I’m a researcher on voting theory, with a focus on voting over how to divide a budget between uses. Sorry I found this post late, so probably things are already decided but I thought I’d add my thoughts. I’m going to assume approval voting as input format.
There is an important high-level decision to make first regarding the objective: do we want to pick charities with the highest support (majoritarian) or do we want to give everyone equal influence on the outcome if possible (proportionality)?
If the answer is “majoritarian”, then the simplest method makes the most sense: give all the money to the charity with the highest approval score. (This maximizes the sum of voter utilities, if you define voter utility to be the amount of money that goes to the charities a voter approves.)
If the answer is “proportionality”, my top recommendation would be to drop the idea of having only 3 winners and not impose a limit, and instead use the Nash Product rule to decide how the money is split [paper, wikipedia]. This rule has a nice interpretation where let’s say there are 100 voters, then every voter is assigned 1/100th of the budget and gets a guarantee that this part is only spent on charities that the voter has approved. The exact proportions of how the voter share is used is decided based on the overall popularity of the charities. This rule has various nice properties, including Pareto efficiency and strong proportionality properties (guaranteeing things like “if 30% of voters vote for animal charities, then 30% of the budget will be spent on animal charities”).
If you want to stick with the 3 winner constraint, there is no academic research about this exact type of voting situation. But if proportionality is desired, I would select the 3 winners as not the 3 charities with the highest vote score, but instead use Proportional Approval Voting [wikipedia] to make the selection. This would avoid the issue that @Tetraspace identified in another comment, where there is a risk that all 3 top charities are similar and belong to the largest subgroup of voters. Once the selection of 3 charities is done, I would not split the money in proportion to approval scores but either (a) split it equally, or (b) normalize the scores so that a voter who approved 2 of the 3 winners contributes 0.5 points to each of them, instead of 1 point to each. Otherwise those who approved 2 out of 3 get higher voting weight.
This maximizes the sum of voter utilities, if you define voter utility to be the amount of money that goes to the charities a voter approves
This definition of “voter utility” feels very different to how EAs think about charities: the definition would imply that you are indifferent between all charities that you approve of.
A better definition of “voter utility” would take into account the relative worth of the charities (eg a voter might think that charitiy A is 3x better than charity B, which is 5x better than charity C).
I’m a researcher on voting theory, with a focus on voting over how to divide a budget between uses. Sorry I found this post late, so probably things are already decided but I thought I’d add my thoughts. I’m going to assume approval voting as input format.
There is an important high-level decision to make first regarding the objective: do we want to pick charities with the highest support (majoritarian) or do we want to give everyone equal influence on the outcome if possible (proportionality)?
If the answer is “majoritarian”, then the simplest method makes the most sense: give all the money to the charity with the highest approval score. (This maximizes the sum of voter utilities, if you define voter utility to be the amount of money that goes to the charities a voter approves.)
If the answer is “proportionality”, my top recommendation would be to drop the idea of having only 3 winners and not impose a limit, and instead use the Nash Product rule to decide how the money is split [paper, wikipedia]. This rule has a nice interpretation where let’s say there are 100 voters, then every voter is assigned 1/100th of the budget and gets a guarantee that this part is only spent on charities that the voter has approved. The exact proportions of how the voter share is used is decided based on the overall popularity of the charities. This rule has various nice properties, including Pareto efficiency and strong proportionality properties (guaranteeing things like “if 30% of voters vote for animal charities, then 30% of the budget will be spent on animal charities”).
If you want to stick with the 3 winner constraint, there is no academic research about this exact type of voting situation. But if proportionality is desired, I would select the 3 winners as not the 3 charities with the highest vote score, but instead use Proportional Approval Voting [wikipedia] to make the selection. This would avoid the issue that @Tetraspace identified in another comment, where there is a risk that all 3 top charities are similar and belong to the largest subgroup of voters. Once the selection of 3 charities is done, I would not split the money in proportion to approval scores but either (a) split it equally, or (b) normalize the scores so that a voter who approved 2 of the 3 winners contributes 0.5 points to each of them, instead of 1 point to each. Otherwise those who approved 2 out of 3 get higher voting weight.
I’m happy to discuss further.
This definition of “voter utility” feels very different to how EAs think about charities: the definition would imply that you are indifferent between all charities that you approve of. A better definition of “voter utility” would take into account the relative worth of the charities (eg a voter might think that charitiy A is 3x better than charity B, which is 5x better than charity C).