Causal Decision Theory reckons the choice-worthiness of an option to be completely independent of its evidential bearing on its non-effects. But after one has made a choice this bearing is relevant to future decisions. Therefore it is possible to construct problems of sequential choice in which Causal Decision Theory makes a guaranteed loss. So Causal Decision Theory is wrong. The source of the problem is the idea that agents have a special perspective on their own contemplated (...) actions, from which evidential connections that observers can see are either irrelevant or invisible. (shrink)

An agent whose preferences violate the Independence Axiom or for some other reason are not representable by an expected utility function, can avoid 'dynamic inconsistency' either by foresight ('sophisticated choice') or by subsequent adjustment of preferences to the chosen plan of action ('resolute choice'). Contrary to McClennen and Machina, among others, it is argued these two seemingly conflicting approaches to 'dynamic rationality' need not be incompatible. 'Wise choice' reconciles foresight with a possibility of preference adjustment by rejecting (...) the two assumptions that create the conflict: Separability of Preferences in the case of sophisticated choice and Reduction to Normal form in the case of resolute choice.. (shrink)

Decision theory is a theory of rationality, but the concept of rationality has several different dimensions. Making decision theory more realistic with respect to one dimension may well have the result of making it less realistic in another dimension. This paper illustrates this tension in the context of sequential choice. Trying to make decision theory more realistic by accommodating resoluteness and commitment brings the normative assessment dimension of rationality into conflict with the action-guiding dimension. In the case of (...) resolute choice the conflict comes because of a clash of perspectives. The perspective from which resolute choice seems normatively compelling is not the perspective from which it can serve the purpose of guiding action. (shrink)

Within the last decade, there has been a dramatic bloom in ridesharing businesses along with the emergence of new enabling technologies. A central issue in ridesharing, which is also important in the general domain of cost-sharing in economics and computer science, is that the sharing of cost implies positive externalities and hence coordination problems for the network users. We investigate these problems experimentally in the present study. In particular, we focus on how sequential observability of transportation mode choices can (...) be a powerful facilitator of coordination in ridesharing. Our study abstracts the essential issues of coordination in ridesharing into a directed network game with experimentally testable predictions. In line with the theoretical analysis, our experimental evidence shows that even a limited extent of sequential choice observability might lead to efficient coordination. However, convergence to efficiency is slower with more limited observability, resulting in a significant increase in travel cost. (shrink)

There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for (...) the SEU preference axioms, but go on to formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted. (shrink)

We show that the property of sequential compactness for subspaces of.

Under the axiom of choice, every first countable space is a Fréchet-Urysohn space. Although, in its absence even ℝ may fail to be a sequential space.Our goal in this paper is to discuss under which set-theoretic conditions some topological classes, such as the first countable spaces, the metric spaces, or the subspaces of ℝ, are classes of Fréchet-Urysohn or sequential spaces.In this context, it is seen that there are metric spaces which are not sequential spaces. This (...) fact raises the question of knowing if the completion of a metric space exists and it is unique. The answer depends on the definition of completion.Among other results it is shown that: every first countable space is a sequential space if and only if the axiom of countable choice holds, the sequential closure is idempotent in ℝ if and only if the axiom of countable choice holds for families of subsets of ℝ, and every metric space has a unique equation image-completion. (shrink)

Decision-makers frequently struggle to base their choices on an exhaustive evaluation of all options at stake. This is particularly so when the choice problem at hand is complex, because the available alternatives are hard to compare. Rather than striving to choose the most valuable alternative, in such situations decision-makers often settle for the choice of an alternative which is not inferior to any other available alternative instead. In this paper, we extend two established models of boundedly rational (...) class='Hi'>choice, the categorize then choose heuristic and the rational shortlist method, to incorporate this kind of “indecisive” choice behavior. We study some properties of these extensions and provide full behavioral characterizations. (shrink)

According to T. M. Scanlon’s anti-aggregation principle, it is wrong to save a larger number of people from minor harms rather than a smaller number from much more serious harms. This principle is a central part of many influential and anti-utilitarian ethical theories. According to the sequential-dominance principle, one does something wrong if one knowingly performs a sequence of acts whose outcome would be worse for everyone than the outcome of an alternative sequence of acts. The intuitive appeal of (...) the sequential-dominance principle should be obvious; everyone is knowingly made worse off if it is violated. In this paper, I present a number of cases where one is forced to violate either the anti-aggregation principle or the sequential-dominance principle. I show that these principles conflict regardless of whether one accepts a counterfactual or a temporal, worsening view of harm. Moreover, I show that this result holds regardless of how much worse a harm has to be in order to count as a much more serious harm. (shrink)

How do activist groups instigate institutional change within an organizational field? Studying the global sports and apparel industry, we explore how activist groups applied different tactics over time, including conflict and collaboration, and how the accumulation of these tactics led to the build-up of pressure on firms within the industry to change their policies and activities on labor issues in their supply chains. Building on interorganizational conflict literature, we show how an industry-level approach is helpful to understand the sequential (...) patterning of tactical choices in evoking institutional change. These findings contribute to the growing literature of activists’ influence strategies. (shrink)

We show that the property of sequential compactness for subspaces of.

Prioritarianism is a variant of utilitarianism. It differs from utilitarianism in that benefiting individuals matters more the worse off these individuals are. On this view, there are two standard ways of handling risky prospects: Ex-Post Prioritarianism adjusts for prioritizing the worse off in final outcomes and then values prospects by the expectation of the sum total of those adjusted values, whereas Ex-Ante Prioritarianism adjusts for prioritizing the worse off on each individual's expectation and then values prospects by the sum total (...) of those adjusted expectations. A standard objection to Ex-Post Prioritarianism is that it violates Ex-Ante Pareto, that is, it prescribes choices that worsen the expectations for everyone. In this article, I argue that Ex-Ante Prioritarianism suffers from much the same problem: it violates a sequential version of Ex-Ante Pareto, that is, it prescribes sequences of choices that worsen the expectations for everyone. (shrink)

Rational individuals who perceive information sequentially are confronted to cognitive dissonance and dynamic uncertainty in a way that sets a natural limit to the ex post efficiency of their choices. From the normative perspective which ignores this dynamic uncertainty, their rationality seems limited. Sequential perception is assumed in a model of Bayesian revision of the contingent preference in a repeated choice. This model predicts both the cognitive dissonance phenomenon studied by Festinger and the formation of stable habits. It (...) also shows how an ordinary man can be rational with bounded informational and computational abilities and, for the same reasons, give a disproportionate weight to impressions without any normative value in his own choices and judgments. Sequential perception and cognitive consistency offer a credible alternative to the cognitive bias paradigm for predicting anomalies in choice and game behavior.Des individus logiques percevant l’information de manière séquentielle sont soumis à une dissonance cognitive et une incertitude dynamique qui limitent naturellement l’efficacité ex post de leurs choix. Du point de vue normatif, qui ignore cette incertitude dynamique, leur rationalité apparaît limitée. L’hypothèse de perception séquentielle est introduite dans un modèle de révision bayésienne de la préférence contingente lors d’un choix répété. Ce modèle prédit à la fois le phénomène de dissonance cognitive étudié par Festinger et la formation d’une habitude stable. Il montre aussi comment un homme ordinaire peut être rationnel sans disposer de capacités d’information et de calcul démesurées et, pour les mêmes raisons, subir l’influence disproportionnée d’impressions dénuées de valeur normative dans les choix ou les jugements qu’il porte. La perception séquentielle et la cohérence cognitive offrent une alternative crédible au paradigme des biais cognitifs pour expliquer tous les comportements humains qui réfutent la théorie normative des choix et des jeux. (shrink)

We show that an individual using a choice function is sequentially rational and the decisions he makes are independent of the order of implementation of the rationales if and only if he is rational with the union of the rationales as a base binary relation. When he makes his decisions following a choice correspondence, the sufficiency part of this claim still holds, the necessity part of it does not.

Politics, Philosophy & Economics, Volume 21, Issue 4, Page 347-371, November 2022. We sometimes have to choose between options that are seemingly incomparable insofar as they seem to be neither better than, worse than, nor equal to each other. This often happens when the available options are quite different from one another. For instance, consider a choice between prioritizing either criminal justice reform or healthcare reform as a public policy goal. Even after the relevant details of the goals and (...) possible reforms are filled in, it is plausible that neither goal is better than, worse than, nor equal to the other. Such seemingly incomparable options present a problem for rational choice since it is unclear how an agent might rationally choose between them. What we need are some principles to help govern rational choice when faced with seemingly incomparable options. I here present three such principles. While each principle is individually compelling, I show that they are jointly incompatible. I then argue that the correct response to this inconsistent triad is to reject the principle that rationally censures performing a sequence of choices one knows will result in a suboptimal outcome. The upshot is that when seeming incomparability is involved, an agent can money pump themselves without being less rational for it. (shrink)

The research reported here was the first empirical examination of strategic voting under the Sequential Voting by Veto (SVV) voting procedure, proposed by Mueller (1978). According to this procedure, a sequence of n voters must select s out of s+m alternatives (m=n=2; s>0). Hence, the number of alternatives exceeds the number of participants by one (n+1). When the ith voter casts her vote, she vetoes the alternative against which a veto has not yet been cast, and the s remaining (...) non-vetoed alternatives are elected. The SVV procedure invokes the minority principle, and it has advantages over all majoritarian procedures; this makes SVV a very desirable means for relatively small groups to make collective decisions. Felsenthal and Machover (1992) pointed out three models of voting under SVV: sincere, optimal, and canonical. The current research investigated, through laboratory experiments, which cognitive model better accounts for the voters' observed behavior and the likelihood of obtaining the optimal outcome as a function of the size of n (when s=1). The findings suggest that while voters under SVV use all three models, their choice is conditioned by group size. In the small groups (n=3), the canonical mode was a better predictor than the sincere model. In the larger groups (n=5), the sincere model was a better predictor than the canonical model. There is also evidence of players' learning during the experiment. (shrink)

We prove James's sequential characterization of reflexivity in set-theory ZF + DC, where DC is the axiom of Dependent Choices. In turn, James's criterion implies that every infinite set is Dedekind-infinite, whence it is not provable in ZF. Our proof in ZF + DC of James' criterion leads us to various notions of reflexivity which are equivalent in ZFC but are not equivalent in ZF. We also show that the weak compactness of the closed unit ball of a reflexive (...) space does not imply the Boolean Prime Ideal theorem : this solves a question raised in [6]. (shrink)

Activating relevant responses is a key function of automatic processes in De Neys's model; however, what determines the order or magnitude of such activation is ambiguous. Focusing on recently developed sequential sampling models of choice, we argue that proactive control shapes response generation but does not cleanly fit into De Neys's automatic-deliberative distinction, highlighting the need for further model development.

Consider an agent who faces choice problems and learns information about an objective state of the world through a technology of sequential experiments. We consider two cases of learning costs. In the first, the agent discounts future payoffs geometrically. In the second, she incurs a constant flow cost of time. If the observable data consist only of the joint distributions over chosen actions and decision times, an analyst can uniquely identify the discount factor in the first case and (...) the flow cost of time in the second case. Moreover, we show how an analyst can recover the agent’s ex ante welfare in both cases, besides identifying her prior belief. Our approach does not rely on any knowledge about the underlying sequential experiment. (shrink)

Tiebreak rules are necessary for revealing indifference in non- sequential decisions. I focus on a preference relation that satisfies Ordering and fails Independence in the following way. Lotteries a and b are indifferent but the compound lottery f, 0.5b> is strictly preferred to the compound lottery f, 0.5a>. Using tiebreak rules the following is shown here: In sequential decisions when backward induction is applied, a preference like the one just described must alter the preference relation between a and (...) b at certain choice nodes, i.e., indifference between a and b is not stable. Using this result, I answer a question posed by Rabinowicz (1997) concerning admissibility in sequential decisions when indifferent options are substituted at choice nodes. (shrink)

In this note we show that the Axiom of Countable Choice is equivalent to two statements from the theory of pseudometric spaces: the first of them is a well-known characterization of uniform continuity for functions between metric spaces, and the second declares that sequentially compact pseudometric spaces are \—meaning that all real valued, continuous functions defined on these spaces are necessarily uniformly continuous.

We work in set-theory without choice ZF. A set is Countable if it is finite or equipotent with ${\Bbb N}$ . Given a closed subset F of [0, 1] I which is a bounded subset of $\ell ^{1}(I)$ (resp. such that $F\subseteq c_{0}(I)$ ), we show that the countable axiom of choice for finite sets, (resp. the countable axiom of choice AC N ) implies that F is compact. This enhances previous results where AC N (resp. the (...) axiom of Dependent Choices) was required. If I is linearly orderable (for example $I={\Bbb R}$ ), then, in ZF, the closed unit ball of the Hilbert space $\ell ^{2}(I)$ is (Loeb-)compact in the weak topology. However, the weak compactness of the closed unit ball of $\ell ^{2}(\scr{P}({\Bbb R}))$ is not provable in ZF. (shrink)

It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be (...) borne out by the sharp model but not by any promising incarnation of its imprecise counterpart. After first pointing out that Elga has fallen short of establishing that his principle is indeed uniquely borne out by the sharp model, I cast aspersions on its plausibility. I show that a slight weakening of the principle is satisfied by at least one, but interestingly not all, varieties of the imprecise model and point out that Elga has failed to motivate his stronger commitment. (shrink)

review of McLennen's *Rationality and Dynamic Choice*. The topic is important and the discussion is powerful. Some connection with modelling and simulation would be valuable.

An agent who violates independence can avoid dynamic inconsistency in sequential choice if he is sophisticated enough to make use of backward induction in planning. However, Seidenfeld has demonstrated that such a sophisticated agent with dependent preferences is bound to violate the principle of dynamic substitution, according to which admissibility of a plan is preserved under substitution of indifferent options at various choice nodes in the decision tree. Since Seidenfeld considers dynamic substitution to be a coherence condition (...) on dynamic choice, he concludes that sophistication cannot save a violator of independence from incoherence. In response to McClennen’s objection that relying on dynamic substitution when independence is at stake must be question-begging, Seidenfeld undertakes to prove that dynamic substitution follows from the principle of backward induction alone, provided we assume that the agent’s admissible choices from different sets of feasible plans are all based on a fixed underlying preference ordering of plans. This paper shows that Seidenfeld's proof fails: depending on the interpretation, it is either invalid or based on an unacceptable assumption. (shrink)

Seidenfeld (Seidenfeld, T. [1988a], Decision theory without 'Independence' or without 'Ordering', Economics and Philosophy 4: 267-290) gave an argument for Independence based on a supposition that admissibility of a sequential option is preserved under substitution of indifferents at choice nodes (S). To avoid a natural complaint that (S) begs the question against a critic of Independence, he provided an independent proof of (S) in his (Seidenfeld, T. [1988b], Rejoinder [to Hammond and McClennen], Economics and Philosophy 4: 309-315). In (...) reply to my (Rabinowicz, W. [1995], To have one's cake and eat it too: Sequential choice and expected-utility violations, The Journal of Philosophy 92: 586-620), in which I argue that the proof is invalid, Seidenfeld (Seidenfeld, T. [2000], Substitution of indifferent options at choice nodes and admissibility: A reply to Rabinowicz, Theory and Decision 48: 305–310 this issue) submits that I fail to give due consideration to one of the underlying assumptions of his derivation: it is meant to apply only to those cases in which the agent's preferences are stable throughout the sequential decision process. The purpose of this note is to clarify the notion of preference stability so as meet this objection. (shrink)