Why is the collective decision of the three judges wrong? Two of the judges believe there was no breach of contract, although for different reasons. Therefore the defendant is acquitted. It seems to me clearly wrong to prefer a separate vote on A and B, round the results off to true/false, and then use those fictitious values to infer C.
The two judges for acquittal need not even have been disagreeing about any matter of substance. Judge 2 found that the defendant’s actions did not meet the contractual definition of what was forbidden, while Judge 3 found that the contractual definition was not what the defendant did, a distinction without a difference. (Judge 1 thinks the other two are just splitting hairs and expects to be vindicated when the plaintiff appeals.)
But here’s the paradox: if the majority of the judges thought (a) was true and (b) was true, then it should have implied that the majority thought (c) was true.
But it doesn’t imply that. There is no such thing as “the” majority. It’s a different majority every time. One might as well say that if someone believes (a) and someone believes (b), then someone must believe (c).
Logical reasoning only preserves truth, not probability, plausibility, desirability, or anything of that sort. So surely property (2) is a non-starter.
Why is the collective decision of the three judges wrong? Two of the judges believe there was no breach of contract, although for different reasons. Therefore the defendant is acquitted.
The paradox demonstrates that there are differences in outcome based on the way you aggregate majorities. It doesn’t claim that one aggregation rule is superior to the other.
That’s another way to say that collective decision isn’t “wrong”—the point of the paradox is to show that it depends on how you choose to measure that decision.
It seems to me clearly wrong to prefer a separate vote on A and B, round the results off to true/false, and then use those fictitious values to infer C.
Naturally. But there are cases where you can’t avoid separate votes on A and B. Pettit provides two cases, which I have reproduced above (see “it is not the case that organizations can always choose to vote directly and ignore preserving collective consistency”).
The obvious case is where you are required to vote on A and B, and infer C from there. This can happen in a procedural context, because that’s just the way someone specified it.
The less-obvious case is where acquiring consensus on C directly is prohibitive or does not reflect the same result as acquiring consensus on A and B. Perhaps C is controversial or people have incentives to lie, but A and B are not. Perhaps A and B were ratified by Congress and now it is upto constitutional scholars to decide on the merits of C without being able to consult Congress as a whole.
Whatever the case, the consequences for decision-making are clear. We cannot build inferences of the form “the majority agreed on A”, “the majority agreed on B” so this implies “the majority agreed on C”. Yet, as the foregoing illustrates, such inferences are sometimes made out of necessity.
The obvious case is where you are required to vote on A and B, and infer C from there. This can happen in a procedural context, because that’s just the way someone specified it.
Nothing is just the way someone specified it. They specified it that way for a reason. It is standard wisdom in politics that if you control the agenda, it doesn’t matter how people vote. If you actually want the voters to decide on C, put that question to them. If the real question of the day is not being put to them, ask why.
It is standard wisdom in politics that if you control the agenda, it doesn’t matter how people vote.
I think I understand the confusion. When I say “vote”, I am not necessarily talking about electorates or plebiscites. In fact, Pettit’s paper is remarkable precisely for also considering situations that have nothing to do with politics or government.
Consider the case of a trust fund that must make decisions for the trust based on how the original creator specified it. For example, they may be charged to make investment decisions that best support a specific community or need. The executors of this trust try their hardest to meet the spirit as well as the letter of these instructions, so they end up adopting rules that require members to vote separately on whether a proposed action meets the spirit of the instructions and whether it meets the letter of the instructions. The rationale is that this ensures the executors as a whole have done their homework and cannot be held liable for missing one or the other requirement through a single vote.
The doctrinal paradox in this case demonstrates you can get different outcomes if you had them vote directly on whether it met spirit and letter, or had them vote separately on the components of the question.
I hope that this explains what I mean by “required to do it” by providing an incentive that has nothing to do with politics. I hope it also encourages a shift towards thinking in terms of systems and their consistency criterions.
I won’t respond to the rest of the comment because discourse about political agenda is not relevant to this discussion.
I think I understand the confusion. When I say “vote”, I am not necessarily talking about electorates or plebiscites.
Neither am I. The “standard wisdom” I quoted applies to the very broadest understanding of “politics”: the theory of collective decision-making.
they end up adopting rules that require members to vote separately on
They didn’t “end up” adopting those rules, they chose those rules. Which are clearly the wrong rules.
In all this I’m also not seeing a place for the people participating in these joint decisions to discuss matters. Having each “voter” (see above) make their decision in isolation, on an agenda set by someone else, who will then combine the votes into a joint decision on questions never put, is a prima facie absurd way to do business, except for the one setting those rules and choosing the questions.
Why is the collective decision of the three judges wrong? Two of the judges believe there was no breach of contract, although for different reasons. Therefore the defendant is acquitted. It seems to me clearly wrong to prefer a separate vote on A and B, round the results off to true/false, and then use those fictitious values to infer C.
The two judges for acquittal need not even have been disagreeing about any matter of substance. Judge 2 found that the defendant’s actions did not meet the contractual definition of what was forbidden, while Judge 3 found that the contractual definition was not what the defendant did, a distinction without a difference. (Judge 1 thinks the other two are just splitting hairs and expects to be vindicated when the plaintiff appeals.)
But it doesn’t imply that. There is no such thing as “the” majority. It’s a different majority every time. One might as well say that if someone believes (a) and someone believes (b), then someone must believe (c).
Logical reasoning only preserves truth, not probability, plausibility, desirability, or anything of that sort. So surely property (2) is a non-starter.
The paradox demonstrates that there are differences in outcome based on the way you aggregate majorities. It doesn’t claim that one aggregation rule is superior to the other.
That’s another way to say that collective decision isn’t “wrong”—the point of the paradox is to show that it depends on how you choose to measure that decision.
Naturally. But there are cases where you can’t avoid separate votes on A and B. Pettit provides two cases, which I have reproduced above (see “it is not the case that organizations can always choose to vote directly and ignore preserving collective consistency”).
The obvious case is where you are required to vote on A and B, and infer C from there. This can happen in a procedural context, because that’s just the way someone specified it.
The less-obvious case is where acquiring consensus on C directly is prohibitive or does not reflect the same result as acquiring consensus on A and B. Perhaps C is controversial or people have incentives to lie, but A and B are not. Perhaps A and B were ratified by Congress and now it is upto constitutional scholars to decide on the merits of C without being able to consult Congress as a whole.
Whatever the case, the consequences for decision-making are clear. We cannot build inferences of the form “the majority agreed on A”, “the majority agreed on B” so this implies “the majority agreed on C”. Yet, as the foregoing illustrates, such inferences are sometimes made out of necessity.
Nothing is just the way someone specified it. They specified it that way for a reason. It is standard wisdom in politics that if you control the agenda, it doesn’t matter how people vote. If you actually want the voters to decide on C, put that question to them. If the real question of the day is not being put to them, ask why.
I think I understand the confusion. When I say “vote”, I am not necessarily talking about electorates or plebiscites. In fact, Pettit’s paper is remarkable precisely for also considering situations that have nothing to do with politics or government.
Consider the case of a trust fund that must make decisions for the trust based on how the original creator specified it. For example, they may be charged to make investment decisions that best support a specific community or need. The executors of this trust try their hardest to meet the spirit as well as the letter of these instructions, so they end up adopting rules that require members to vote separately on whether a proposed action meets the spirit of the instructions and whether it meets the letter of the instructions. The rationale is that this ensures the executors as a whole have done their homework and cannot be held liable for missing one or the other requirement through a single vote.
The doctrinal paradox in this case demonstrates you can get different outcomes if you had them vote directly on whether it met spirit and letter, or had them vote separately on the components of the question.
I hope that this explains what I mean by “required to do it” by providing an incentive that has nothing to do with politics. I hope it also encourages a shift towards thinking in terms of systems and their consistency criterions.
I won’t respond to the rest of the comment because discourse about political agenda is not relevant to this discussion.
Neither am I. The “standard wisdom” I quoted applies to the very broadest understanding of “politics”: the theory of collective decision-making.
They didn’t “end up” adopting those rules, they chose those rules. Which are clearly the wrong rules.
In all this I’m also not seeing a place for the people participating in these joint decisions to discuss matters. Having each “voter” (see above) make their decision in isolation, on an agenda set by someone else, who will then combine the votes into a joint decision on questions never put, is a prima facie absurd way to do business, except for the one setting those rules and choosing the questions.