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Uncommon Priors Require Origin Disputes
Abstract
In standard belief models, priors are always common knowledge. This prevents such models from representing agents’ probabilistic beliefs about the origins of their priors. By embedding standard models in a larger standard model, however, pre-priors can describe such beliefs. When an agent’s prior and pre-prior are mutually consistent, he must believe that his prior would only have been different in situations where relevant event chances were different, but that variations in other agents’ priors are otherwise completely unrelated to which events are how likely. Due to this, Bayesians who agree enough about the origins of their priors must have the same priors. Copyright Springer 2006
... Yet the common prior assumption is more wide-ranging than is often presumed such that it applies to first-order morality as much as second-order public reason. Hanson (2006) demonstrates that among rational individuals "uncommon priors require origin disputes." Rational individuals who agree enough about the origins of their priors will mean that they should agree enough for identical posteriors. ...
... This is true even when we share common priors. No amount of historical analysis of our origins (Hanson, 2006) will change it. Something resembling this line of thought might be gleaned from Brian Barry in Justice as Impartiality. ...
Aumann’s theorem states that no individual should agree to disagree under a range of assumptions. Political liberalism appears to presuppose these assumptions with the idealized conditions of public reason. We argue that Aumann’s theorem demonstrates they nevertheless cannot be simultaneously held with what is arguably political liberalism’s most central tenet. That is, the tenet of reasonable pluralism, which implies we can rationally agree to disagree over conceptions of the good. We finish by elaborating a way of relaxing one of the theorem’s axioms that arguably lends itself to a coherent account of political liberalism, namely, the condition of indexical independence.
... Moreover, this convergence can be achieved with a reasonable amount of 137 effort [41]. The requirement of common priors may appear stringent; however, it can be replaced by 138 milder ones [42]. Even without common priors, Bayesian Alice and Bob willing to share information 139 must eventually converge. ...
... Bayesian Alice and Bob committed to full Bayesian inference cannot agree to disagree [41][42]. 144 ...
Bayesian inference offers an optimal means of processing environmental information and so an advantage in natural selection. We consider the apparent, recent trend in increasing dysfunctional disagreement in, for example, political debate. This is puzzling because Bayesian inference benefits from powerful convergence theorems, precluding dysfunctional disagreement. Information overload is a plausible factor limiting the applicability of full Bayesian inference, but what is the link with dysfunctional disagreement? Individuals striving to be Bayesian-rational, but challenged by information overload, might simplify by using Bayesian networks or the separation of questions into knowledge partitions, the latter formalized with quantum probability theory. We demonstrate the massive simplification afforded by either approach, but also show how they contribute to dysfunctional disagreement.
... Yet the common prior assumption is more wide-ranging than is often presumed such that it applies to first-order morality as much as second-order public reason. Hanson (2006) demonstrates that among rational individuals "uncommon priors require origin disputes." Rational individuals who agree enough about the origins of their priors will mean that they should agree enough for identical posteriors. ...
... This is true even when we share common priors. No amount of historical analysis of our origins (Hanson, 2006) will change it. Something resembling this line of thought might be gleaned from Brian Barry in Justice as Impartiality. ...
Aumann's theorem states that no individual should agree to disagree under a range of assumptions. Political liberalism appears to presuppose these assumptions with the idealized conditions of public reason. We argue Aumann's theorem demonstrates they nevertheless cannot be simultaneously held with what is arguably political liberalism's most central tenet. That is, the tenet of reasonable pluralism, which implies we can rationally agree to disagree over conceptions of the good. We finish by elaborating a way of relaxing one of the theorem's axioms that arguably lends itself to a coherent account of political liberalism, namely the condition of indexical independence.
... Yet the common prior assumption is more wide-ranging than is often presumed such that it applies to first-order morality as much as second-order public reason. Hanson (2006) demonstrates that among rational individuals "uncommon priors require origin disputes." Rational individuals who agree enough about the origins of their priors will mean that they should agree enough for identical posteriors. ...
... This is true even when we share common priors. No amount of historical analysis of our origins (Hanson, 2006) will change it. Something resembling this line of thought might be gleaned from Brian Barry in Justice as Impartiality. ...
... Thus, when A has shown the novel premise to be consistent with Common Knowledge, B is forced to accept the novel premise or stand accused of acting irrationally. More precisely, A and B can only 'agree to disagree' insofar as they refuse to discuss the basis of their beliefs (Hanson 2006). Given that A's premise is neither faulty nor leads to a contradiction, such a debate would effectively force B to concede a contradiction in his belief system. ...
We propose a model of cognition grounded in ancient Greek philosophy which encompasses Aristotle’s categories. Taking for First Principles the brute facts of the mental actions of separation, aggregation and ordering, we derive Aristotle’s categories as follows. First, Separation lets us see single entities, giving the simple concept of an individual. Next, Aggregation lets us see instances of some kind, giving the basic concept of a particular. Then, Ordering lets us see both wholes-with-parts as well as parts-of-some-whole, giving the subtle concept of a relational or Gestalt. The basic and the subtle concept give us the major and minor categories. The categories constitute a top-level ontology and describe universal usage so that any other category necessarily describes particular or domain usage.
... Voters seek new and other information which confirm rather than challenge their ideological preferences (Iyengar & Hahn, 2009;Taber et al., 2001;Taber & Lodge, 2006) and seem to have systematically biased beliefs as a result (Caplan, 2002(Caplan, , 2007. Disagreement over matters of fact is a fundamental part of political discourse, despite its questionable rationality (Aumann, 1976;Cowen & Hanson, 2004;Hanson, 2006). These findings are at odds with the instrumental account of voting. ...
This thesis by papers uses rational choice theory to consider the relative
performance of individual exit and collective voice in politics, as well as the causal
relationships between exit and voice as individual strategies and institutionalised
means of controlling government behaviour. Following the methodological
approach of Geoffrey Brennan and Alan Hamlin, the papers of this thesis are
examples of ‘revisionist public choice theory,’ retaining the broad framework of
rational choice while relaxing one or more of the standard assumptions generally
made by economists. In particular, the papers of this thesis consider otherregarding
preferences, non-instrumental preferences, dispositional choice,
epistemic rationality, non-efficiency evaluative standards, and non-equilibrium
dynamics. By taking a revisionist approach, I am able to steer a path between the
excessive abstraction of much public choice theory and the insufficient rigour of
much normative political theory. Jointly, the papers of this thesis contribute to
broad debates over the relative value of exit and voice in political settings, with
relevance to questions of democracy versus the market, centralism versus localism,
and bureaucracy versus market-like modes of governance. Though I cover a range
of diverse topics in this thesis, I generally argue for a strongly revisionist approach
to political analysis which sees significant behavioural differences between
individual and collective decisions while grounding all action in common
motivational assumptions.
... (Christensen 2009) and (Feldman & Warfield 2012). 15 Attempts to weaken this assumption have been made; see (Hanson 2006). 16 (Cox & Isaac 1984) 17 In actual cases, the other agents are likely to have different priors and nonindependent information, plus uncertainty about the number of agents. ...
This paper presents a simple model of an AI (artificial intelligence) arms race, where several development teams race to build the first AI. Under the assumption that the first AI will be very powerful and transformative, each team is incentivised to finish first—by skimping on safety precautions if need be. This paper presents the Nash equilibrium of this process, where each team takes the correct amount of safety precautions in the arms race. Having extra development teams and extra enmity between teams can increase the danger of an AI disaster, especially if risk-taking is more important than skill in developing the AI. Surprisingly, information also increases the risks: the more teams know about each others’ capabilities (and about their own), the more the danger increases. Should these results persist in more realistic models and analysis, it points the way to methods of increasing the chance of the safe development of AI.
... The n target shareholders do not know the acquirer's type. They share a common prior β (Aumann (1976), Yildiz (2003), and Hanson (2006)), where bid. This model applies to cash tender offers and exchange offers. ...
Using text-based media content, this paper develops and empirically confirms a theory that explains how the media predicts takeover outcomes. It shows that positive media content about the acquirer predicts takeover success. Relative to other predictors proposed in the literature, the media measure is the most important explanatory variable in terms of marginal effect, significance, and goodness of fit.
... Ultimately, after exchanging information and fully discussing the matter with your friend, you should expect to come to the same conclusions regarding factual matters. Persistent disagreements might seem possible due to differing prior beliefs, but as discussed by Hanson (2006), this is possible for fully rational observers only if they disagree about the processes by which they came to hold these prior beliefs. Agreement with hypothetical friends has been used as a test of reasoning in the past -in particular, Nozick (1969) uses it in his discussion of Newcomb's Problem, as described in the next section. ...
I consider the puzzles arising from four interrelated problems involving `anthropic' reasoning, and in particular the `Self-Sampling Assumption' (SSA) - that one should reason as if one were randomly chosen from the set of all observers in a suitable reference class. The problem of Freak Observers might appear to force acceptance of SSA if any empirical evidence is to be credited. The Sleeping Beauty problem arguably shows that one should also accept the `Self-Indication Assumption' (SIA) - that one should take one's own existence as evidence that the number of observers is more likely to be large than small. But this assumption produces apparently absurd results in the Presumptuous Philosopher problem. Without SIA, however, a definitive refutation of the counterintuitive Doomsday Argument seems difficult. I show that these problems are satisfyingly resolved by applying the principle that one should always condition on all evidence - not just on the fact that you are an intelligent observer, or that you are human, but on the fact that you are a human with a specific set of memories. This `Full Non-indexical Conditioning' (FNC) approach usually produces the same results as assuming both SSA and SIA, with a sufficiently broad reference class, while avoiding their ad hoc aspects. I argue that the results of FNC are correct using the device of hypothetical ``companion'' observers, whose existence clarifies what principles of reasoning are valid. I conclude by discussing how one can use FNC to infer how densely we should expect intelligent species to occur, and by examining recent anthropic arguments in inflationary and string theory cosmology.
One of the most important challenges in decision theory has been how to reconcile the normative expectations from Bayesian theory with the apparent fallacies that are common in probabilistic reasoning. Recently, Bayesian models have been driven by the insight that apparent fallacies are due to sampling errors or biases in estimating (Bayesian) probabilities. An alternative way to explain apparent fallacies is by invoking different probability rules, specifically the probability rules from quantum theory. Arguably, quantum cognitive models offer a more unified explanation for a large body of findings, problematic from a baseline classical perspective. This work addresses two major corresponding theoretical challenges: first, a framework is needed which incorporates both Bayesian and quantum influences, recognizing the fact that there is evidence for both in human behavior. Second, there is empirical evidence which goes beyond any current Bayesian and quantum model. We develop a model for probabilistic reasoning, seamlessly integrating both Bayesian and quantum models of reasoning and augmented by a sequential sampling process, which maps subjective probabilistic estimates to observable responses. Our model, called the Quantum Sequential Sampler, is compared to the currently leading Bayesian model, the Bayesian Sampler (J. Zhu et al., 2020) using a new experiment, producing one of the largest data sets in probabilistic reasoning to this day. The Quantum Sequential Sampler embodies several new components, which we argue offer a more theoretically accurate approach to probabilistic reasoning. Moreover, our empirical tests revealed a new, surprising systematic overestimation of probabilities.
Aumann's agreement theorem and subsequent work shows that people who are rational in a certain Bayesian sense cannot agree to disagree on matters of fact. This result hinges on a type of epistemic impartiality: a rational person will not give extra weight to a piece of evidence simply because they themselves discovered it rather than someone else. We extend this argument by questioning the possibility of reasonable political disagreement for political liberals. On our reading, a “Good Liberal” must not give extra weight in public deliberations to their own preferences or values simply because they are their own. This political impartiality mirrors the epistemic impartiality of Aumann's theorem and we argue that disagreement on policy is impossible in a world of “Good Liberal Bayesians,” assuming common knowledge of both Bayesian rationality and Liberal reasonableness. The persistence and predictability of disagreement in the real world provides support for expressive accounts of political behaviour and points to the important role of epistemic trust in politics. This issue of epistemic trust provides insight into recent trends in political polarization in the United States and elsewhere.
In some situations a number of agents each have the ability to undertake an initiative that would have significant effects on the others. Suppose that each of these agents is purely motivated by an altruistic concern for the common good. We show that if each agent acts on her own personal judgment as to whether the initiative should be undertaken, then the initiative will be undertaken more often than is optimal. We suggest that this phenomenon, which we call the unilateralist's curse, arises in many contexts, including some that are important for public policy. To lift the curse, we propose a principle of conformity, which would discourage unilateralist action. We consider three different models for how this principle could be implemented, and respond to an objection that could be raised against it.
Michael Huemer's aim in his chapter is to defend a fully agent-centered epistemological perspective. An agent-centered epistemological perspective is opposed to an agentneutral view. Huemer claims that a consequence of his agent-centered view is that two subjects with perfect knowledge of one another's epistemically relevant states who make no procedural errors in belief formation may still rationally disagree because each might assign different weight to the evidence of the other person than that other person may assign-evidence is not agent-neutral. Huemer also defends the stronger thesis that only one's own mental states can provide justification for one for believing anything. Part of the motivation for Huemer's view comes from his noting analogies between ethics and epistemology, particularly between ethical egoism and agent-centered epistemology. Despite this analogy between ethical egoism and agent-centered epistemology, he argues there is an important asymmetry between ethics and epistemology.
Critics of the expressive account of voting have argued that it is inconsistent with strategic voting. Since there is strong evidence that people vote strategically, this has been taken to show that many voters are at least partially instrumentally motivated. This paper argues that strategic voting in the relevant sense is consistent with entirely expressive political motivation. Building on an earlier suggestion by Geoffrey Brennan, I model voters as expressively valuing ideological position as well as the strategic pursuit of expressively-defined preferences. This model predicts strategic voting without instrumental preferences entering the voter’s calculus at all. I also suggest that expressive preferences for strategic behaviour can be usefully analysed in terms of dispositional choice.
Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior μ, that it is the common prior; (2) that agents commonly know that each of them updates on the prior by conditionalization; (3) that agents commonly know that if an agent knows a proposition, she knows that she knows that proposition (the “KK” principle); (4) that agents commonly know that they each update only on true propositions. It is shown that natural weakenings of any one of these strong assumptions can lead to countermodels to Aumann’s key conditional. Examples are given in which agents who have a common prior and commonly know what probability they each assign to a proposition nevertheless assign that proposition unequal probabilities. To alter Aumann’s famous slogan: people can “agree to disagree”, even if they share a common prior. The epistemological significance of these examples is presented in terms of their role in a defense of the Uniqueness Thesis: If an agent whose total evidence is E is fully rational in taking doxastic attitude D to P, then necessarily, any subject with total evidence E who takes a different attitude to P is less than fully rational.
How should you take into account the opinions of an advisor? When you completely defer to the advisor's judgment (the manner in which she responds to her evidence), then you should treat the advisor as a guru. Roughly, that means you should believe what you expect she would believe, if supplied with your extra evidence. When the advisor is your own future self, the resulting principle amounts to a version of the Reflection Principle—a version amended to handle cases of information loss.
When you count an advisor as an epistemic peer, you should give her conclusions the same weight as your own. Denying that view—call it the “equal weight view”—leads to absurdity: the absurdity that you could reasonably come to believe yourself to be an epistemic superior to an advisor simply by noting cases of disagreement with her, and taking it that she made most of the mistakes. Accepting the view seems to lead to another absurdity: that one should suspend judgment about everything that one's smart and well-informed friends disagree on, which means suspending judgment about almost everything interesting. But despite appearances, the equal weight view does not have this absurd consequence. Furthermore, the view can be generalized to handle cases involving not just epistemic peers, but also epistemic superiors and inferiors.
The genetic basis of individual differences in attitudes was examined in a survey of 195 pairs of monozygotic twins and 141 pairs of same-sex dizygotic twins. A principal components analysis of the 30 attitude items in the survey identified 9 attitude factors, of which 6 yielded significant heritability coefficients. Nonshared environmental factors accounted for the most variance in the attitude factors. Possible mediators of attitude heritability were also assessed, including personality traits, physical characteristics, and academic achievement. Analyses showed that several of these possible mediators correlated at a genetic level with the heritable attitude factors, suggesting that the heritability of the mediator variables might account for part of the heritable components of some attitudes. There was also some evidence that highly heritable attitudes were psychologically "stronger" than less heritable attitudes.
Why is (it that) common priors are implicit or explicit in the vast majority of the differential information literature in economics and game theory? Why has the economic community been unwilling, in practice, to accept and actually use the idea of truly personal probabilities in much the same way that it did accept the idea of personal utility functions? After all, in (Savage's expected utility theory), both the utilities and probabilities are derived separately for each decision maker. Why were the utilities accepted as personal, and the probabilities not?
Thesis (Ph. D.)--Harvard University, 1976. Bibliography: leaves 196-201.