Suppose Socrates sidles up to you as you head towards the agora. He wants to ask you a series of questions. You let him to do so and, after each question is asked, you pretend to think about it and then agree with him. Socrates is delighted. He then says 'since you have agreed to everything else so far you must agree to whatever stupid shite I'm babbling about'. You tell him you don't agree at all. Nothing at all is entailed by your assenting to a series of propositions. He may hope otherwise because he thinks those propositions are closely tied to states of the world. But they aren't really. They are merely words. One way forward is to say 'we are not concerned with words but the beliefs that words testify to. Beliefs are important because they cause actions.' However this is not necessarily the case. There is nothing stopping us from having all sorts of crazy, mutually contradictory beliefs. Thus talk of 'belief merging' adds no value. All we can say is that such and such action correlates with such and such expected state of the world. One can always fudge the aggregation or merging rule after the fact to show consistency. But one could equally explain everything by referring to the misadventures of the Nicaraguan horcrux of the neighbor's cat.
Of course, in practical matters, there may be contractual or other obligations which require you to act as a 'reasonable person' or to have acceptable 'beliefs'. It may be that this is defined by relevant authorities to mean accepting a close link between propositions or beliefs and states of the world. To give an example the proposition 'serve tea to customers by giving them tea not by pissing in their mouth' entails, by prevailing custom, actually serving tea to customers in the manner stipulated in your contract. Your contention that the tea purveyed by your employer is an inferior type of piss and thus your action in micturating into the open mouths of customers was actually a superior type of fidelity to your contract of employment may not find widespread credence. Still, it may be accepted as a defense in law against an action for breach of contract. What matters is whether the employer considered this a likely outcome at the time when the contract was made. Thus, if a restaurant hires a person who is notorious for pissing in the mouths of customers who are foolish enough to ask for tea rather than whiskey, then no matter what the wording of the contract suggests, no breach actually occurred.
Propositions aren't states of the world. Nor are beliefs necessarily connected to actions which alter states of the world. We may, for a specific purpose, say that assenting to such and such proposition means holding a particular belief and then doing a particular action intended to bring about a specific state of the world. Failure in such a case may be justiciable or otherwise attract a penalty. However, in this case it is not the proposition but the action which is relevant. A person who reliably performs the action required may gain the stipulated consideration even if she explicitly rejected the proposition or had no belief in its efficacy.
It follows that there is no 'discursive dilemma' or 'doctrinal paradox' because neither discourse not doctrine is closely tied to states of the world either at the level of the individual or the group. Justiciability, however, may arise purely on the basis of consideration passing without the required action being performed. However, there may be non judicial penalties which are of greater salience.
The Stanford Encyclopedia of Philosophy says re. The ‘doctrinal paradox’ and the ‘discursive dilemma’
Kornhauser and Sager (1986) described the following problem. (A structurally similar problem was discovered by Vacca 1921 and, as Elster 2013 points out, by Poisson 1837.) A three-judge court has to make judgments on the following propositions:
- p: The defendant was contractually obliged not to do action X.
- q: The defendant did action X.
- r: The defendant is liable for breach of contract.
According to legal doctrine, the premises p and q are jointly necessary and sufficient for the conclusion r. Suppose the individual judges hold the views shown in Table 5.
Table 5: An example of the ‘doctrinal paradox’
p (obligation) q (action) r (liability) Judge 1 True True True Judge 2 False True False Judge 3 True False False Majority True True False
Although each individual judge respects the relevant legal doctrine, there is a majority for p, a majority for q, and yet a majority against r—in breach of legal doctrine. The court faces a dilemma: it can either go with the majority judgments on the premises (p and q) and reach a ‘liable’ verdict by logical inference (the issue-by-issue or premise-based approach); or go with the majority judgment on the conclusion (r) and reach a ‘not liable’ verdict, ignoring the majority judgments on the premises (the case-by-case or conclusion-based approach). Kornhauser and Sager's ‘doctrinal paradox’ consists in the fact that these two approaches may lead to opposite outcomes.
But the Judges could simply award trifling damages or else invoke an equitable doctrine (such that Judges decide the facts) . However, to properly discharge their duties, Judges are obliged to argue over 'p'. If one judge has a different opinion it ought to be on good enough grounds to merit setting out in detail in a minority opinion. This would also give us information about the Judge's 'ideology'- e.g is he a positivist, an originalist, or whatever. Disagreements about facts should trigger asking for more information or else if the thing is de minimis or if it would be inequitable and against public interest to put the defendant through any more pain, then the case may be dismissed with trifling damages. Higher courts- e.g in Florida- may uphold a patently illogical decision of a lower court on the 'tipsy coachman' principle. It doesn't matter if the thing was not done properly provided the right destination was reached.
We can learn another lesson from this example. Relative to the legal doctrine, the majority judgments are logically inconsistent.
Judges may screw up same as other people. It sounds as though there are grounds for appeal in this case.
Formally expressed, the set of majority-accepted propositions, {p, q, not r}, is inconsistent relative to the constraint r if and only if (p and q). This observation was the starting point of the more recent, formal-logic-based literature on judgment aggregation (beginning with a model and impossibility result in List and Pettit 2002).
List and Pettit write-
Thus we are not really speaking of legal judgments where degree of confidence is very important. A conviction is unsafe if the degree of confidence in it is not very high relative to the severity of the verdict. Thus, a Civil action- where liberty is not imperiled- may have a different outcome from a Criminal action. Thus O.J had to pay damages for a crime of which he was not convicted.
This suggests that judgments which have big consequences are essentially different from those which don't much matter. We may be willing to judge the actions of some far away country to be wrong. We may not at all be willing to go to war with them- more particularly if this would involve a total mobilization of our resources which would have profound sociological effects.
More generally, there is an 'aggregation problem' at both the individual and the group level with respect to 'life changing' decisions. Most of us behave sub-optimally because the underlying utility function is not decomposable or amenable to 'divide and conquer' type heuristics. Thus mimetic effects may lead to saltations rather than 'incremental' change. It as though we were one type of person for the longest time and then abruptly become a completely different type. One reason why has to do with regret-minimization under uncertainty. A set of non-decomposable relations may have two different 'common knowledge' 'concrete models' with very different characteristics but nothing in-between. It is 'regret minimizing' to allow sub-optimality to increase till one is ready to leap to the next 'concrete model'. C Northcote Parkinson observed that Chinese entrepreneurs remained poorly housed- which was sub-optimal given their income- but then suddenly broke 'the hound barrier'- i.e. moved into a mansion with a big garden and fierce attack dogs to protect the property. Why was this regret-minimizing? How come the Chinese entrepreneur didn't make step by step progress up the property ladder? The answer has to do with 'concrete models' (i.e. models of 'belief-fusion' which are robust by common knowledge) of 'face' (i.e. what is required of an agent discharging a particular socio-economic function of a hierarchical type) and what 'face' involved in terms of 'guanxi' (i.e. power within relationships). Back then, in Hong Kong, there was the type of face possessed by a small time hustler living in the slums and then there was the very different type of face possessed by the rich guy living cheek by jowl with the Colonial masters. No doubt, there was something in-between, in terms of housing, but that was for professionals, not business people, who had a different type of face. An entrepreneur in the slums could break the 'hound barrier'. One who moved to the professional neighborhood might cease to be an entrepreneur and lapse into genteel poverty.
Individuals don't act like the individuals they actually are (from the perspective of 'functional dependencies')- e.g a guy living like a menial worker though he is earning more than a Doctor- because of problems of decomposability and regret minimization. But the same is true of groups large and small. In both cases, there is 'buck stopping' featuring abrupt saltations. In America we might speak of the Roe v Wade era which some fear may now be coming to an end. No doubt, one can see incremental processes at work but the fact remains that these were saltation events. What had happened before could be dismissed as 'noise' not signal. Then the signal changed and everything changed.
Why? The answer is that the focus had shifted from 'propositions' and 'assent' or 'dissent' to an accomplished 'state of the world' which supported a new type of lebenswelt and created a new type of politics.
At any given moment, there may be plenty of 'discursive dilemmas' or 'doctrinal paradoxes'. But few- or none- of them will be associated with any actual change in the state of the world. This is because they are merely mental masturbation.
Consider the following-
The possibility of inconsistent majority judgments is not tied to the presence of a legal doctrine or other explicit side constraint (as pointed out by Pettit 2001, who called this phenomenon the ‘discursive dilemma’).
So the thing isn't tied to states of the world. This is genitalless wanking.
Suppose, for example, an expert panel has to make judgments on three propositions (and their negations):
Expert panels will talk worthless virtue signaling bollocks because 'expert' is a posh word for lying bastard.
- p: Atmospheric CO2 will exceed 600ppm by 2050.
- if p then q: If atmospheric CO2 exceeds this level by 2050, there will be a temperature increase of more than 3.5° by 2010.
- q: There will be a temperature increase of more than 3.5° by 2010.
If individual judgments are as shown in Table 6, the majority judgments are inconsistent: despite individually consistent judgments, the set of majority-accepted propositions, {p, if p then q, not q}, is logically inconsistent.
Table 6: A majoritarian inconsistency
p if p then q q Expert 1 True True True Expert 2 False True False Expert 3 True False False Majority True True False
As a matter of fact lots of 'expert committees' do talk this sort of bollocks. It may have some signaling effect and help some of them make more money. But you can always pay people to talk stupid shit. Alternatively, you can recruit nutters specifically for the task.
Proposition-wise majority voting may appear 'strategy proof'. But it isn't really. A particular proposition may mean something different to different people. It is not closely enough tied to a state of the world. Furthermore, if there is a mechanism by which some may escape the consequences of a particular decision, you could get perverse results. It may also appear that such decision making is inconsistent. However, a rational explanation can always be found which removes the supposed inconsistency.
Dietrich & Liste (2013) write approvingly of the notion that a
group’s judgment on any proposition should be determined by the individual members’ judgments on it. Call this the idea of propositionwise aggregation, or technically, independence. This idea is naturally reflected in the way in which we normally make decisions in committee meetings, conduct referenda or take votes on issues we want to adjudicate collectively.
Actually, provided transparency is lacking, people within groups let themselves be influenced by those who seem smarter or better informed. The feeling that occult coalitions exist and that we aren't getting paid off like other people may cause us to demand 'independence'. But this is sub-optimal if information asymmetry obtains.
Propositionwise aggregation can further be shown to be necessary for the non-manipulability of the decision process, both by strategic voting (Dietrich and List2007b, see also Nehring and Puppe 2002) and by strategic agenda setting (Dietrich2006a;List 2004).
Only if you accept various crazy or incompossible assumptions.
Yet the recent literature on judgment aggregation demonstrates that propositionwise aggregation is surprisingly hard to reconcile with the rationality of the resulting group judgments.
We all agree that we should have our cake and eat it too.
A sequence of by-now much-discussed results (beginning with List and Pettit 2002,2004) shows that, for many decision problems, only dictatorial or otherwise unattractive aggregation rules fulfil the requirement of propositionwise aggregation while also ensuring rational group judgments
In other words, we only get smart decisions if we let smart people make them.
Algorithmic decision procedures of any sort must have limited domains and 'fail safe' features- i.e. meta rules such that they are disregarded if nonsensical. There may be, after the fact, a way to give 'univalent foundations' or 'harmonious construction' to a body of judgment but this would involve type theory and 'buck stopping' mechanisms.
It would be crazy to consider the following to be desirable conditions on an aggregation rule:
Universal domain: The domain of F is the set of all logically possible profiles of consistent and complete individual judgment sets.
In this case, it would be okay for the individuals involved to agree to just spin things out or otherwise benefit from this activity without giving a damn for their public or other duty.
As a matter of fact, the domain of any judicial procedure explicitly excludes all self-serving profiles. It is a requirement that only individual judgment sets which are wholly disinterested and animated by professional zeal and integrity be included in the domain. Where there can be any shadow of doubt that this is the case, the Judge must recuse herself.
Collective rationality: For any profile <J1, J2, …, Jn> in the domain of F, the collective judgment set J is consistent and complete.
This is crazy shit. Only some issues are justiciable. J must not be complete. It can also have 'hidden' meta-rules or equitable exceptions- e.g. disregard rule x if y is the case- and thus could always be said to be consistent. In Judaism there is the notion of halachah vein morin kein- the rule which, if known, must not be acted upon. Robert Aumann has pointed out that the Sanhedrin also had a rule against unanimity!
Anonymity: For any two profiles <J1, J2, …, Jn> and <J*1, J*2, …, J*n> that are permutations of each other, F(J1, J2, …, Jn) = F(J*1, J*1, …, J*n).
Yet a Judgment derives much prescriptive force from being the utterance of a venerable person. Why throw away information as to who is saying what? Uncorrelated asymmetries re. Information, Zeal for the Commonweal, etc, exist. They should be the basis of eusocial public signals.
Systematicity: For any two profiles <J1, J2, …, Jn> and <J*1, J*2, …, J*n> in the domain of F and any p, q ∈ X, if for all i ∈ N p ∈ Ji if and only if q ∈ J*i, then p ∈ J if and only if q ∈ J*.
However, alternatives aren't 'irrelevant'. They change the information set. This information should not be thrown away. It is better to get things right in an unsystematic way then to go to the dogs doing things by the book.
Theorem (List and Pettit 2002): If {p, q, p∧q} ⊆ X (where p and q are mutually independent propositions and ‘∧’ can also be replaced by ‘∨’ or ‘→’), there exists no judgment aggregation rule satisfying universal domain, collective rationality, anonymity, and systematicity.
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