I am thinking about how to calucate the Shapley values for policy work. So far I am just getting confused wo would love your input.
1.
How to think about the case where the government is persuaded to take some action. In general how would you recommend calculating the Shapley value of persuading someone to do something?
If I persuade you to donate out of the goodness of your heart to a charity then I assume you would say that value is impact split between me as the persuader you as the giver (and the charity and other actors). But what if I persuade you to do something for a non-altruistic reason, like I tell you that donating would be good for your companies image and sales would go up, would you imagine that is the same? My naive reading of your post is that in the second case is that I get 100% of the value (minus split with charity and other actors).
2.
How to think about crowd actions. If I organise a ballot initiative on good thing x and then 1.5million people vote for it and it happens and makes the world better. I assume I claim something like 50% of the value (50% responsible for each vote)? What about in the case where there is no actual vote but I use the fact (gathered from survey data) that 1.5million people say they would vote for good thing x and persuade policy makers to adopt x. I assume in this case I get 100% of the value of x as the population did not take action. Is that how you would see it?
Initially I thought I’d calculate the SV by looking at:
Value of coalition {}:
Value of coalition {Gov}:
Value of coalition {Lobbying group}:
Value of coalition {Gov, Lobbying group}:
But this feels a bit ackward, because you’d have to calculate the value of the whole government. So I’d be inclined to do something like:
Value of coalition {}: 0 // State of the world in which neither the government department nor the lobbying group exists.
Value of coalition {Part of the government department}: What would the government department otherwise do.
Value of coalition {Lobbying group}: What would the lobbying group otherwise do.
Value of coalition {Part of the government department, Lobbying group}: What will they both do.
Assuming that Value of coalition {Part of the government department} = 0, Value of coalition {Lobbying group} = 0, they do split the gains, so this is just counterfactual value / 2. If that is not the case, this becomes more complicated, because you’d have to incorporate whatever other group the lobbying group would lobby into the calculation.
But what’s the point of just dividing all counterfactual values by 2? There is no point. The fun begins is there are projects with more stakeholders and projects with fewer stakeholders, in which case the SV would divide total impact by a higher number, i.e., optimizing SV would recommend projects with fewer stakeholders over projects with a larger number, given the same impact.
Also, note that you have to include raised taxes in your calculation, e.g., if you lobby for some large amount of spending, that spending doesn’t come from the void but corresponds to some mix of larger taxes, more debt, prioritization amongst programs, etc.
II.
Well, this depends on whether:
All the votes were necessary
There were plenty enough of votes
If 1, then each participant would get 1/n of the impact. If 2., then this depends, but as there are more and more extra votes, more of the credit goes to the organizer.
I’ve added an example to the shapleyvalue.com website here: <http://shapleyvalue.com/?example=11>, where “An organization organizes a costless online vote to pass a measure of value 1, and it passes if it gets more than 3 votes. 7 people vote in favour.”
Hi Nuno, Great post.
I am thinking about how to calucate the Shapley values for policy work. So far I am just getting confused wo would love your input.
1.
How to think about the case where the government is persuaded to take some action. In general how would you recommend calculating the Shapley value of persuading someone to do something?
If I persuade you to donate out of the goodness of your heart to a charity then I assume you would say that value is impact split between me as the persuader you as the giver (and the charity and other actors). But what if I persuade you to do something for a non-altruistic reason, like I tell you that donating would be good for your companies image and sales would go up, would you imagine that is the same? My naive reading of your post is that in the second case is that I get 100% of the value (minus split with charity and other actors).
2.
How to think about crowd actions. If I organise a ballot initiative on good thing x and then 1.5million people vote for it and it happens and makes the world better. I assume I claim something like 50% of the value (50% responsible for each vote)? What about in the case where there is no actual vote but I use the fact (gathered from survey data) that 1.5million people say they would vote for good thing x and persuade policy makers to adopt x. I assume in this case I get 100% of the value of x as the population did not take action. Is that how you would see it?
Hey,
I.
Initially I thought I’d calculate the SV by looking at:
Value of coalition {}:
Value of coalition {Gov}:
Value of coalition {Lobbying group}:
Value of coalition {Gov, Lobbying group}:
But this feels a bit ackward, because you’d have to calculate the value of the whole government. So I’d be inclined to do something like:
Value of coalition {}: 0 // State of the world in which neither the government department nor the lobbying group exists.
Value of coalition {Part of the government department}: What would the government department otherwise do.
Value of coalition {Lobbying group}: What would the lobbying group otherwise do.
Value of coalition {Part of the government department, Lobbying group}: What will they both do.
Assuming that Value of coalition {Part of the government department} = 0, Value of coalition {Lobbying group} = 0, they do split the gains, so this is just counterfactual value / 2. If that is not the case, this becomes more complicated, because you’d have to incorporate whatever other group the lobbying group would lobby into the calculation.
But what’s the point of just dividing all counterfactual values by 2? There is no point. The fun begins is there are projects with more stakeholders and projects with fewer stakeholders, in which case the SV would divide total impact by a higher number, i.e., optimizing SV would recommend projects with fewer stakeholders over projects with a larger number, given the same impact.
Also, note that you have to include raised taxes in your calculation, e.g., if you lobby for some large amount of spending, that spending doesn’t come from the void but corresponds to some mix of larger taxes, more debt, prioritization amongst programs, etc.
II.
Well, this depends on whether:
All the votes were necessary
There were plenty enough of votes
If 1, then each participant would get 1/n of the impact. If 2., then this depends, but as there are more and more extra votes, more of the credit goes to the organizer.
I’ve added an example to the shapleyvalue.com website here: <http://shapleyvalue.com/?example=11>, where “An organization organizes a costless online vote to pass a measure of value 1, and it passes if it gets more than 3 votes. 7 people vote in favour.”
Hope this was of help