Choosing voting methods is difficult, and no voting method is without flaw. Nevertheless, I am somewhat unhappy with the method proposed here, because it is very difficult for users to support multiple candidates. The problem arises because the method tried to do two things: (1) determine which candidates are in the top three, and (2) determine their relative popularity.
The problem: as a voter who likes two candidates A and B, I cannot support A without harming B, and vice versa. My rational behavior is to allocate all points to either A or B, to maximize the chance that one of them ends up in the top three. If I split my points between two candidates, I face the risk that neither makes it in the top three.
Other voting methods behave better with respect to this problem. For example, if we used approval voting to determine the top three, I could vote for both A and B without one vote harming the other. Similarly, in classical instant runoff voting without weights, I can put A and B at the top of my list, without having to work about negative consequences for either of them.
I think that this problem is best solved with a two-step voting process. In a first step, determine the top three candidates. In a second step, determine relative allocation of money. The second step would probably use different information than the first. This could be done with the current weights, if the first step considered only the order of candidates on the ballots.
My rational behavior is to allocate all points to either A or B, to maximize the chance that one of them ends up in the top three. If I split my points between two candidates, I face the risk that neither makes it in the top three.
I think you are misunderstanding the mechanics of the elimination here. If you allocate nonzero points to both charities, then after one of A and B will be eliminated, all points will be reallocated to the remaining charity. So, to maximize the chance that one of them ends up in the top three, it doesn’t matter much weather to put 50 points on A and B each, or 99 points on A and 1 point on B (and actually, putting all points on one of A and B will do worse than these).
What you write is almost right, but not 100%… we are getting at the heart of the problem here. Thanks for making me re-think this and state it more clearly!
Edited to add: I’ve now also read the discussion that you’ve linked to in your comment. It is now clear to me that the team has thought through issues like this… so I wouldn’t be angry if you prefer to use your time more wisely than for responding to my ramblings :)
Assume as an example that, without my vote, there is the following situation:
candidate A received 933 points from other voters
candidate B: 977 points
candidate C: 1000 points
candidate D: 1001 points
In this case:
If I put most of my votes to A, it gets in the top three along with C and D
If I put most of my votes to B, it gets in the top three along with C and D
If I split my 100 points just right, A and B both get in the top three
I understand that this is a constructed example with low probability of happening. It is meant to illustrate the case where, as a voter, I would like to support two candidates, but my support for one will hurt the other, and vice versa.
As a voter, I’d be particularly vexed if I had allocated 60 votes to A and 40 to B. In that case, I would have caused B to eliminate A, despite having more strongly supported A. This could not happen in approval voting, non-weighted instant run-off voting, or any Condorcet voting method.
As I wrote earlier, no voting system is perfect. For each system, one can construct silly counter-examples for which the system behaves counter-intuitively. For the subproblems “top-3 election” and “funding allocation”, there are known solutions, for which the counter-intuitive situations are somewhat well understood. In your case, you have combined the two sub-problems into one harder combined problem. This makes it more difficult to reason about corner-cases, and creates a few more undesired incentives for strategic voting.
I don’t think this is a critical flaw, so there is no urgent need to change things. If you did choose to change the approach, you might end up with two separate voting steps that are simpler and require fewer explanations than the current system.
Thanks for setting up this donation election!
Choosing voting methods is difficult, and no voting method is without flaw. Nevertheless, I am somewhat unhappy with the method proposed here, because it is very difficult for users to support multiple candidates. The problem arises because the method tried to do two things: (1) determine which candidates are in the top three, and (2) determine their relative popularity.
The problem: as a voter who likes two candidates A and B, I cannot support A without harming B, and vice versa. My rational behavior is to allocate all points to either A or B, to maximize the chance that one of them ends up in the top three. If I split my points between two candidates, I face the risk that neither makes it in the top three.
Other voting methods behave better with respect to this problem. For example, if we used approval voting to determine the top three, I could vote for both A and B without one vote harming the other. Similarly, in classical instant runoff voting without weights, I can put A and B at the top of my list, without having to work about negative consequences for either of them.
I think that this problem is best solved with a two-step voting process. In a first step, determine the top three candidates. In a second step, determine relative allocation of money. The second step would probably use different information than the first. This could be done with the current weights, if the first step considered only the order of candidates on the ballots.
I think you are misunderstanding the mechanics of the elimination here. If you allocate nonzero points to both charities, then after one of A and B will be eliminated, all points will be reallocated to the remaining charity. So, to maximize the chance that one of them ends up in the top three, it doesn’t matter much weather to put 50 points on A and B each, or 99 points on A and 1 point on B (and actually, putting all points on one of A and B will do worse than these).
What you write is almost right, but not 100%… we are getting at the heart of the problem here. Thanks for making me re-think this and state it more clearly!
Edited to add: I’ve now also read the discussion that you’ve linked to in your comment. It is now clear to me that the team has thought through issues like this… so I wouldn’t be angry if you prefer to use your time more wisely than for responding to my ramblings :)
Assume as an example that, without my vote, there is the following situation:
candidate A received 933 points from other voters
candidate B: 977 points
candidate C: 1000 points
candidate D: 1001 points
In this case:
If I put most of my votes to A, it gets in the top three along with C and D
If I put most of my votes to B, it gets in the top three along with C and D
If I split my 100 points just right, A and B both get in the top three
I understand that this is a constructed example with low probability of happening. It is meant to illustrate the case where, as a voter, I would like to support two candidates, but my support for one will hurt the other, and vice versa.
As a voter, I’d be particularly vexed if I had allocated 60 votes to A and 40 to B. In that case, I would have caused B to eliminate A, despite having more strongly supported A. This could not happen in approval voting, non-weighted instant run-off voting, or any Condorcet voting method.
As I wrote earlier, no voting system is perfect. For each system, one can construct silly counter-examples for which the system behaves counter-intuitively. For the subproblems “top-3 election” and “funding allocation”, there are known solutions, for which the counter-intuitive situations are somewhat well understood. In your case, you have combined the two sub-problems into one harder combined problem. This makes it more difficult to reason about corner-cases, and creates a few more undesired incentives for strategic voting.
I don’t think this is a critical flaw, so there is no urgent need to change things. If you did choose to change the approach, you might end up with two separate voting steps that are simpler and require fewer explanations than the current system.