This is a shorter and less rushed version of the argument I made in an earlier post on counterfactual impact, which could have been better in a few ways. Hopefully, people will find this version clearer and more convincing. 

Suppose that we are assessing the total lifetime impact of two agents: Darren, a GWWC member who gives $1m to effective charities over the course of his life; and GWWC, which, let’s assume in this example, moves only Darren’s money to effective charities. If Darren had not heard of GWWC, he would have had zero impact, and if GWWC had not had Darren as a member it would have had zero impact.

When we ask how much lifetime counterfactual impact someone had, we are asking how much impact they had compared to the world in which they did not exist. On this approach, when we are assessing Darren’s impact, we compare two worlds:

Actual world: Darren gives $1m to GWWC recommended charities.

Counterfactual worldD: Darren does not exist and GWWC acts as it would have if Darren did not exist.

In the actual world, an additional $1m is given to effective charities compared to the Counterfactual WorldD. Therefore, Darren’s lifetime counterfactual impact is $1m. Similarly, when we are assessing GWWC’s counterfactual impact, we compare two worlds:

Actual world: GWWC recruits Darren ensuring that $1m goes to effective charities

Counterfactual worldG: GWWC does not exist and Darren acts as he would have done if GWWC did not exist.

In the actual world, an additional $1m is given to effective charities compared to the Counterfactual WorldG. Therefore, GWWC’s lifetime counterfactual impact is $1m.

This seems to give rise to the paradoxical conclusion that the lifetime counterfactual impact of both GWWC and Darren is $2m, which is absurd as this exceeds the total benefit produced. We would assess the lifetime counterfactual impact of both Darren and GWWC collectively by comparing two worlds:

Actual world: GWWC recruits Darren ensuring that $1m goes to effective charities

Counterfactual worldG&D: GWWC does not exist and Darren does not exist.

The difference between the Actual world and the counterfactual worldG&D is $1m, not $2m, so, the argument goes, the earlier method of calculating counterfactual impact must be wrong. The hidden premise here is:

Premise. The sum of the counterfactual impact of any two agents, A and B, taken individually, must equal the sum of the counterfactual impact of A and B, taken collectively.

In spite of its apparent plausibility, this premise is false. It implies that the conjunction of the counterfactual worlds we use to assess the counterfactual impact of two agents, taken individually, must be the same as the counterfactual world we use to assess the counterfactual impact of two agents, taken collectively. But this is not so. The conjunction of the counterfactual worlds we use to assess the impact of Darren and GWWC, taken individually, is:

Counterfactual worldD+G: GWWC does not exist and Darren acts as he would have done if GWWC did not exist; and Darren does not exist and GWWC acts as it would have done if Darren did not exist.

This world is not equivalent to Counterfactual worldD&G. Indeed, in this world Darren does not exist and acts as he would have done had GWWC not existed. But if GWWC had not existed, Darren would, ex hypothesi, still have existed. Therefore, this is not a description of the relevant counterfactual world which determines the counterfactual impact of both Darren and GWWC. This shows that you cannot unproblematically aggregate counterfactual worlds, it does not show that we assessed the counterfactual impact of Darren or GWWC in the wrong way.

To reiterate this point, when we assess Darren’s lifetime counterfactual impact, we ask: “what would have happened if Darren only hadn’t existed?” When we assess Darren and GWWC’s lifetime counterfactual impact, we ask “what would have happened if Darren and GWWC hadn’t existed?” These questions inevitably produce different answers about what GWWC would have done: in one case, we ask what GWWC would have done if Darren hadn’t existed, and in another we are assuming GWWC doesn’t even exist. This is why we get surprising answers when we mistakenly try to aggregate the counterfactual impact of multiple agents. 

Comments (3)

Comment author: Denise_Melchin 29 May 2018 12:27:00PM 2 points [-]

I think it would have been better for you to post this as a comment on your own or Joey’s post. Having a discussion in three different places makes the discussion hard to follow. Two are more than enough.

Comment author: Halstead 29 May 2018 01:29:58PM 0 points [-]

yes fair comment

Comment author: Halstead 29 May 2018 11:14:42AM 0 points [-]

Note that if we make a credit adjustment to the counterfactual impact of each individual agent, such that each gets (say) 50% credit and the aggregated impact adds up to $1bn, it would still be wrong to aggregate this counterfactual impact for the reasons outlined in the last three paragraphs.